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We cant have 30year morgages here because we are Canadainas, and as such we have to pay more than our neighbours for everything, it is the premium we pay for having good governance I guess...

In the US prior to the depression the typical mortgage was a 5 year balloon payment.

Under this norm the home ownership rate was about 40%.

After the 30 year mortgage became the norm the home ownership rate rose to about 60% and had small cyclical moves around this level until recent years when it rose significantly from this level -- largely because of "liar" loans and other declines in lending standards.

If you think home ownership is a good thing the shift from 4 year balloon mortgages to 30 year
amortized mortgages was a good thing.

I have seen estimates that the average age of a US mortgage is around four years.

So while I found your post to be very good and highly educational, I still come out with the conclusion that there is not a great deal of difference between the US 30 year mortgage and the Canadian 25 year reset mortgage except that the Canadian borrower takes on more interest rate risk.

"Except for the fact that mortgages are typically not indexed for inflation, a 30 year fixed rate closed mortgage looks close to ideal. And if the Bank of Canada sticks to its 2% inflation target, this concern matters less than it did in the past."

Locking into a 30-year commitment based on a policy that is less than 30 years old seems ... dangerous. And over reasonable periods of time, floating rate mortgages are effectively indexed to inflation (plus a spread). And wages are (for the population as a whole) indexed to inflation (wage growth basically is inflation).

The problem with your idea of arguing that the market should go closed is that the consequences of getting it wrong are significant for both sides; the consequences of getting a floating - and hence open - mortgage is that the consequences and costs are less significant.

Alternatively, if the costs ex ante of a closed mortgage are not reasonably estimable or there is no market, the upfront cost may be too high. Could this be why there is no market for it?

I'm not an expert, but I really don't think the market for 30-year interest rate derivatives/swaps/options in Canadian dollars is deep.

Yield curve anyone?

When people shop for mortgages, they have two instincts. One is to pay as little money as possible, the other is to get the security of payment predictability. The first is a purely logical consideration, the second has a significant emotional component. The US achieves the second goal by sacrificing the first.

The entire thrust of microeconomic research into mortgage strategy in Canada has been to show that shorter terms are better, even when we try to stack the deck as much as we can against that strategy. The corollary is that the choice of a 5-year fixed term is motivated primarily by fear. As this fear is greater than the actual risk, a borrower pays a net premium for their peace of mind that is over and above the actual value of the risk being transferred.

Second, when we look at the mortgage market and its history, the entire thrust in Canada has been to ensure that as large a pool of capital as possible is available for mortgage lending. This has been an explicit goal of the CHMC since its founding.

It has been noted before that mortgages are like annuities. In fact, before 1954 chartered banks were banned from loaning mortgages. Life Insurance companies were in fact the largest players in the mortgage market. They used mortgages to invest their annuity and life insurance premium income. Insurance and annuities were their deposit base. However banks and trust companies had larger pools of capital available, so the role of insurers faded.

Banks were allowed into the market in 1954 when CHMC began its current insurance operations. However their participation dwindled in the 1960's as rates climbed. They had a legal limit of 6% interest on all loans under the Bank Act. Trust Companies didn't have this same limit and became the main mortgage lenders. The 6% cap was lifted in 1967 and banks entered the mortgage market with a vengeance. Banks had and still have the deepest pockets, which was why the government made the changes it did.

Second, there is also the problem of intermediation. Banks of course borrow short and lend long. But in the US they do that to the extreme, borrowing short CD's and lending long 30-year mortgages. With rising interest rates in the 1960's many mortgage lenders faced a shortage of deposits with which to make loans. The secondary market was designed to fill this gap. Banks could originate a mortgage, get a payment and get around the deposit problem. If a lender makes a mortgage it doesn't want to keep, it can always sell it.

In Canada we never had a secondary market like that. Banks here were concerned in the 1960's about getting caught with an inverted portfolio: low long-term mortgages with high-rate deposits. Borrowers, looking backward also didn't want to keep what they thought of as high-rate mortgages and refinanced often (see Nick previously). The answer was to invent the rollover mortgage which met borrowers and lenders needs halfway. Canadian banks still engage in duration transformation, but they do it be transforming mismatched 0-5 year deposit yields with corresponding mortgage rates. They don't engage in transformation of 1-year GIC's into 30-year mortgages. They view this as too risky. Look what happened to the US Savings & Loan industry.

If the mortgage is only for 5 years, are housing prices significantly lower? Are down payments 20%+? I can't imagine the fall in housing prices if America allowed only 5 year loans. No one could afford houses here under those terms at the current price level.


The ultimate testament to the fact that there is not so much practical difference between the two forms of mortgage is that home ownership rates in the US and Canada are identical. In fact due to the US mortgage crisis we now have a 1% advantage. The additional interest rate risk has not in fact proved to be a detriment in Canada


In Canada the "term" of a mortgage is not the same thing as the amortization. Canadian mortgages are amortized as instalment loans over a 25-year period, just like US mortgages are amortized over 30 years. However the interest rate is "fixed" for a term, which is 1-5 years. When the "term" expires you can pay off the mortgage in full without penalty or renew for the remaining balance with your lender. The mortgage "rolls over". You can think of a bit of a balloon loan, but since we only have 6 national chartered banks, a few trust companies and the credit unions, banks are very willing to roll over their own mortgages. They prefer the income and want to keep their customers. Canadians can and do change mortgage lenders frequently and easily so the market is competitive.

Furthermore, the Canada Mortgage and Housing Corporation insures all mortgages against default. This is why banks are willing to roll over mortgages so easily.

The minimum for "standard" mortgages is a 20% downpayment. Buyers can pay as little as 5% down if they pay an additional premium to the CMHC for default insurance.

In short, in Canada mortgages are for 25-year amortizations, 20% down for regular loans, 5% down for insured loans.

In Denmark, the 30-year FRM is open -- full prepayment is allowed at par. Alternatively, Denmark has offered Adjustable Rate Mortgages for the last 15 years or so. Rates on these "adjustable" mortgages are fixed for set periods, with rate resets coming at 1, 3, 5 or 10 years. With these mortgages, you can only prepay at a rate reset (unless you buy them back at market prices, which is equivalent to paying a full prepayment penalty). So a 5-year ARM seems similar in this respect to a 5-year Canadian closed FRM. Yet 30-FRM open mortgages continue to exist in Denmark, and have at times in the past decade constituted more than 50% of mortgages sold. Does this pass the test of the market? What's more, Denmark mortgages are required to be "match-funded." This means that rather than trust the banks and the financial system to allocate risk through the market, the government requires that specific bonds be issued that have liability profiles equivalent to the asset terms (including prepayment where applicable). And so there is a market for sellers (owners) of these bonds as well.

The average duration of 30 year fixed mortgages is 7 years. Competition drives pricing to be approximately equivalent to a 7 year adjustable. Over the business cycle, adjustables will be less expensive than 30 years, then match and exceed them. The popularity of adjustable and fixed mortgages vary over the cycle, but fixed remains popular, largely because it removes uncertainty, of payments but not of wages. A recession will lower rates and refinancing to a fixed will lock in rates at the low for the cycle even though adjustables will be slightly cheaper then. Disinflation favors adjustables, inflation favors fixed, and short term favors adjustables, and long term favors fixed. There is little difference between 7 year adjustables and 30 year fixed otherwise and neither has won out, but the fixed remains more popular and has increased market efficiency as a result. Plenty of people should like to lock in 30 now, but few would have liked to lock in 30 when inflation peaked, so their popularity would vary. This may be driven by past memories of inflation or future expectations. Adjustables are assumable but that is largely irrelevant since differences in the amount of the existing loan and future loan would necessitate an expensive second offsetting any benefit from assuming it. Portability is also irrelevant for the same reason, due to differences in housing market prices and whether you are moving up or down scale. A closed 30 would fluctuate in value more due to its duration than an open one though.

Nick, you have been confusing me with these last two posts.

My immediate reaction from reading these posts is that all these different products can be priced, and so any of them can become "the" main product. What will determine this will be custom, maybe tax policy, or some other sunspot.

One is not inherently better than the other.

But you seem to argue that the market can only price one type of product, and not the other, or both. Why?

Is it really so much more expensive and difficult to price a fixed rate mortgage over a variable rate mortgage? One would assume that if anyone had the resources to do this, it would be the financial sector, and not households. And therefore there would be some economic value to having the creditors do this instead of households, providing households with some certainty at a small profit.

And it's pretty clear, if you look at what is happening in other countries, that mortgage terms are all over the map, some predominantly fixed, and others predominantly variable, with a lot of heterogeneity. It doesn't seem to be the case that the financial sector can only handle one type of mortgage product.

@determinant: You write that CMHC insures all mortgages - to be exact, it (or its competitor...) insures all mortgages that do not have a 20% downpayment.

@RSJ: it's not quite so easy to structure and price a fixed 30-year mortgage, especially with no prepayment restrictions. Not many banks or other borrowers can borrow that long. Yes, some of the necessary can be done using derivatives, interest rate swaps, etc, but that means finding counterparties that you would take the risk of for 30 years. (I know of a Russian mortgage securitization that went bad due to Lehmann Bros' failure and the swaps needed).

In many countries, yield curves don't go out to 30 years, and the other capital markets tools are not there to price these things. Even in Canada, the differential between 1-year and 20-year govt bond yields is about 3% today (and you would expect the yield to grow larger for less credit-worthy borrowers - if it was possible for them to borrow).

So it's not clear that 'anyone has the resources to do this' except government - even in the U.S. the full 30-year fixed is entirely dependent on government support.

You say that 'mortgage terms are all over the map', some predominantly fixed, some predominantly variable. I would be grateful for a resource on this - to my knowledge, there are only two markets in which long-term fixed rate is a dominant product, US and Denmark. I know of no others where it is a product commonly available in domestic currency without direct government support. (I may not be up-to-date, though, particularly as regards some EU markets).

