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Who needs math? He commits the usual sins of the finance industry right in the blog.

Sin 1: Aggressive return assumptions.

8% on a balanced portfolio of 60% growth (read equities) and 40% fixed (read interest bearing debt instruments)??? :rolling on the floor laughing:

Not anymore. Not on equities. Not in Canada. 8% after Management Expense Ratios? Try 5% before, 3% after. Besides, the Canadian equities market is hardly diversified. It consists of mining plays, RIM and the financial sector.

Sin 2: Not remembering these are not normal times.

We hit the zero-lower-bound in 2008. As his other newspaper columnists will happily point out that for once in several generations we can be sure (nominal) interest rates are headed in one direction: up. Rising interest rates will bite this portfolio and its leverage expenses.

Sin 3: Are real estate and equities correlated? Yes, to a significant degree. Both are pro-cyclical, ultimately deriving from or reflecting incomes. Hmm, what happened to the equities market and real estate in the US?

Sin 4: Getting caught up in tax deductions.

These sell products. They seem like guaranteed returns. Except the risk has been amplified by leverage. See Sin 5.

Sin 5: Not seeing the risks of leverage.

Nick explained this above.

Garth used to be Minister of National Revenue under Kim Campbell. Maybe we're lucky she only served nine months.

Unfortunately CAPM can't help you here. It just says that everyone should hold a combination of cash (T-Bills) and the market portfolio. But the amount of each depends on your risk tolerance. The average person will hold the market portfolio, but if some people want to hold some cash, others will have to be short cash, ie leveraged long market. Because our system is so badly broken, however, only banks and large institutions can borrow efficiently against collateral. So, in the real world, you are probably right, Nick. Individuals just can't construct an efficient levered portfolio, even if in an ideal world they ought to (according to CAPM) if they have a higher risk tolerance than average.

The math is pretty straightforward, I think. From the Wikipedia article on Variance, the formula for the variance of a weighted sum:

Var (aX + bY) = a^2Var(X) + b^2Var(Y) + 2abCov(X,Y)

So suppose you have a certain amount to invest without leverage, and let a and b represent the fractions of your portfolio, so that a+b=1. To make it simple, assume the variances of the each asset return X and Y are the same Var(X)=Var(Y) (which makes the problem symmetrical) and compare (a=1,b=0) to (a=.5,b=.5). For the a=1 case, the portfolio variance is the same as Var(X). For the a=.5 case, the portfolio variance is .5Var(X) + .5Cov(X,Y). So if Cov(X,Y) < Var(X) (which is to say, if some of the variance of X is not shared by Y, i.e., they are not perfectly correlated), then the variance of the portfolio is less than the a=1 case.

Now free up a and b so that you can use leverage, i.e., take away the constraint that a+b=1. Suppose you compare the (a=1,b=0) portfolio with a (a=1,b=1) portfolio. For the latter, the variance is Var(X)+Var(Y)+2Cov(X,Y), so unless Cov(X,Y) is a sufficiently large negative number, the variance of the return on the diverse, levered portfolio will be strictly higher than the variance of the single-asset portfolio.

To make the point more general, take the case of uncorrelated assets, where Cov(X,Y)=0, maintain the assumption that a=1, and allow b to vary from zero. The portfolio return is Var(X)+b^2*Var(Y), so raising the value of b unambiguously adds variance to the portfolio return.

This is why, when I inherited enough money to pay off my mortgage, I went ahead and did so rather than refinancing at a lower interest rate. Even after the tax deduction (in the US) it's not worth taking out a mortgage you don't need unless you are doing so as part of an intentionally aggressive investment strategy. I wasted some time with spreadsheets before coming to this conclusion, but the point is really analytical.

I'm not sure that folks are born with a short position in housing, any more than they are short on food and clothing and all sorts of other goods. If you think that house prices are going to fall, it makes sense to sell the house and rent, putting your money in low-risk investments. And perhaps mortgagors should be regarded as glorified renters, especially since the subprime crisis. But mortgage interest is rather more expensive than paying rent, so Turner's plan is still problematic.

Andy: that's very clear. Just what was needed. Thanks.

anon: we are born with a short position in all those other goods too. Ideally, to minimise risk, we want to sell our human capital forward and buy all our future consumption streams forward. Suppose we can't sell our human capital forward, but have some savings. To minimise risk we should use those savings to buy our future consumption streams forward, where it's easily doable. It is doable with housing.