"The entire thrust of microeconomic research into mortgage strategy in Canada has been to show that shorter terms are better, even when we try to stack the deck as much as we can against that strategy."

Determinant: can you provide some references for this microeconomic research? I'm interested in getting deeper into this topic. Thanks.


Believe it or not, there is a ton of documentation. The Eurozone has a Mortgage Product Experts Group that busy themselves issuing reports.

But here I found a nice summary of the market via Google

Nation: Home Ownership Rate Predominant Type Of New Mortgage Amortization Period
Canada 66 Variable 40%Initial Fixed 60% 25
Finland 58 Variable 97% 15-20
Germany 42 Mostly Initial Fixed Or Fixed 28
Italy 80 Fixed 28% 10-15
Norway 77 Variable 90% 15-20
UK 70 Initial Fixed 28% Variable 72% 25
USA 69 Fixed 74% 30

The default provisions differ. The downpayment and mortgage insurance requirements differ. In some countries, the loan is attached to the person while in others to the property. Refinancing penalties differ. Heloc options are different. Tax treatment is different. Use of securitization is different. Existence of subprime lending options are different.

And add to that that you can get foreign (euro) loans.

To the naive observer, it at least seems that the varying products are the result of custom -- and this includes how each nation handles defaults and the nature of government support -- rather than any market optimization process per se. Or rather, a combination of random custom initial conditions and then market optimization within that context.

And this isn't even considering mortgages in Asia. I think in Japan, the majority of mortgages are long term fixed rate. You can get variable if you want. South Korea requires 80% downpayments. In Singapore, you can get a long term fixed, but no one can afford to buy their own house.

"I think in Japan, the majority of mortgages are long term fixed rate. "

If that's true then Nick would surely argue that's why Japan never had any serious real estate bubbles... Oh wait, forget it.

@RSJ: I see no evidence whatsoever that contradicts what I wrote - not many markets where fixed are predominant. I've seen lots of these studies and when I've looked at the comparisons in detail, very few are full-term fixed.

From your link, "initial fixed" (e.g. as in Canada, fixed for some period, floating or re-fixable thereafter, also known as hybrid ARM in the U.S.) and floating dominate. Only Italy gives a concrete figure for fixed with no qualifier of 28% - and notice the limited term. Germany's is vague as they've combined initial fixed and fixed, which are quite different.

I'd be grateful for a source for your Japan comment: this source says the opposite, that floating in a broad sense represents 70%. (The graph in the text shows about 5% 'fixed whole period' but I can't comment on the discrepancy).


In previous rounds of looking at quite detailed global reports/comparisons, I repeat, I've only seen USA and Denmark as having very considerable portions of market in fixed rate. (Terminology is a big issue and you have to look at details - such as what 'fixed rate' means in Canada is really an initial fixed rate term). Again, I might well be out of date, but every time I've seen detailed info, the conclusion has been that most of the world has floating or hybrid floating/fixed as the standard product.

@RSJ: Clarified the Italy issue. Your source above appears to be, ahem, modest in its accuracy or at least in terminology. BIS says: 'More than three quarters of credit for house purchases is at variable rates or rates renegotiable in less than one year. Only a small fraction of new lending is at rates fixed for 10 years or more.' http://www.bis.org/publ/wgpapers/cgfs26gobbi.pdf

I heard that during the Japanese housing bubble that Japanese banks were actually writing multi-generational 100 year mortgages.

I do not know how accurate this is, but I heard it multiple times.

In London many people do not own the land they build on. rather they have a 100 year lease.
It must really make for confusing mortgages.

RSJ: All products (actual and hypothetical) can be priced. There is the "supply price" (the lowest price at which a potential seller would be willing to sell them). And there is the "demand price" (the highest price at which a potential buyer would buy them).

But for some products (sardine-flavoured ice cream, maybe) the supply price exceeds the demand price. These products fail the test of the market. They could exist, but they don't.

So, of all the potential products out there, some exist in the market, some fail the test of the market, and some are banned. In Canada, 1 to 5 year closed mortgages, and 1 year open mortgages, pass the test of the market. Greater than 1 year open mortgages fail the test of the market (they are sardine-flavoured ice cream). And greater than 5 year closed mortgages are banned.

I now have a second source confirming that 25 year mortgages did once exist in Canada. Lisa tells me that her parents had a 25 year mortgage in the late 1960's. (It would have been an open mortgage, of course, de facto, given Section 10. I do not know how common these mortgages were. I couldn't find any references by Googling.

Section 10 is over 100 years old. I don't know of any change in the law around the early 1970's. My guess is that maybe section 10 plus the increase in inflation uncertainty, and hence interest rate uncertainty, is what killed off the Canadian 25 year mortgage? But it's still surprising that they haven't returned recently, now that inflation has stayed lower. But interest rates do fluctuate more nowadays than they did in the 1950's and 1960's.

eliminating the prepayment penalty does not BAN 5+ year mortgages. 30 year American mortgages are NOT closed and can be prepayed at anytime WITHOUT penalty.

To understand the difficulty facing a bank who lends this product you have to understand that the bank has sold a 30 year option on rates. Buying the requisite hedge to offset this risk is difficult to price, and expensive. A bank lending a 30 year mortgage faces a lot of risk whether rates go up or down and many banks have gone under with the wrong hedges (in the 80s).

markets for 30 year capital and options on interest rates are very inefficient and illiquid. They would probably not exist without government support (FHA, HUD, Fannie, Freddie)going back to 1930s. In many other markets (i.e. commodities like oil, natural gas, corporate bonds) which are as widespread as mortgages, it is not typical to see markets for 30 year capital. There is just too much uncertainty.

dwb: that's what I was saying.

Banning (limiting) prepayment penalties after 5 years bans 5+ years closed mortgages. Open mortgages are not banned. US 30 year mortgages are open.

And yes, those difficulties of supplying 30 year open mortgages are one of the reasons I suspect they wouldn't exist without government support.

But 30 year closed mortgages might maybe exist without government support, if they weren't banned.

Determinant @5.16:

Yes, banks who borrow with 5 year GICs wouldn't want to lend on 30 year fixed rate mortgages. But what about pension plans? According to Eric Lascelles, pension plans already own a significant minority of mortgages. Wouldn't pension plans prefer 30 year fixed rate closed mortgages to 5 year fixed rate closed mortgages? I would think they would. Their liabilities are much closer to 30 year fixed rate mortgages, so they would get a much better maturity match than at present.

Much to my surprise Royal bank is advertising a 25-year fixed. I haven't tried calling to get info or to confirm that this is really truly fixed throughout the term.


But here's the interesting bit (from my perspective anyway): rates at five year fix are 4.5% ('special' price but it's always special), and 8.25% at 25-year. But the jump in rates happens at 7-year fix at 6.85%. Note the difference in monthly payment (25-year, monthly) between 4.5%@ $553/mo and 8.25%@ $779/mo is almost 40% per month!

Given the Bank Act restriction on penalties, it should not be difficult to figure out the cost of the option of prepaying (that is, between a 7-year truly closed and 7-year closed for only five years. I forget how to do the detailed analysis, but to give a sense, the difference between current BoC yield on the five-year (2.598%) and this Royal Bank rate is 1.89%, and between the seven-year BoC (3.059%) and the Royal rate is 3.79%. This is not the proper analysis, but rough difference of 1.9% gives an idea of the magnitude of the premium one is paying just to have the two-year quasi-open option. (For anyone who remembers how to do this analysis or has the time to look it up, the BoC 25-year yield is 4.149% and the difference to the Royal rate is 4.1%).

Hope I've not misunderstood anything here.

Nick: "The typical American 30 year open mortgage would probably fail the test of the market."

Hello, argument or explanation???? You said at the beginning of the post that "there's a general assumption that the US 30 year mortgage only exists because of government support. I'm not sure that's right." So if that's not right, doesn't that imply that the mortgages don't fail the test of the market?


You'd think they would, but then again why do pension funds invest in stocks instead of bonds? I believe that they are chasing returns in order to increase the discount rate and therefore lower their required contributions.

It is the old story of safety and security vs. price.

Secondly, Mortgage-backed securities have a prepayment risk that government securities don't. Every time a borrower prepays his mortgage, the lender loses principal and interest. CMHC explicitly insures against this loss to bond holders. However this program has only been active for the last decade or so.

Furthermore for many years many large public pensions like the CPP, Ontario Teacher's Pension Plan and the federal Public Service Superannuation Plan were required to be exclusively invested in government bonds. Mortgages just didn't make the cut.


The NHA creates recourse to CMHC on all NHA mortgages up to 80%. On high-ratio mortgages up to 95% the borrower has to pay an extra premium. However you are right in that the majority of default risk is in high-ratio mortgages.

Adam P:

I made two arguments for why a 30 year open mortgage would probably fail the test of the market (assuming 30 year closed mortgages were allowed):

1. Empirical A: In Canada closed and open mortgages are in direct competition for terms of up to 5 years. Nearly all mortgages from 2 to 4 years are closed, so open mortgages fail the test of the market from 2-5 years. Extrapolate from that to 30 years.
Empirical B: At greater than 5 years, closed mortgages are banned, but opens are allowed, in Canada. 30 year open mortgages don't exist, so they fail the test of the market in competition against 5 year closed.
In other words, in Canada, 30 year open mortgages don't exist, and so they fail the test of the market *even when their closest competitor (30 year closed) is banned*.
That empirical argument looks pretty strong to me.

2. My theoretical arguments that both borrower and lender would prefer a 30 year closed to a 30 year open.

"My theoretical arguments that both borrower and lender would prefer a 30 year closed to a 30 year open."

this is my point, you haven't made any good theoretical argument here. Isn't it just as plausible to suppose that in Canada 30 year open mortgages don't exist because they're not offered? And the reason they're not offered is because the canadian mortgage market is far, far less competitive then the US market?

Adam: continued. My argument that a 30 year closed *might* pass the test of the market is weaker.

Empirical: the 5 year fixed closed is the most popular Canadian mortgage. That looks very much like a "censored?" distribution, where the right hand tail has been cut off, by Section 10. Extrapolate out to 30 years, and maybe there's still some tail out there?

Theoretical: as above. A 30 year closed looks like the sort of product that some borrowers and some lenders would want, because it allows them to hedge their liabilities better than anything else.

Adam @ 11.15 (we were posting at the same time):

My 2 paragraphs beginning "Let's start with the borrowers" and "Now for the lenders". That's my theoretical argument. I thought it was a good one.

Ok, Nick: "Let's start with the borrowers. We are born with a long position in human capital, and a short position in housing. We will need somewhere to live for the rest of our lives. Buying a house is a way to cover your short position in housing, and protect yourself against the risk that future rents may rise. If our only asset is human capital, the stream of our future wage income, but we can't sell our human capital in the futures market, the next best thing may be to finance the house with a 30 year mortgage with a fixed interest rate."

The only part of this paragraph that is relevant to the discussion of closed vs open mortgages is the last sentance (the rest bears on the rent vs buy decision).

And there is no argument here, "the next best thing may be..." is not an argument, it's an assertion

Futhermore, it's an incorrect assertion. It's surely the case that real wage growth is lowest in recessions which is when interest rates fall. The ability to refinance in order to mitigate falls in real disposable income is valuable to the individual agent and valuable to the macro economy as it helps the monetary policy transmission mechansim.

Now, as for the empirics surely you'd agree that really what matters in determining whether borrowers would prefer the prepayment option or not is the price of the option. It should be obvious that the Canadian mortgage market, with so much less competition amongg lenders, may well be simply pricing that option at a prohibitively high premium. How is that less plausible?

Continuing: "(The ideal mortgage would be one where the monthly payments were positively correlated with our wage income, but that vehicle might not exist). "

Actually, with respect to aggregate wages such a mortgage does exist. It is called a rental contract (sometimes called a lease) and you can leave at little cost if you have an idiosyncratic negative wage shock.

Then you say: "A variable rate mortgage might be better, if the level of interest rates were positively correlated with the level of our wages (as opposed to the rate of change of our wages, i.e. wage inflation), but they might not be. And the market shows that more Canadians chose a 5 year fixed than a variable rate mortgage."

Again, the part about what "the market shows" needs to account for pricing (in particular monopolisitc pricing).

finally: "And the open mortgage is a weird hybrid, that is fixed when interest rates rise, but variable when interest rates fall. Except for people planning to sell their house in the next year, who want to minimise the hassle of dealing with a closed mortgage, I can't think why it would meet the needs of borrowers."

Once again, " I can't think why..." is not an argument, it is an assertion.

Nick, no doubt that 30 year fixed closed mortgages satisfy both sides of any interest rate uncertainty for the entire duration of the loan. But let me give an argument in favour of the five year fixed. The shorter duration encourages lenders to provide better service to borrowers, because 5 years hence, borrowers could be shopping around to other banks. It also incentivizes borrowers to maintain good credit with their bank because in five years, the bank may choose not to refinance. Overall, this prevents people from gaming the system, because they know that the system will eventually catch up to them, within 5 years.

@determinant: Could you provide a reference that states that all mortgages are insured by CMHC? My understanding is that mortgages in NHA MBS are insured, but this is by no means all mortgages.

rogue: your argument makes logical sense. But I don't believe it. Once you've got the mortgage, the only thing left is to make the monthly payments. The bank doesn't need to do anything thereafter. I can't think of any way (ooops! Adam will be after me for that argument;-) ) in which the performance of the bank could be unsatisfactory thereafter.

Adam: "I've looked for the Loch Ness monster, but can't find it" is an argument that Nessie does not exist. Not a 100% proof, of course. The strength of the argument depends on how hard you have looked, and whether Nessie would be visible if she existed. Bayes Theorem probably applies here. If the likelihood of seeing Nessie if she existed is high, then if you look and don't see her, your posterior is low.

Nick, on what basis do you claim to have looked for the reason that pre-payment options make sense?

You did not say "I've looked for the Loch Ness monster, but can't find it", you said "I needn't bother looking for the Lcoh Ness monster because I can't really imagine it actually existing".

After all, you claimed that the prepayment option is socially inefficient because it increases the consumption variance of both borrowers and lenders. You didn't back the claim up with any reasoning, I keep giving you an argument that pre-payment options in fact reduce the consumption variance of the borrower. Your response was "you may have a point but wouldn't a two way bet be better?". You gave no argument as to why the 2 way bet would be better. You gave no argument for why I'm wrong. You're not giving any argument about anything, just assertions.

It is impossible to say whether it would pass or fail the market without knowing the environment and pricing. A closed 30 year fixed means the lender is taking on a lot of credit risk and a lot of inflation risk. Their liabilities are real not nominal after all, a retiree wants a constant real income, not a constant nominal income. A few years ago they would probably have been eager to do so, now days I expect much less so. A borrower would be taking on a lot of risk as well from moving, default, death, and destruction that assumability and portability can't fully adjust for. The price different between 5 year open and closed is probably small and closed may be chosen for convenience rather than cost, but a 30 year would be much more costly than either 5 year and even a 30 year open. At times, when rates are low, it would be popular among borrowers but less so lenders, while when rates are high, it would be popular among lenders but less so borrowers. Its popularity would probably wax and wane with exuberance.

Some loans do have prepayment penalties but these are a few months interest for a few years of a mortgage, and most loans have prepaid penalties in the form of points.

@greg, the idea you are thinking of is called the "option-adjusted spread": the parallel spread over a reference curve that will yield the market price, when the all-in curve is used to discount all cashflows, ignoring their contingency. But you need to to start with a zero curve for reference, not a par curve.

@Nick, it seems to me that others have raised a material objection to your "natural supply and demand" argument that I have not seen you address. The trouble is that the market demands a price ("higher yield") to accept interest rate risk, but mortgage borrowers have a degree of natural protection against interest rate risk that make this price unappealing. That is because much of the variability in nominal rates is due to inflation rather than real rates, but wages rise with inflation.

@Phil - yes, the option-adjusted spread. And I know it's more complicated than starting with the par curve, but it is an interesting starting point.

And thank you for putting the argument on inflation so simply. I agree completely (and have been trying to say this) - it's overly simplified, but in general terms (over long haul), inflation and wage increases are basically the same thing. (Actually wages tend to rise more quickly than inflation).

So Nick: if wages rise roughly at inflation (or slightly above) over long haul, don't we all have natural hedges?

Assume that (ex post) real interest rates were constant, so that changes in nominal interest rates always reflected, one for one, changes in actual inflation. Assume that real wages were constant, so that nominal wages also reflected inflation. Then a variable rate mortgage would give perfect indexation for inflation, and would dominate a fixed rate closed mortgage.

Under those assumptions, a variable rate mortgage would also dominate an open mortgage. Because an open mortgage is indexed to inflation if inflation falls, so nominal rates fall. But is not indexed to inflation if inflation rises, so nominal rates rise.

Now make the exact opposite assumption. Assume the Bank of Canada does its job perfectly, so that actual and expected inflation stays constant, and all changes in nominal rates reflect changes in real rates, and bear no relation to real wages. Under that assumption, the fixed closed mortgage, lent by a pensioner, borrowed by a wage-earner, dominates the variable rate and the open mortgage.

The real world is some sort of average of those above two extremes.

In other words, out of the three types of mortgage, there are circumstances in which the variable rate is best, and circumstances in which the closed rate is best, but none where the open mortgage is best.

While I have the utmost respect for the Bank of Canada, assuming anyone, anywhere does their jobs perfectly for a 25-year mortgage's lifespan - and doesn't change the monetary regime in that period - is not something I'm comfortable with stating is a 'dominant strategy.'

To extend this argument slightly, what's the downside of one to the other? It seems to me the downside is pretty clear with the fixed close - what if there's a global financial collapse (even if the BoC is well run, or some external shock? - and not so much with the variable. With the variable, as long as you're careful to avoid payment shocks during periods of increased inflation, the 'average borrower' doesn't have much to worry about.

Mark to market matters.  That's what's been bothering me about a thread that's been going through the comments for the last few days.  When I wrote my initial comment on the "US mortgages are weird..." post, saying that 30y fixed is bad because people could suffer a big loss when they move, what I really meant was that the value of things matters.  Changing life circumstances like a a big move/divorce/loss of job can cause unseen paper losses to turn very real.  And even if the losses aren't suddenly realized, they are still there resulting in long term accrued pain over the lifetime of the mortgage.

But even if the borrower for some reason (that I don't understand) is indifferent to the value of his/her mortgage, the bank certainly isn't.  A 30 yr fixed mortgage currently has a duration of about 20 years.  That means that every 1% change in the 30 yr rate causes a 20% swing in the value of the mortgage.  So it's just too volatile to be consistent with lending someone a significant fraction of the value of their house. 80% mortgage is too much, never mind 95%.  What if the housing market drops and the borrower has to move?  The new house may not support the old mortgage and if the borrower has lost a job she/he wont be able to service it.  There is just way too much leverage required to buy a house to be consistent with 30 yr fixed and the banks would never do it.  And if you really think banks should do this, why shouldn't they just give you a 40% bigger mortgage with a 2% higher rate right upfront when you first got the mortgage?  The mark-to-market of your mortgage would exceed the value of your house which is unacceptable whether it's a new mortgage or an old one.

And even if they wanted to do 30 yr fixed mortgages, most banks would not be able to hedge themselves either by issuing 30yr fixed notes or through interest swaps.  They also have too much leverage to be good credits for that kind of risk.  In the OTC derivatives market it's known as contingent credit risk.  It is a major consideration for the BIS, played a significant role in the dynamics of the crisis, and it cuts most institutions out the market for swaps over 10 years.

So maybe in a world less leveraged, things would be different.  And maybe Nick's intuition that 30 yr fixed is somehow right, is correct, and it's just distortions in our economy that have put us in a very suboptimal equilibrium where it's not possible.  Which leads me to my next point...