Actually, the expense of interest has nothing to do with it. However the construction of the rent vs. owning question does affect the analysis.

Question 1: How much does a house cost? If you answer the sticker price you paid the seller, you don't pass.

Answer: It costs as much equity as you put in your home.

You pay rent in any case, this is the price of living somewhere. You don't forego it either buying or owning.

Question 2: When is it better to own than rent?

Answer: If and only if the monthly payment for owning is less than the monthly payment for renting.

Corollary 1: Given downpayment E, monthly payment P, and rent R, either A or B can accommodate the extra cost of upgrading to ownership. If P-R>0 you are paying a monthly premium (with interest) to own your home. Most people pay this premium if it's modest because they want the lifestyle upgrade. If you want P=R then then excess has to be absorbed by E. If your desired E allows R=P then you are lucky, but this usually isn't the case.

Corollary 2: The actual return on real estate to an owner is the discounted value of the present sale value less the downpayment E and the present value of (P-R), not the downpayment plus the sum of payments P.

You pay R in any case to live somewhere.

When you calculate the return of real estate according to (2) with compound interest you do get a return, but not necessarily a nice return. The use of compound interest makes for a very large discounting function.

Andy: what you are saying amounts to: "more asset means more risk". That's not saying very much. More asset also means more return. The point is risk *vs* return. The basic tool for understanding that, and its implications for capital allocation, is CAPM.

K: agreed. But the point here is just that it *is* more risk. Unlike normal diversification, diversification via extra leverage increases risk. It's not a way to reduce the risk of having all your equity in one asset -- your house.

The "ideal world" I'm referring to, by the way, is the one i proposed here a while back in which banks finance their balance sheets via debt/equity rather than deposits, and money is created when investors take that debt and equity and repo it at the central bank for money. Assume two investors start with an equal endowment of capital assets. Then, one who is more risk averse sells some of his assets to the second, who pays for them via a repo loan at the CB. Nothing wrong with leverage. Perfectly sensible behaviour for both. Just different risk preferences. The problem in the real world, as mentioned above, is that investor 2, if he's a regular consumer, is unable to get a repo loan at anywhere near the risk free rate.

K, What Nick said.

As I noted in the example of myself, "it's not worth taking out a mortgage you don't need unless you are doing so as part of an intentionally aggressive investment strategy." I realized that my own portfolio was probably less risky than my best guess at the Tobin-Markowitz efficient portfolio, so if I wanted a higher-risk higher-return portfolio, increase my leverage was not the efficient way to get it.

Anyone else puzzled by the suggestion to go short debt/bonds with a HELOC in order to go long debt at a lower yield? At the very least, his 60/40 allocation should be just 60 percent equity with the smaller HELOC.

Tax deductibility of investment loans plus looking at the entire expected return of the portfolio it what explains it, I think.

totally agreed Nick / Andrew! thanks for this blog! Garth is a clever guy (we went to the same high school, decades apart) but his idea of levering up via home equity to invest in 40/60 is off the mark.

(btw I am "LH" on Garth's forum)

Is diversification risk-reducing, collectively? What happens if everybody adopts highly diversified portfolios? To pose an extreme case, what if everybody invested exclusively in index funds? What would that mean for corporate governance (a diffuse, weak board, presumably)? How would our system of financial intermediation ensure that capital flowed toward promising enterprises, instead of bad ones? Indeed, in a world of index funds we would put more money into overvalued companies that have higher market capitalizations.

And if we are heading to such a world, how do we change course?

Andy:"I realized that my own portfolio was probably less risky than my best guess at the Tobin-Markowitz efficient portfolio"

I don't understand this. Less risky per unit return is not possible, so I assume you mean less risky than the market portfolio (without cash or leverage). But in that case, that means you were on the capital-market line, between the two points. In which case, increasing leverage (trading cash for assets) is exactly what you should do to increase risk.

I see where you guys are coming from, but I think you are seeing it wrong. The question is, why are you not diversified in the first place? Why do you have so much house, if you can't afford stocks, bonds, education, etc? And if you were diversified, and you suddenly received a windfall inheritance, why would that suddenly decrease your risk tolerance? Assuming logarithmic utility, you would just scale up all your allocations, *including your borrowing* to match your new total wealth.