If it wasn't for meddlesome governments we would be able to cover our house funding risk the same way we cover our housing risk:  by just getting the same mortgage as everyone else.  Once we own all the assets of the world in exactly the same proportions as everyone else, we will be devoid of risk that our relative claim to the earth will be diminished by exogenous factors, and the world will be in a state of glorious utility optimum.  

And a form of that meddling, of course, is by way of telling banks what kinds of mortgages they are allowed to underwrite.  Nick, for example, can't get the 30 yr fixed mortgage that he might like to have, because the banks can't enforce the terms against him.  But what about meddlesome deposit insurance?  Banks (especially in Canada as far as I remember) fund a large portion of their balance sheet for little (M2) or no (M1) cost.  This represents a permanent endowment of hundreds of billions of dollars.  Some of that benefit certainly goes directly to bank managers and shareholders, but lending competition drives a large chunk of it towards reduced lending rates.  So the price of credit is vastly reduced compared to a free market system in which banks would likely have to depend to a much greater extent on wholesale borrowing.  People therefore are able to borrow vastly more than otherwise thereby driving up property (principally land) values, thereby increasing the capacity for borrowing, thereby increasing M1/M2...  big paper asset values, big debts, big money supply, big bank profits.  If you live in the US it's even worse.  The mortgage tax deduction inflates housing/mortages vastly higher again, and insures people never pay them off.  It's like paying a permanent land value tax in the form of seignorage.  And this high state of leverage, as discussed above, has a significant impact on the kinds of mortgage choices we are able to make.  It probably makes them very unnatural which I think is part of the reason why it's so hard to reason about them.

I'm still trying to figure out what the right mortgage is in terms of hedging wage risk.  (Nick, you pointed out that I was confusing risk in the level of wages with risk in the rate of change of wages.  That was exactly my mistake; thanks. But now it looks like you are making the same mistake in your last post which looks similarly motivated to mine. What gives?).  Part of the answer, I think, is in looking at mark-to-market of the mortgage (same as looking at the mortgage as a wage hedging problem).  When people look at the floating rate mortgage they look at the risk that they might pay e.g. 2% more next year, which they see as a loss.  In fact it's not a risk as you can always terminate the mortgage at zero cost and not pay next years interest.  But lets imagine that you are stuck paying it for a year.  And then lets imagine that you are in a fixed mortgage instead.  A 2% surprise is nothing compared to the 20% surprise in mark-to-market you might experience with the latter.  So I think the risk of the floater is overstated, and the low risk of going fixed a mere illusion (the "accrual illusion"?).  You'd really have to make a strong case for fixed being a good hedge for your income stream.

But either way, the issue might be a lot smaller and the choices less critical if our world was freer and our governments less meddlesome.

Quoted from Adam P at 11:54 am:

It's surely the case that real wage growth is lowest in recessions which is when interest rates fall. The ability to refinance in order to mitigate falls in real disposable income is valuable to the individual agent and valuable to the macro economy as it helps the monetary policy transmission mechansim.

I'm far from an expert in economics, but Adam P's argument makes sense to me. I was very confused when you wrote that a 30-year open mortgage -- a mortgage whereby in effect the interest rate can only decrease -- would fail to meet the needs of borrowers. Why would a borrower NOT want the option to pay less interest whenever possible? Am I missing something? I think I might be ...

Winston: "Why would a borrower NOT want the option to pay less interest whenever possible? Am I missing something? I think I might be ..."

A borrower certainly WOULD want that option, if it were free. But it won't be free, since the lender loses if he exercises it, so the lender will make him pay for the option. Open mortgages always have a higher interest rate than closed mortgages (without that option). It's my contention that the borrower would never want that option if he had to pay for it (except in a few special circumstances, like where he expects to sell the house soon, and doesn't want the hassle of transferring the mortgage). Adam says I haven't proved my contention, and I might be wrong.

K: interesting comment. Thinking about mark-to-market values is a good heuristic. The mark-to-market value of a variable rate mortgage is always equal to the book value, right? (Unless there's default risk). But the two can deviate wildly for a 30 year fixed closed. (And they can deviate, but only in one direction, for a 30 year fixed open??)

I don't think banks would want to hold fixed rate 30 year closed, for just this reason. But I think pensioners, or pension plans, would. So they could issue 30 year annuities (or life annuities, which must look similar in aggregate). Better even than a 30 year bond, which pays a lump sum principal at the end.

(There was some discussion by Eric Lascelles about converting mortgages into bullet bonds, but I didn't understand it, because I don't know what a bullet bond is.)

"(Nick, you pointed out that I was confusing risk in the level of wages with risk in the rate of change of wages. That was exactly my mistake; thanks. But now it looks like you are making the same mistake in your last post which looks similarly motivated to mine. What gives?)."

Maybe I'm making the same mistake too! My head is not totally clear on this. The case I was assuming is where all changes in the price level (and level of nominal wages) were anticipated just as they happened, and reflected in short-term nominal interest rates.

So the price (and wage) level goes 100, 100, 110, 110, and the 1 year ahead nominal interest rate goes 5%, 5%, 15%, 5%.

OK, I think I've got it now!

There's a difference between "variable rate" and "adjustable rate" mortgages. Eric Lascelles talks about it. I forget which one's which, but in one of them you would pay that extra 10% interest immediately, so your annual payments would go 100, 100, 150, 100. And in the other one the extra 10% interest is added to the principle, so your payments go 100, 100, 110, 110, which is exactly what we want, for full indexation.

My numerical example above assumes an interest-only mortgage (infinite amortisation) for simplicity of doing the math.

Here's another simple example to illustrate the difference between closed, open, and variable rate mortgages. And which is better.

Assume a 2 year mortgage. The variable interest rate will be 5% in the first year, and either 4% or 6% in the second year, with a 50% probability of each.

If the lender is risk neutral, the interest rate on a closed mortgage will be 5%, the same as the average expected rate on a variable. And the interest rate in the first year of an open mortgage will be 5.33%, and either 5.33% or 4% in the second year.

All three mortgages have the same expected cost to the borrower and lender. The lender, being risk-neutral, is indifferent between all three.

If inflation is zero, a risk-averse borrower will prefer the closed mortgage, and a risk-lover will prefer the variable (or just go to the casino instead). If inflation in the second year is unknown, but fully reflected in interest rates, a risk-averse borrower will prefer the variable. The only case where a borrower would prefer the open to the other two is if interest rates reflect inflation, and the borrower is risk-averse for interest rates above 5.33% and risk-loving for interest rates below 5.33%. Which is a weird assumption. Which is why I say open mortgages are weird. And in any case, he could just buy the closed, and spend the 0.33% interest saved on lottery tickets or the casino.

That's my argument, Adam. Not quite a "proof", by JET standards. But it is an argument.

Nick @ 7:42

Looks right. So the ideal mortgage has payments of short rate minus inflation minus amortization. Inflation is added to the principal. Fully indexed, no mark to market risk, and payment shocks are in the form of changes to real rates only - exactly what the Bank is trying to achieve when it changes real rates. 

And as far as lenders go, I don't se why pensioners would want to hold fixed rather than floating. They don't need market risk either and they do need inflation protection. The above mortgage seems an ideal investment. 

The only remaining problem is the rate index. Libor/prime are strongly linked to bank credit. In a crisis libor can/did stay elevated frustrating attempts at easing. Why should your payments be linked to someone elses credit? They should be based on the Bank target rate plus spread.     

Ok, Nick that's fine. Now here's the thing, as far as I can tell you seem to be assuming deterministic consumption for the borrower (maybe not constant if the economy is growing, but not random, or at lest uncorrelated with interest rates).

Suppose we tweak your example by adding a Phillips curve. So, as before inflation is unknown but fully reflected in interest rates. This time though, lower interest rate, lower inflation rate state goes with lower real income growth (real income doesn't have to fall, it just needs to grow less than expected).

In this case the fixed mortgage generates a variable consumption path because the monthly payments stay the same in the face of lower real income (again, relative to its ex-ante expected value) while the open mortgage provides a hedge against lower real income growth by lowering the monthly payments in the lower income state and thus allowing consumption to be maintained.

Might a risk-averse borrower happily pay 33 basis points more in interest to have such consumption insurance? Perhaps he'd even pay more than that for such insurance.

Wait though, there's more. Since the open mortgage insures against falling consumption but allows the borrower to spend his extra income in the high inflation/high income growth state then it actually increases the expected consumption level vs the closed mortgage (or the variable rate mortgage). Thus, some of the 33 basis points is goes back to the borrower in the form of higher expected consumption implying that 1)the price paid for the lower variance of consumption is less than 33bp, and 2) the open mortgage dominates the variable rate mortgage.

Thus, I claim that with my small tweak to the model specification you conclude that the open mortgage dominates both the variable rate mortgage and the closed mortgage.

Now Nick, does assuming a Phillips curve make the model more or less realistic than a model with variable inflation but no variation in consumption?

K: "And as far as lenders go, I don't se why pensioners would want to hold fixed rather than floating. They don't need market risk either and they do need inflation protection. The above mortgage seems an ideal investment."

If all changes in interest rates reflect inflation, then pensioners too would want floating. But suppose inflation is always zero, so all changes are changes in real interest rates. To make it simpler, assume the pensioner is very risk-averse, and will live for 30 years. He needs to consume $100 each period, or will die. But any consumption over $100 gives him no extra utility. It is as if he has a short position in a stream of payments of $100 per year for the next 30 years. And he wants to cover that short position. If interest rates change, the Present value of $100 will change too. (The mark-to-market value of his 30 year annuity will vary.) But he doesn't care about that. Or rather, he *wants* the mark to market value of his annuity to vary in exact proportion with the PV of his required consumption stream. And a 30 year fixed rate mortgage is a 30 year annuity.

You lost me on the rate index. Sorry.

If wages didn't track inflation closely, but could be expected to do so over 5 years, you might prefer a 5 year adjustable. An absence of inflation risk would imply an absence of recession risk, so the only reason to prefer a 30 year open over closed would be that you might not need the money, or need more or less of it in the future, (say have to move to an area too expensive to own and have to rent), but an adjustable would still seem more attractive then. Isn't everyone risk seeking if they believe rates are below what they believe to be a natural rate and risk adverse if they believe them above that?

Adam: Wow! this is getting very hard!

Let me see if I can get the intuition.

A fixed closed nominal mortgage won't be ideal, because it's not indexed.

A mortgage that is fully indexed to inflation is good, but is not ideal, because it's not indexed to real income as well.

The ideal mortgage, for someone who spends (say) half his income on the mortgage payments, in expected terms, would be a mortgage that is double-indexed to nominal income. (If nominal income falls 1%, the mortgage principle would fall 2%). That way, his disposable real income (after mortgage payments) would be constant.

Make the right assumptions about how nominal interest rates are correlated with nominal and real income (Phillips Curves), and I can easily see how a variable (or adjustable) rate mortgage would come closer to that ideal than a fixed rate closed mortgage. Make *exactly* the right assumptions, and I can even see that a variable rate mortgage could be ideal.

But I still can't see any assumptions under which the open mortgage would dominate *both* fixed closed and variable. That's because the variable rate mortgage will (under the right assumptions) make mortgage payments follow nominal income in *both* directions, up and down. But an open mortgage has payments that can go down, but not up. So if there were a very big inflationary boom, with nominal interest rates and real and nominal income rising a lot, the open mortgage wouldn't make payments go up to follow. So the borrower's consumption would rise in very good states. And full insurance being optimal, he wouldn't want to pay an amount equal to the expected value for that to happen.

@Adam P: You write 'lower interest rate, lower inflation rate state goes with lower real income growth (real income doesn't have to fall, it just needs to grow less than expected).'

A variable rate mortgage does provide higher consumption to the borrower in the situation you mention - the rate goes down with lower real income growth. It adjusts automatically, assuming the monetary authorities respond to lower inflation by lowering rates.

This is one of the advantages: there is no need to have an open mortgage to benefit from falling inflation (income growth). Except that in the case of the fixed rate mortgage, the borrower has to exercise the option to refinance - and, for another fixed rate, pay the option price again.

"But I still can't see any assumptions under which the open mortgage would dominate *both* fixed closed and variable. "

Re-read my argument, it's because the open mortgage gives a higher expected consumption growth rate than the variable mortgage plus the downside insurance which is valuable to a risk averse agent. (The variable mortgage does, I agree, provide consumption insurance.) Your argument that full consumption insurance is optimal is only valid assuming a fixed expected value of consumption. Here we are comparing two possibilities with different variances of consumption but also different expected values, thus which is better will be determined by the preferences of the borrower.

Now, of course it's all in the pricing. The degree of risk aversion vs the option price will determine which is preffered but it should be very, very easy to see that a moderately risk averse borrower may prefer the open mortgage to either of the others.

PS: let's imagine for a second that we agree that depending on the pricing and the consumption risk that agents face, either of the mortgages might dominate the others. For open mortgages, how do we go from "sometimes better and sometimes worse" to "weird, stupid and dangerous"?

@Nick: yes, in a fairly simple model of asset pricing, the variable rate mortgage is carried at book value (ceteris paribus). There is also no expectation that borrowers will refinance except in the case of spread compression (hence reducing earning assets which would have to be lent at new prevailing rates ... which can roughly be assumed to be lent at the same rate for new variable rate loans).

An extreme example of the issue with US fixed rate mortgages is that servicing portfolios (which is no longer the mortgages, but the contract to service an existing pool of e.g. Fannie and Freddie mortgages on a fee for service basis) fluctuate wildly with repayment expectations. (Because as rates go down, it is assumed more mortgages will be refinanced, hence reducing the size and the expected present value of the existing pool - in the rising interest rate scenario, they go up in value).

Just as an example of how a bank/financial institution can work, I work for one that prices and places effectively all of its non-treasury loan assets to re-price to six-month Libor. Likewise all borrowings. Fixed rates, foreign currency, EVERYTHING is swapped and/or hedged to get back to the base currency/term. Options to repay are typically done on a complete 'make whole' basis (equivalent to paying for cancelling the existing swaps or funding arrangements, like buying back the borrower's own bonds at current market prices - which would have gone up if fixed rate and interest rates have fallen). And yes, the loans - all floating - would generally be priced at outstanding principle (less reserves), ignoring the more complicated accounting cases and whether hedges would be applied directly against the loan or liabilities going up and down separately (but with, theoretically, same net effect).

Nick: "So the borrower's consumption would rise in very good states. And full insurance being optimal, he wouldn't want to pay an amount equal to the expected value for that to happen."

that's the point, the variable rate mortgage gives both lower variance of consumption and lower consumption growth rate. The open mortgage gives a higher variance to the consumption path but also a higher growth rate. It is easy then to choose values for risk aversion coefficients and consumption paramters that make the open mortgage dominate.

GA, you've comletely misunderstood the argument.

PS: I was responding just now to GA @2:10pm.

We were posting at the same time.

PPS: at 2:25pm (just above) when I said "The open mortgage gives a higher variance to the consumption path but also a higher growth rate" that is relative to the variable mortgage.

Relative to the fixed rate closed mortgage the open mortgage gives both higher expected consumption growth and lower variance. Thus the closed mortgage is entirely dominated by the open mortgage!

@Adam: I get, I just believe you're not accounting sufficiently for the up-front cost of the option (it reduces consumption now) nor the cost of refinancing each time to benefit from the open option. Whether one can choose parameters to make it dominate may be possible, but I still think this hasn't got to the point where one can say "financial institutions can or will offer this at reasonable prices." Even if the borrower might prefer.

Adam: I have re-read your original argument @12.45, and I'm still not getting it.

All three consumption streams (for each of the three types of mortgage) should have the same expected value, given a risk-neutral, competitive lender.

Since the actual interest paid on an open mortgage will tend to fall over time (it will fall unless interest rates rise faster than the falling value of the option), the open mortgage will tend to give a rising consumption stream over time, if real wages have no up or down trend. That may be a good or bad thing. It is usually a bad thing, if the borrowers rate of time preference proper equals the interest rate. But in any case, an upward or downward trend in mortgage payments, wages, and consumption, can presumably be offset by varying your savings outside the mortgage.

What am I missing?

I see fixed as reducing borrower default risk and open as reducing borrower timing risk, adjustables being preferred but caps not necessarily providing sufficient limits to avoid potential loss, so open as insurance worth paying for by preventing catastrophic loss even if expensive. Extreme at 30 though simple to analyze, a sufficiently long adjustable should do as well or better. We buy fire insurance though we don't expect to profit from it.


When you mention life annuities, I must mention that I have life insurance training. The life annuity market in Canada is actually underdeveloped. Canada Life holds 40% of the market share, IIRC. Canada has shown itself to be averse to purchasing life annuities for a couple of reasons.

1) Life Annuities are one of two options for taking an income from an RRSP, the other being a RRIF. RRIF's are far more popular because you can structure them to create an inheritance, whereas life annuities revert to the insurer on the annuitants death. Furthermore life annuities have generally had poor indexation options and with Canada's history of inflation prior to the 1990's RRIF's have been seen as a better option for income. There is also the fact that the bull market of the 1990's led many financial advisors to counsel their clients to pursue active management. This of course entails higher fees. This is not a coincidence. "Financial Planner" = "Salesman". Canadians would be very much better off if they kept this in mind at all times.

2) Pension funds in this country are generally structured as trusts. While Sun Life does offer a Group Annuity product to trade away pension risk through a group life annuity, the pension industry has generally seen this sort of product as an extremely expensive option. My brother is an accountant and he has told me that companies strongly prefer to keep their funds (even pension funds) under direct control. Again I believe they prefer to run an aggressive strategy in order to increase the rate at which they may discount contributions.

I find this lamentable because this annuity product has Assuris protection. In the case of default (which would have to be Sun Life in this case) you are guaranteed an income of 100% up to $60,000/year and are guaranteed 85% of your income above that. This is light-years ahead of the Ontario Pension Benefit Guarantee Fund and is available in all provinces.


Here is a good jump-off page.


Dr. Moshe Milevsky is the leading light in this area of research.


Here's a good interview with the VP of CMHC, Pierre Sarre. http://www.canadianmortgagetrends.com/canadian_mortgage_trends/inside-cmhc.html.

In addition to high-ratio insurance, CHMC offers "portfolio" insurance to lenders who wish to optimize their risk and capital usage. This is a policy paid for strictly by the lender, the borrower never sees it.

@determinant: Thanks for the cite. It's certainly a much higher percentage of mortgages insured than I realised at about 2/3s, but not all.


But what if discount factor differs between lender and borrower? In your numerical example, I believe that the discount factor of both lender and borrower is assumed to be 1. However, if lender's discount factor is 0.7 instead of 1, he will set the interest rate of the open mortgage as 5.26. (In general, if lender's discount factor is d, the interest rate will be set as (10+6d)/(2+d).) In that case, if borrower's discount factor is 1, then he will choose the open mortgage over the other two.


Let's take your example from before with a Phillips curve added. The borrower has a current real incomeof 100 (measured in units of the consumption basket excluding housing) and spends 50 on the mortgage leaving a consumption of 50 plus the house. Since in all cases the housing conumption is the same we'll just say he has consumption of 50.

Now, tomorrow two states are possible each with 50% probablility. In the boom state his income goes to 101 but rates rise as well. In the recession state his income falls to 99 but rates fall as well.

Let's suppose, for simplicity, that the rate changes are such that a variable rate mortgage fully insures consumption, thus in the boom state mortgage payments to the variable mortgage go up by 1 and in the recession state the variable mortgage payment falls by 1.