Here's how one *should* look at it. Everyone should hold their wealth in some multiple (more or less than one, depending on risk preference) of the market portfolio. Now, some people would prefer more housing than is contained in that portfolio. If so, they should rent it, not buy it. Wanting more housing is just a higher than normal preference for housing *consumption*. But, nobody said we all have to have the same consumption basket. If the cost of housing rises, then that person would want to consume less housing, so it would be wrong to buy it. So there's no excuse to be overexposed to housing (ignoring the effects of totally inefficient tax/banking systems).

Because diversification usually loses against paying off mortgage debt in Canada, for two really micro reasons.

Reason 1: You already own the house, so you already have the mortgage debt. You are legally required to pay off the debt out a more-risky income stream. Therefore reducing your future payment obligations reduces risk.

Reason 2: Mortgage payments are paid out of after-tax dollars. Therefore to normalize it to a pretax return like the ones advertised by financial products, you have to mark it *up* by your marginal rate. A related observation here is that you borrow money at the commerical lending rate from banks, which is always higher than the deposit rate. If you borrow at 6% your pretax return is more like 9.5%. Guaranteed.

So looking at these two observations, we see that paying off mortgage debt will always beat out holding debt investments.

Will it beat out holding equities? Well, paying off mortgage debt gets a marginal tax rate markup which is a unique advantage here, and when you do that you'll also get to take possession of your imputed rent payment stream sooner. You have also reduced the total risk of your financial position by eliminating your payment obligation out of your income stream. No tax liability comes out of any of this.

Equities in this case have a tax liability in capital gains and dividend income. Forget RRSP's for simplicity. Add in management expenses of a greater or lesser extent and this strategy has at best a slightly greater return for a lot more risk.

Furthermore a sale of primary residence is tax-free in Canada so capital invested in a home compounds tax-free. The equity position in this example doesn't, the dividends are taxed.

Frictional costs and legal obligations are what defeat the equity strategy. Equities really have to perform strongly to beat paying off a mortgage. The competition just isn't equal.


I was born short a house, because I have to live somewhere, and without a house I am exposed to future changes in market rents. Owning a house is less risky than not owning one. I am also always long human capital. Ideally, I would have sold off part of my human capital in the beginning and used it to buy a house, but that isn't possible. So I took a second best solution by buying a house with a mortgage. So before receiving the inheritance I had a net levered position in human capital and no net position (two offsetting positions) in real estate. The critical point is that I would not have chosen to lever my human capital if I could have sold it.

After I received the inheritance, I had the option of de-levering my human capital, which is what I would have preferred initially. (This is what I mean by "a mortgage you don't need" as opposed to one I previously "needed" in the sense that it was the only way to finance my human capital while netting out my real estate exposure.) But I faced the question, do I want to hold other leveraged assets instead?

To analyze my decision, it's necessary to recognize that the capital market line is not really a line. Even with a house as collateral, there's a large spread between my lending rate and my borrowing rate. If I could really borrow at the risk-free rate, I would probably be holding a slightly levered portfolio with a large fraction of bonds. In practice, the allocation of the risky assets in my portfolio serves not just to find the optimal relative proportions of risky assets but also to control the overall risk level. I decided that I had a pretty timid portfolio and that, if I wanted more risk, the efficient way to get it would be to allocate my portfolio more aggressively rather than leverage it.

I think it's a bit more complicated. I see two main arguments for increasing leverage:

1) You have a small or negative equity value.
In this situation you don't really own your house, you mostly own an option on your house, so re-paying the mortgage actually increases your delta (exposure) to the housing market. This is only true if you have a no-recourse mortgage or you are very poor (total negative equity). It also requires you have no additional cost to defaulting (e.g. in the UK if you default, you might get in trouble in your profession).

2) You are relatively young.
This is mostly an inter-temporal asset allocation question. It's analogous to the fact that you want to reduce your risk as you get older, at the beginning you might not have enough risk and it would be better to leverage (and repay as you get older) than run that risk later on (as I think it's reasonable to assume return in the stock market to be temporally uncorrelated). Assuming that you know your total earning capacity through life (or at least the lower bound), it might make sense. Taxes are a big drag though, so while it's an interesting theoretical idea, I wouldn't do it (unless you can do it in a pension fund that pays no taxes, at which point it might be a good idea, mostly if the above is true)...

What do you think?