Now, let's see how the mortgages do:

Variable mortgage: income 101, payment 51, consumption 50.
Closed Fixed : income 101, payment 50, consumption 51.
Open Fixed : income 101, payment 50, consumption 51
(since open acts like fixed when rates go up).

Variable mortgage: income 99, payment 49, consumption 50.
Closed Fixed : income 99, payment 50, consumption 49.
Open Fixed : income 99, payment 49, consumption 50
(since open acts like variable when rates go down).

Thus, as I said before, when income and rates fall the open insures consumption just like a variable rate mortgage but when income and rates rise the variable mortgage reduces consumption while the open mortgage allows the extra income to be consumed.

Since both states have 50% probability we get:
Variable mortgage: mean consumption 50, variance 0
Closed Fixed : mean consumption 50, variance 1.
Open Fixed : mean consumption 50.5, variance .25.

It should be quite obvious that whatever numbers we chose for how mortgage payments change with rates that it will always be the case in this two state world that the open mortgage dominates the closed mortgage and depending on risk preferences may well dominate the variable mortgage.

Adam: those numbers for the boom can't be right. An open fixed mortgage must have a higher initial rate than a closed fixed. Because otherwise the lender is providing the option for free. With a risk neutral lender, all three mortgages must have the same mean consumption. So in a boom, where interest rates rise, the borrower with the open mortgage, who does not exercise his option, must face higher payments and lower consumption than the borrower with a fixed mortgage.

A risk neutral lender would require the mean payments be the same for all 3 mortgages, and so the mean consumption would be the same also.

In a 2 state world (boom or bust), the open mortgage would give the same interest rate as the variable in the boom. You would need a 3 state world (boom, bust, or middling) to distinguish all 3 mortgages. In boom: fixed beats open beats variable. In bust, variable=open beat fixed. In middling, fixed=variable beat open.

himaginary: sorry, you lost me there. I will try to think about it.

Yes Nick, you're right on the means, my mistake.

So, price the open mortgage so it costs .5 units more in all states (say). The mean consumption is the same for all mortgages yet the open mortgage dominates the closed, due to its lower variance, right?

So, in this example the variable rate mortgage dominates all.

That still leaves two points, first of all if I recall you have actually been claiming (on the other post) that closed mortgages should dominate open ones, is that not right?

Second, we seem to be moving further and further from "weird, stupid and dangerous", do you not agree?

PS: I did say several times yesterday that it will depend on how the pre-payment option is priced. My guess is that we could in fact produce examples where the open mortgage is best.

Let me clarify a bit.

I assumed that 5.33% of your example in Nick@09:06AM was derived from solving the following equation:
x + (x*0.5+4*0.5) = 5 + 5
where x is the interest rate of the open mortgage. The LHS of this equation is the total expected earning of the lender of the open mortgage, which earns x in the first year, and, x or 4, with a 50% probability of each, in the second year. And the RHS of the equation is the total expected earning of the lender of the closed mortgage or the variable rate mortgage, which earn 5 each year. For lender to be indifferent between all three mortgages, these earnings must equal.

Now, if you introduce discount factor d, the above equation becomes like this:
x + d*(x*0.5+4*0.5) = 5 + d*5
If you solve this for x, you get x=(10+6d)/(2+d), which I showed in my previous comment. If you set d=1, then x=5.33, which is your example.

But, suppose that the lender's discount factor is 0.7. In that case, x=5.26. If the borrower's discount factor is 0.7, too, then all three mortgages have the same expected cost to the borrower, which is 8.5. However, from the point of view of the borrower whose discount factor is 1, the expected cost of the open mortgage is 9.89, whereas the expected cost of the other two mortgages is 10. So the expected cost of the open mortgage to such a borrower is lower than those of the other two mortgages.

Adam: "That still leaves two points, first of all if I recall you have actually been claiming (on the other post) that closed mortgages should dominate open ones, is that not right?"

I may have said that. If so I was wrong. All these comments have clarified my thinking. I now think that closed will dominate under some circumstances, and variable will dominate under others. I still can't think why open should ever dominate both the other two.

"Second, we seem to be moving further and further from "weird, stupid and dangerous", do you not agree?"

Here's a rambling reply: about a year ago, there was talk about some financial products being, let's say, weird, stupid, and dangerous. Like "end of the world insurance", "financial instruments of mass destruction", etc. They didn't seem to serve any useful purpose, so that someone, either the buyer, or the seller, or perhaps both, must be making a mistake. Long term open mortgages look like that to me.

I could never really back up the "dangerous" part. This was a hunch. (I said in the original post I didn't understand this bit as well as I wanted). They looked like very difficult instruments for banks to handle, and I had a hunch that in trying to handle them banks might end up doing something dangerous. I was hoping I might get more back-up for this claim in the comments.

I think I stick by the "weird and stupid" bit, unless someone can explain to me their rationale.

A better title might have been: "30 year open mortgages, WTF?"

If we take the POV of a consumer reports journalist, there is nothing strange about saying that a certain car is not a good buy, at the price. Or an industry consultant might say that a certain car is unprofitable to sell, at the price.

The economist's POV is a bit different. Sometimes we look at a certain car and say we think that there is no price at which it could make sense both for anyone to buy and for anyone to sell. Like a sports car with drum brakes. It would only cost (say) $50 extra to put disc brakes on it, and any buyer should rationally pay the extra $50 for disc brakes. So when we see the market actually existing in one of these products, our reaction is: WTF?

Normally, when we economists see a WTF product, we think there must be something we are missing, because sellers and buyers are rational, so there must be a reason why the market produces a sports car with drum brakes, and it's our job as economists to try to figure out what that reason is. But the first part is to explain that there is indeed a puzzle there to explain, that it is indeed a WTF product.

I think I have shown that 30 year mortgages are a WTF product. What next?

Maybe someone can come up with a deeper explanation that shows, when you add in certain tweaks to the model, they can be rational for both buyer and seller after all.

Maybe there's some sort of legal restriction, or implicit subsidy, that explains their existence despite being a WTF product. (That's my hunch).

Or maybe, just maybe, either buyer or seller, or both, are just making a mistake. People do make mistakes. They don't always buy the best car, because they don't understand cars very well. They don't always buy the right financial instrument because they don't understand financial instruments very well.

But I'm really still at the first stage. 30 year open mortgages are a WTF product. There's a puzzle there. Why the F do they exist??

I'm now a bit clearer, thanks to these comments (yours especially), on what POV I am taking.

himaginary: OK. I think I follow you now.

Yep, you have reproduced the math behind my example (it took me several attempts to get it right!).

I will trust your math on your example better than I would my own math. But I trust my intuition better. And I think I've got an intuitive understanding of why your example works.

Here's what my intuition tells me: some borrowers will want their payments to be rising over time (either they have high time preference, or they expect their wages to be rising over time). Others will want their payments to be falling over time (because they have low time preference, or expect their wages to be falling over time).

Open mortgages will *usually* tend to have payments falling over time. Some borrowers will prefer this, and this feature of open mortgages might (sometimes) outweigh the benefit of certainty of payments in a closed mortgage, and outweigh the indexation benefits in a variable mortgage.

Have I understood the intuition behind your argument correctly?

It's clever, but I think I have a counter-argument.

If a borrower wants payments that are falling over time, he could do better still by getting a fixed interest mortgage with a variable amortisation. So the payments are time-varying but not state contingent. So he knows exactly how much he will be paying (no uncertainty), but knows the payments will trend down. (Or in the case of a variable rate mortgage, just accelerate the payments as time goes by.)

Nick: Actually, I wasn't thinking along those lines.

Nick@07:55AM:"An open fixed mortgage must have a higher initial rate than a closed fixed. Because otherwise the lender is providing the option for free."

What I wanted to address is this option premium. The lender sets this premium based on his time preference. What I wanted to say is that if the borrower's time preference is higher than the lender's one, he thinks that this premium is cheap and worth paying, because, in his POV, he can save his money compared to the alternative choice. So, making payment falling over time is not his supreme purpose; making the lowest payment is. Note that this comparison of payment involves future uncertainty, so it depends on one's subjective discount factor.

Why doesn't the open mortgage dominate under the middle ground version of your simplified example from 906am on June 26?

Same basic facts. Period 1 rates are 5%. Period 2 rates are still 50/50 4% or 6%. Closed/Variable cost=5% and Open cost=5.33%. But period 2 rates can be further split into four possible worlds:

25%: Rates down to 4% reflecting 1% drop in inflation
25%: Rates down to 4% reflecting 1% drop in real rates
25%: Rates up to 6% reflecting 1% increase in inflation
25%: Rates up to 6% reflecting 1% increase in real rates

I'm ignoring the more interesting Phillips curve type arguments here to stick with this example and assuming we only care about the volatility of real payouts among possible scenarios. Isn't the risk averse borrower here neutral between a Closed FRM and Variable, but prefers Open to both? For example, the real rate shock is higher in the worst case scenario for both the Closed (when inflation declines) and the Variable (when real rates increase) than in the worst case scenario for the Open.

The LIBOR Index

Libor is a bad index for floating rate loans because it is calculated from interbank borrowing rates. So even if the Bank of Canada is at zero, LIBOR (CDOR in Canada) can be arbitrarily high depending on whether banks trust each others credit. So the banks might borrow at 0 at the discount window while floating loans resetting off LIBOR can be way higher. If they were linked to the borrowers credit, that would be fine. But the fact that someone with a 25% LTV mortgage could pay 200-300 bps over the discount rate because banks suddenly become crappy credits makes no sense. And even for a Canadian 95% mortgage, CMHC is taking all the credit risk. Floating rate mortgages should be set at a fixed spread to the discount rate (or t bills). That way payments can actually go down when the Bank starts easing.

Floating, Fixed and Open...