Actually the pension fund angle is interesting as well, as those assets are usually safe from default (at least in the UK). So you can salt money away... Again only worth it if you have no added costs...

acarraro: OK. But Canadian mortgages are generally recourse.

Second arguement still stands, I think. What do you think about it?

In 1999 Garth Turner advised to short residential investment (your home) and leverage up deep into equities.

Since then I can't figure out why anyone listens to him. And I'm not arguing that real estate is overvalued.

He will be right the same way a broken clock is right twice a day.

A quibble with Andy's math: when we remove the constraint that a + b = 1, we have not removed the total portfolio constraint. Our new portfolio is a + b + c, where c is the negative bond (mortgage) holding, and we are still constrained by a + b + c = 1. If we had no liquidity constraints, and if we were an investment bank operating on a mark-to-market basis, this bond holding would provide diversification benefits to our portfolio, assuming it is a fixed mortgage (because bond and house prices are positively correlated.)

But if you saw the value of your house fall, would you feel happier because you had a mortgage and could see that mortgage rates were rising? I wouldn't. There is nothing irrational about this; the diversification strategy has introduced the possibility of bankruptcy that was not present when we had a plain unleveraged position in a house. That is not, in my view, an ideal risk-reduction strategy.

One more general observation: that variance formula depends on realized variances and covariances. Another way of saying this is that we will only achieve the diversification implied by past behaviour of asset prices if the joint distribution of these prices is stationary. This is not a reasonable assumption over the investment horizon of a mortgage; thus the actual diversification benefit (or penalty) of the portfolio is unknown.

"Mortgage payments are paid out of after-tax dollars."

Even in Canada, if you take out a mortgage specifically for the purpose of funding an investment that has a reasonable expectation of positive return, the interest is an investment expense. It is not unusual for wealthier Canadians for whom the value of a house is not a big deal to adopt this strategy. I still think it is crazy for most of us.

I should have mentioned for the benefit of American readers that Canadian mortgages are balloon-style, needing to be refinanced over their lifetime.

It’s a tax deductible carry trade.

The correct comparison is between a portfolio of say, two houses, versus a portfolio of one house and a stock portfolio, where either alternative is financed by a combination of equity (net worth) and tax deductible debt.

The second alternative is more diversified than the first.

But both are riskier than one house financed by equity (net worth).

And the correct risk analysis must include an examination of cash flow (liquidity) risk, which the covariance stuff doesn’t get you, and as Phil points out neither does the mark to market on the debt.

But it’s not a terrible strategy from a risk perspective, provided the stock selection is sensible.

From that starting balance sheet, I’d do it in about a second with Canadian bank stocks, with the dividend covering the after-tax interest cost, provided HELOC repayment is not conditioned against stock price volatility (in the reasonable short run). It’s a risk, but it’s one of the more sensible risks you could take in North American stock markets.

Although there's interest rate risk on HELOC interest payments, so I'd probably prefer to do a 5 year fixed mortgage, long amortization. That might present a cash flow constraint, depending on the starting income statement. Also, bank stocks are a bit expensive right now.

The portfolio is not housing vs financial assets by the way but income vs housing and financial assets and the trade off is between a stable income source and riskier assets offering potentially greater returns. Variance is larger and tends to be correlated as well as people lose their jobs during recessions. Acceptance of higher risk is reasonable for the young with long careers ahead of them, but less so as that window shrinks. It can also be useful in retirement as an inflation hedge providing nominally fixed expenses against a nominally fixed pension. Circumstances matter.

"Mortgage payments are paid out of after-tax dollars."

Even in Canada, if you take out a mortgage specifically for the purpose of funding an investment that has a reasonable expectation of positive return, the interest is an investment expense. It is not unusual for wealthier Canadians for whom the value of a house is not a big deal to adopt this strategy. I still think it is crazy for most of us.

True Phil, but that wasn't what I was trying to get at. I meant that in order to compare the return of paying off your non-deductible primary mortgage (the one you took out to buy your home) and say the return on a bank stock, your mortgage payment is paid out of after-tax dollars and you need to mark up your return by your marginal rate.

I wasn't addressing the deductibility of housing-secured investment loans, which are tax deductible in Canada and in the extreme lead to the dreadful Smith Manoeuvre.

With respect to accarro, in Canada and the UK you can hold your own residential mortgage in your retirement fund (RRSP in Canada, Personal Pension Plan in the UK). In Canada the mortgage has to be at market rates, administered by a trust company and insured by CMHC against default. It's costly, has a lot of frictional costs and generally isn't recommended.

If you do default, you will be in a nightmare with the Bankruptcy & Insolvency Act as RRSP's are also protected from bankruptcy but that kind of transaction is frequently voidable as a "fraudulent conveyance". Like I said, a legal nightmare.

As a sidenote, Canada allows you to contribute 18% of your income up to a maximum contribution of $18,000 a year to a Registered Retirement Savings Plan, tax deductible. The UK is more generous and lets you contribute 100% of your income to a Personal Pension Plan, tax deductible with an asset limit of 1.2 million pounds in the fund.

I like to read up on UK tax and pension laws as I find their perspective refreshing and generally more pertinent than American sources.

BTW, what is the "Smith Manoeuvre"?

Determinant: yes, it is clear (at least to me) that when the choice is between using a dollar to pay down an existing mortgage and investing that dollar in equities, paying down the mortgage is the winner on a risk-adjusted after-tax basis.

But the premise of the Garth Turner spiel is that the mortgage is paid down: "Al’s 45, two kids, wife. Townhouse in Oakville worth maybe $425,000, paid off six years ago." etc. The proposal is to borrow 200,000 and invest it in a "40% fixed 60% growth" portfolio "making 8% or so." The 40% fixed part is indeed an old-fashioned carry trade, funding a long-term loan with a short-term one. It is only the "generationally-low interest rates" that make this carry even conceivable for retail investor, as the bid-ask would normally prohibit it. I think Nick kind of ignored this part of the recommendation because it's so silly.

Turner's analysis deals only with expectations; and very doubtful expectations at that. He does not consider the question of risk at all, except to say that his proposal "mitigates against having the bulk of your net worth in one asset alone." Nick and Andy were pointing out that it can only mitigate any risk in the sense of reducing variance under strong covariance assumptions. The (minor) point I was making is that the portfolio variance is the sum of the covariances between the house, the investment, and the debt, as the debt is a risky asset. But certainly there is more to risk than variance.

Nick, the Smith Manoeuvre is a tax strategy that involves using any unregistered investments you may have (possibly zero) to repay your primary residence mortgage, interest on which is not tax deductible. You then readvance that loan using something like a HELOC to invest dividend paying equities. You then use the dividend income to make further payments on the non-deductible mortgage while paying for the HELOC interest through advancements. Eventually you end up paying off the non-deductible mortgage, have a sizable equity portfolio and a deductible line of credit. This strategy doesn't require any additional cash flows and need not result in any higher leverage. It's basically tax arbitrage.

In defense of leveraged investing, if you take a view of your personal balance sheet as your financial assets, as well as other less tangible assets like the present value of your human capital, then it can become clear that your asset allocation doesn't match your risk appetite. For a person with stable income and good job security (public sector worker), their human capital is a bond-like asset, paying regular cash flows with low volatility. Another person may have highly variable, risky income and low job security, (like a fund manager at an investment bank), which is more equity-like.

If your personal balance sheet is dominated by your human capital, and that human capital is bond-like, your bond allocation may be too high for your risk appetite. In which case it can make some sense to short bonds (ie borrow) in order to invest in a leveraged equity portfolio.

However, that a late 50s gentleman has too high a bond allocation seems unlikely to me.

There are lots of websites on the Smith Manoeuvre which explain what it is far better than I could.

The Smith Manoeuvre is controversial because it's tax arbitrage and leveraged investing at the same time, combined with often doubtful investment advice. It's pitched to retail investors as a wealth-enhancement move. "Tax Deductibility" is a classic financial industry sales tactic. This tactic is sold on the basis of creating a "tax-deductible mortgage", something not generally allowed in Canada.

Many observers, including myself, have grave reservations that investors in this tactic overlook the risk of the leverage and the risk of the equities portfolio. In order to make it work you need something that promises a higher return than your investment loan payments, which generally means equities. After the usual MER haircut and the volatility that equities have displayed this decade, you'd have to have a very strong stomach to make this work.

The tax arbitrage part may or may not contravene the General Anti-Avoidance Rule and the Real Expectations of Profit test. My brother, an accountant, has extreme doubts about this tactic. It is in a legal grey area.