What if I'm averse to states of the world with extremely high interest rate volatility? Personally, I find that easy to imagine since it sounds like a state of the world in which both hyperinflation and deflation become more likely. If rates haven't changed much (just the state of realized/implied volatility is high) then nothing has changed for either the fixed or the floating mortgage. But the value of the open mortgage is through the roof because the option value is much higher. And if you'd entered into either the fixed or the floater with some trepidation, you might be feeling a whole lot more trepidation now. And even if you'd gone half fixed and half floating, it doesn't save you from extreme states of the world - you might just be left terrified of both. So the way I see it, the open mortgage is just a view on the level of volatility. And just as I have opinions and preferences on rates, I don't see why I wouldn't have an opinion and preferences regarding volatility relative to the current market consensus.

Personally, I think the floater is the most neutral in terms minimizing my variance of consumption vs total consumption of the planet. I.e. I think it best allows me to maintain my relative consumption rank in society.

But if I was some kind of beta-loving, risk-seeking freak, I would go fixed. That way, as the economy rockets back to its natural 10% annual growth rate, all those open and floating rate payers will be eating my Ferrari dust even faster. And if the economy goes into a spiralling deflationary liquidity trap - well, you go big, or go home.

But if I was really risk-averse or paranoid about the ability of governments and the financial system to just work it all out in the end, I might want to get long vol and go open. Maybe I get infinite joy from being right in a state of the world where the rest of you got burned by your misplaced trust in authority. Is that not a valid form of utility?

The Preferred Investments of Seniors:

Are they really the mirror opposite of the risk-seeking fixed rate payer above (i.e. they only want to own fixed rate bonds)? What kind of hermit fixates on the *absolute* level of consumption? (You only want bread and water???) And has total confidence in the ability of Mark Carney to freeze inflation at 2% in perpetuity??? [Proof by incredulity]

And anyways... Doesn't CAPM say that they (the seniors) are supposed to hold some mix of the whole market and the short rate (i.e. a floating rate note)? If they are risk averse they are supposed to hold more note, less market. But I don't remember 30 yr fixed being on the capital-market line.

Nick @5:02pm,

Yeah, I guess we're pretty much on the same page now. After all, my intent was never to advocate for open mortgages, I just didn't see the argument. I'm pretty willing to believe that floating is better in most cases, for example in the UK the vast majority of mortgages are floating rate.

However, I think you've established "weird" but that "stupid" is still too strong. I mean, you're initial argument for "stupid", as I understood, was that the borrower wasted money on what was basically a lottery ticket, you said things to the effect of "why not just spend the extra .33% on a lottery ticket". But in the recent examples you yourself observed that expected consumption would remain the same for all the mortgages, so actually the borrower isn't throwing away money.

So, in our simple examples, at worst the open mortgage is dominated by floating because it leaves the borrower with a higher variance of consumption, it doesn't involve the borrower spending any more money on average. That's an important point because I'm quite sure we could construct richer examples, (more states of the world, perhaps the possiblity of an inflationary episode without income growth) where the open mortgage comes out better due to how it insures consumption in some particularly bad states of the world.

himaginary: I'm still not getting your argument. It may come to me.

dlr: I think I get your argument. But I think that in that case, a borrower would be better off getting half his mortgage closed fixed, and the other half variable. Some borrowers do that.

K: On LIBOR, yep. I see your point now. Good point. I can't decide if you are right or not. Should the variable rate spread over (say) Tbills depend on the borrower's credit risk, or on the bank's credit risk, which determines the cost of the bank's funds? Dunno.

On closed, open, or variable. If someone is risk averse for falls in consumption, and risk loving for increases in consumption (his utility function is S-shaped), that could explain open, as I said above. But he could also buy fixed, and spend the savings on lottery tickets, and get the same effect. And it's a weird preference. The preference you are positing sounds even weirder, because it's S-shaped like min, but S-shaped and relative too. I can't believe that (half?) of all Americans, who take out open mortgages, have preferences like that.

Now if someone has *opinions* about future interest rates that differ from the market, that could explain almost anything. People take bets if they think they know better, even when they are not buying insurance by taking the bet. But the half of all American home-buyers who take out open mortgages, and buy an option on interest rates, must be bigger than the number of Americans who regularly play the option markets.

Preferred investment of seniors. But they do buy life annuities. Their fixed pension plans give them exactly that.

"Proof by incredulity": a good morning laugh!

Adam: OK, the lottery ticket is actuarily fair. So it's not "throwing away money". But buying an actuarily fair lottery ticket is still a waste of money (not 100% waste) if you are risk averse. I should have been clearer.

Nick:  The cost of credit is not some arbitrary number linked to supply and demand.  It's supposed to be the risk free rate plus the expected loss of the loan under the risk neutral measure.  Now I agree that in times of distress, risk premia will rise even for low risk mortgages.  But a zero risk mortgage (ie a 25% LTV or fully insured by someone else) is supposed to yield the risk free rate.  Otherwise, there is arbitrage.

I didn't mean to suggest that people have *opinions* about rates.  Compared to the market, they may have different utility for different rates because of their life situations.  But different utility is mathematically equivalent to a measure change, i.e. equivalent to saying that they have different expectations for rates.

Adam: The mortgages do not have have the same expected return.  They have the same return (the risk free rate) under the risk neutral measure.  But in the real world (by which I mean CAPM) they have a return equal to r + beta*(r_m - r) where r_m is the market expected return and r is the risk free rate. So the excess return is proportional to the extent to which they add variance to the portfolio of the average investor.

The 3 mortgage debate in general:

If we applied CAPM to the problem of choosing a mortgage, it would tell us that we should hold the same mortgages as everyone else in exactly the same proportions.  But that ignores the fact that there may be regulatory constraints that prevent the market from obtaining the mortgage it wants.  It might still be worthwhile looking at CAPM to tell us how we would optimize if we could.

So for our three mortgages:

Fixed 30 yr:  For this one we could try to solve the problem by doing some work and calculating the empirical beta of 30 yr swap vs the whole market.  But then, its the forward looking measure that matters, so we could justify just pontificating on the likely correlation.  My feeling is that in a portfolio that doesn't hold any 30 yr bonds (e.g. a younger home owner with little savings and a big mortgage), 30 yr bonds would offer good diversification (variance reducing vs the job, house, etc).  And CAPM tells us that we should all hold some bonds.  Paying fixed is the opposite position of 30 yr bonds and would therefore be variance increasing.  Highly risk seeking behaviour.  And even if one had some savings, no one would hold bonds and hold a fixed mortgage: the bonds yield less than the mortgage, just downright stupid.

Floating:  Zero variance, zero beta.  In CAPM this is not even an "asset".  Its just a measure of leverage.

Open:  Lower variance than fixed.  And the big long option position is bound to be negative beta.  Is it overall negative beta?  My gut feeling is yes, but I'm not certain.  Still looks like a weird thing to do compared to the long bond position that you should be looking for in a diversified portfolio.

K: "Adam: The mortgages do not have have the same expected return."

That was Nick's restriction not mine and he got from the assumption that lenders were risk-neutral. Actually my whole argument has exactly been that the open mortgage could dominate if it hedged some risks. It's just that the particular example didn't show that because there wasn't enough risk to hedge. Hence my claim that in richer framework we could easily produce an example where the open mortgage was best.

Adam: I completely agree with you. And I think aversion to volatility risk is exactly the preference that might justify going open.

Let me clarify a bit, again. I was thinking in terms of *Present Value* of total interest payment, discounted by d. I applied that idea to your 2-year-model@09:06, and considered what happens to the three-mortgage-indifference in your model if the discount factors are asymmetric between lender and borrower.


I don't see the problem with CDOR. I don't know much how the guts of LIBOR works, but I do know about CDOR. Canadian interbank rates are tied in with the Large-Value Transfer System. This is the wire system which transfer guaranteed payments in Canada. It handles around 80% of the value transfer of funds each day and therefore handles most bank liabilities.

In order to operate this system, each bank (think the big chartered banks plus the Credit Union Centrals) has to pledge one of two forms of capital: collateral pledged to the Bank of Canada (Tranche 1) or interbank-pledged collateral (Tranche 2). Eligible capital is the kind used in open-market operations.

The Bank of Canada's overnight depository rate is 0.5% below the overnight lending rate. Whenever the interbank rate gets outside of these bounds, it create an immediate and glaringly obvious arbitrage opportunity to move assets between the Bank of Canada and the interbank market, either in or out.

So the CDOR market is narrowly controlled. The only danger is when banks open up the spread of their own prime rates and the CDOR rate. They tried this at the beginning of the Credit Crisis in 2008 but the TD broke ranks and the rest followed suit immediately. Again the arbitrage opportunity (of the foot kind, this time) came into play.


Are you thinking about the CORRA?

I am not aware of any direct relationship between CDOR and LVTS.  The relevant CDOR rates are one and three month BAs (Bankers Acceptances).  This is term bank credit, like commercial paper for banks, and is not "controlled" by anybody that I know of (except maybe one infamous dealer's swap desk).  Here is a history of 3m CDOR vs OIS.  OIS is a swap (3m in this case) the floating leg of which resets off the CORRA, which is an index that sets of the rate on overnight payment balances (collateralized) in LVTS (fourth graph down):


So OIS vs CDOR is a good measure of the health of interbank credit. If you look at Oct 2, 2008 you can see the spike to a 106 bps differential.  In normal times it is 10-25 bps.  Swaps and FRNs reset off the CDOR.  I am not familiar with the link to prime.  But CDOR is clearly a bank credit linked rate and can deviate significantly from expectations of the risk free rate.

K: I agree Libor and its cousins are not necessarily the 'best' rate for mortgage borrowers, although it does have the advantage of being linked to the overall cost of bank funding without being too directly linked to the condition of a particular bank. It doesn't seem to me to be necessarily 'unfair' (if that's the preferred term) to link the cost of the product to the cost of producing it for the 'average market producer.' (Which is a kind of supply/demand test).

And I wouldn't see a problem with, say, government dictating the use of a particular index, even the central bank rate (although this will just create a bunch of different issues in long term, they may be preferable - dunno).

But I think there's a better solution if your real concern is volatility in the spreads as above (leading to payment shock): just introduce smoothing requirements (some kind of averaging), caps when jumps above x bps occur, or some similar. Going by gut feeling, this is going to be cheap enough and manageable enough for the banks - they just have to manage the risk with respect to the known set of mortgages resetting on a given date. (I think Canadian banks are mostly managing risks like this in normal mortgage lending, when they make an offer to lend at a rate, but the borrower benefits from any drops in the rate to closing?)

Of course, for mortgages with periodic fixed (up to five years, say), they've already effectively insured themselves against payment shocks except at the infrequent reset dates; while they have some residual risk for resets at these events, it's getting close to vanishingly small. (And anyone who has a payment shock at that date can choose variable for some period and then refix later, if they really believe the issue is temporary).

In the specific series you show (thanks!), it's worth noting that although the spread jumped (which might seem unfair), the absolute rate plummeted like a rock for about twelve months after that spike. I don't know how many borrowers on open would be complaining through that period, but I guess not many. But yes, the spread was still higher.

Two small corrections: when I say 'they've already effectively insured themselves', I was referring to the borrowers. And for borrowers on 'open' during the fall in rates during 2009, I should have written 'floating rate.'


It's not the level of the spread as much as the dynamic I object to.  And it's not payment shocks either.  If the Bank goes 300 bps, the mortgage rate should go 300 bps too.  A pre-arranged five year floating rate loan should march up and down in lock step with the risk free rate.  What if I lent you money for five years, but if things start going really badly for me down the road then you are going to have to really pay up for that loan.  It doesn't make any sense that you should have to make a credit evaluation of me as your lender!

If the lending rate doesn't go down when the Bank eases, there is a serious problem with transmission of real rates into the economy.  So it should be fixed vs the risk free rate from the start.  And like I said:  the banks are not the "producers" of mortgage credit.  That job is performed by CMHC in Canada.  And most of the funding is provided for free thanks to deposit insurance.  This is not efficient risk intermediation. The only reason the spread only went to 106 is that the crisis wasn't principally here.  Elsewhere, the index tightened much less than the target and still lags.  That's a significant drag on stimulus.

K: As I said, I could live with the rate being tied to the risk-free. I think the cost/basis differential would end up being priced in somehow, but it's not unreasonable as a starting point. I'm just noting that the risk is actually fairly minimal (it's historically been for short periods that these jumps have occurred), and it could be moderated substantially with minor tweaks as I suggested above. And of course, all the Libor-likes are not based on the risk of YOUR lender, but an average of the key players (which given industry concentration in Canada may not amount to much of a difference).

Empirical question: what happened to floating rate loans in Canada during this period? Did the index being used actually jump and reflect the spread increase? Did borrowers end up bearing this? Or did the steps CMHC take to expand its coverage end up removing that (as implied by some others above, if I understood them correctly)?

As far as what actually happened to floating mortgages in Canada I'll admit ignorance. Determinant? But the effect was big in the US where many mortgages are linked directly to LIBOR. I'm sure it was tied to CDOR in Canada or somehow to banks' marginal cost of funding (which looks nothing like their average cost of funding). I don't see any reason why the effect would be either small or temporary in a more Canada centric crisis. And I completely agree that the spread would be priced in - though it wouldn't have been valued very high pre-crisis.

Well, I do disagree with your characterization of CMHC as a "producer" of credit. It's an insurer, it enables loans to be made to a wide variety of customers at a standardized risk. It doesn't lend any money to banks so unlike Fannie and Freddie it has less direct control over commercial rates. It's MBS offerings aren't large enough to dominate mortgage funding markets either.

Variable mortgages, like all commercial loans, are tied to Bank Prime, the posted "risk free" rate at the chartered banks. It's a bit of a mystery as to how this is determined, it's pretty much the net cost of funding plus whatever margin the banks want. This definition is important for explaining what follows.

As you see from those graphs, the interbank market follows the Overnight Rate pretty well. This is actually the worse period we've seen in years.

That spike in August 2008 was the "delink" period I described. The Bank of Canada cut the Overnight Rate but the chartered banks refused to cut their Prime Rates. The media screamed. The VP Finance of the Royal Bank went on television explaining her decision. During the middle of her interview she was informed that the TD had broken ranks and cut their prime rate. She immediately cut the Royal's down too.

As for what happened to variable mortgage borrowers, as I said previously variable mortgages have fixed payment amounts and variable amortizations. When the rate increases the amortization lengthens. Banks don't ask for more payments. As this interest rate fiasco netted itself out in short order, variable mortgage borrowers would have been none the worse off.

I think K is onto something with his talk of CAPM and beta. More of a general equilibrium analysis, where interest rate fluctuations don't just happen exogenously, but must be caused by something.

A quibble first: "And CAPM tells us that we should all hold some bonds."
That can't be right? Couldn't CAPM tell a particular, less risk-averse individual he should hold negative bonds, i.e. use leverage? Plus, someone must have a negative position in bonds, otherwise there wouldn't be any bonds for people to buy?

If everyone had the same degree of risk aversion, and the same variance of income with interest rates, I think that everyone should hold variable rate mortgages in equilibrium.

My brain's frozen.

Determinant: Thanks for the info. I have not really been distinguishing consistently between variable rate and floating rate, more or less assuming that both types expose both types of borrowers equally to the interest rate risk. But actually the distinction may be quite important for some borrowers - especially those most vulnerable to payment shock - whereas they may be quite indifferent to the extended tenor, at least over short time frames.

It always happens in mortgage discussions. Particularly when the US and Canada have different terminology, the discussion easily goes off the rails due to miscommunication. This isn't the first forum where I've seen it.

AIUI most chartered banks don't do floating rate where monthly payments fluctuate. This may be a market chiice because with variable rate (fluctuating amortization) borrowers get the same lower interest rate they want without the payment shock risk.

From the bank's perspective the variable structure is better because floating rate with fluctuating payments would make a mockery of the debt service rules. A customer's payment shock is a bank's non-performing loan. The variable rate fixed-payment structure makes everyone happy it seems.

The people who would face rate shock would be those who have personal lines of credit and personal loans. Those do have fluctuating payments based on bank prime. But those are consumer loans.

BTW whenever a variable mortgage or loan rate is mentioned on a Canadian bank website, it will always be quoted at "Prime+1%" wherein Prime is the published Bank Prime at the top of the web page. I have never seen a Canadian bank expressly tie its personal loan and mortgage rates to an external index.


In CAPM investments at the short rate are special since they are risk free.  If you are relatively risk averse you put some of your money in the bank account (the short rate) and some in the market portfolio which includes all assets in the proportions in which they exist in the market. This includes government bonds from t-bills out to perpetuals.  If you a relatively less risk averse than average, you borrow money at the short rate (line of credit, margin loan, floating rate mortgage, etc.) but still invest everything in the market portfolio.  Nobody ever goes short bonds, unless the whole market is short bonds(???).

As far as someone having to be short bonds for someone to be long, you are right, it's a bit weird.  The way I think of it, companies convert assets (like talented groups of employees, business methods, IP) that are not directly investable by a generic economic agent  into assets (like stocks and bonds) that are.  So IBM is short IBM stock and bonds as a hedge against its organizational assets.  That way the rest of us can be long.  Whether short bonds is a good hedge against their assets I really don't know, and it's probably as long a conversation (or longer) as the one we had about mortgage borrowers.  But that's what they do, so those are the assets that are available to us.

Nick@07:48AM June 28:
Let me add one more comment. The case you discussed at Nick@05:30PM June 27 is where the borrower's discount rate is larger than 1. Yes, in that case, the borrower prefers to have payments falling over time, and variable amortization or accelerating the payment match his demand. On the other hand, I was discussing the case where the borrower's discount rate is still equal or less than 1, but larger than the lender's discount rate. In that case, the borrower doesn't prefer to have payments falling over time, so variable amortization or accelerating the payment is irrelevant.

Nick@10:14AM June 29:
I think CAPM tells us that we should have risky assets in our portfolio according to the weight as they are (i.e., market portfolio). I don't think CAPM works the other way around, i.e., determine the proportion of the world's risky assets according to our portfolio.

K: Got it. Long bonds and mortgages exist, and are risky, so they must be part of the market portfolio, which we all hold (with varying degrees of leverage with the safe asset). I expect I'm trying to think about both sides of the market, and asking what would exist, in equilibrium, in the market portfolio.

Yup. I agree with that. But I think I have an interesting twist. Imagine that everyone has the same risk tolerance, so everyone just has assets; no leverage or bank account savings. Then the women become less risk averse. They borrow some money at the short rate, the bank creates an equal amount of deposits, which they exchange with the men for some more of the market portfolio. So now the men have become relatively more risk averse with a smaller market portfolio and some bank deposits. All fine and consistent with CAPM.

Now imagine that instead of borrowing at the short rate, the women decide to borrow at 5 year fixed (call it a mortgage). The bank now, instead of creating an overnight deposit will create a 5 fixed rate term deposit or issue a 5 year fixed rate bond. (I know they can't force this, but they will adjust the term debt pricing to make sure the men buy it. All modern banks will do this somehow to avoid term mismatch). So now the women hold a bigger "market" portfolio and a short position in 5 yr bond and the men hold a smaller "market" portfolio and a long position in 5 yr bond. But now, what's happened is that no one can be holding an efficient portfolio, because they don't all hold the same position in two risky positions: 5yr mortgage and 5 yr bond. So someone must have done something irrational. That irrational thing was to borrow fixed, thereby introducing an arbitrary position that did not belong in an efficient portfolio.

And to be clear, if the women really wanted to go fixed (i.e. they have wages that are hedged by doing that), they should first sell their long bond positions, not take out expensive fixed rate mortgages. That is a huge position change already since bonds make up a very large fraction of the market. Is the (unexplained) hedging requirement of a large fraction of the population really so big that they actually need to unload all their long bond positions and go fixed?

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