I generally feel that most people are more risk-averse in practice than they believe beforehand. I know I'm that way. I have no problems with leveraged investing as long as somebody truly understands the risks they are taking and is fine with the losses that could result. Smith Manoeuvre sales pitches downplay the loss potential and target a retail-level crowd that doesn't really understand the nuts-and-bolts of this aggressive strategy.

I'm mature enough to say that if you want to leverage, fine, but I'm a financial coward and I won't take leveraged positions myself except a primary residence mortgage.

The SC has ruled on the smith manoeuvre and similar tax arbitrage schemes and deemed them legitimate. If they ruled otherwise, it would throw a bunch of other rules about the tax deductibility of investment expenses into chaos. You don't have to like it, but it is a valid technique.

I agree that SM is only for a particular risk profile. On the other hand, if you are comfortable with a primary residence mortgage and owning an equity portfolio, I don't understand why you're uncomfortable with the SM.


The "Smith manoeuvre" (a goofy name) in it of itself, doesn't neccesarily increase leverage or risk.

Consider the following example. A person has a house worth $1 million, portfolio securities with $1 million and a mortage (which he used to buy the house and for which the interest is not tax deductible) of $1 million. Now, the Smith manoeuvre involves selling your securities, paying off the mortage that you used to buy the house, than taking out a new mortage for $1 million and buying $1 million worth of securities. And the end of the day, you have a house worth $1 million dollars, portfolio securities worth $1 million and a mortgage (which you used to buy the securities which earn income, and for which the interest is tax deductible) of $1 million. Obviously, this is a simplified example (since, among other things, it assumes there's no tax hit on the disposition of the securities - though if you had done in circa 2008, that might have been a reasonable asssumption), but conceptually, there's no need to increase risk or leverage in implementing the "smith mananeuver", since it doesn't change your financial situation, it simply changes the "purpose" for your borrowing.

As for whether it withstands the scrutiny of the fisc, there have been a number of cases which suggest that, if done right, it should survive scrutiny both under the General Anti-Avoidance Rule and the expectation of profits test (although I think what you mean is the income earning purpose test - that's the test for interest deductibility in the Tax Act). In respect of the former, the SCC sided with the taxpayer in a case called Singleton which involved a similar transactions (briefly, IIRC, it involved a lawyer withdrawing money from the capital account at his firm, paying off his non-deductible mortgage, than borrowing money to invest in his business - i.e., investing in his firm (i.e. refloating his capital account). The debt that was paid-off was non-deductible, the new debt was deductible). Similarly, there was a similar case last year in front of the SCC. In that case (Lipson), the taxpayer lost, but the Court appears to have accepted that you could do a "Singleton"-type transaction (it was a badly divided court in terms of the ultimate outcome, but everyone seemed to agree on that point). The problem for the Lipsons was that their transaction differed from the simple version described above, so they ran afoul of another set of anti-avoidance rules (dealing with spousal atttribution).

As for the income earning purpose test, there's a SCC decision from back in the 1990s (Ludco) which suggested that investors will have an "income earning purpose" and should be able to deduct interest in respect of bona fide investments (i.e., in the absence of sham and window-dressing) in dividend paying securities, even if the amount of the dividends are less than the amount of the interest (and in Ludco the difference was of orders of magnitude) or if there's no guarantee that they will, in fact, pay dividends. CRA appears to have accepted the decision in Ludco, but Finance made some noise a few years back about introducing new rules to overturn the Ludco decision (in short order they were told that their proposal was unworkable - for one thing it would kill leveraged buy-outs - and they said that they would go back to the drawing board, though no one has heard anything about the issue since).

Mind you, this isn't to say that your brother is wrong, and there are cases where people get themselves into trouble with schemes like this (typically because they don't do it right or because they get advice from people who don't know what they're talking about). Even sophisticated investors often manage to get themselves into trouble on tax schemes. On that note, I'd like to note that none of the foregoing constitutes legal advice and, if you want to implement the "Smith Manoeuvre" (or anything of that nature) you should talk to your friendly neighbourhood tax lawyer.

What you're describing isn't the full Smith Manoeuvre; I have the book written by Fraser Smith himself on it. His version is the payment-oriented version where you reborrow the capital you pay down each month on your primary mortgage and reinvest that borrowing in securities. Cycle the dividends and tax refunds on the investment through the same procedure and you get what Smith describes. You wind up with a tax-deductible investment loan secured by your house which you never pay down.

In this version you get the capital appreciation of your house and the capital appreciation the investments plus the investment dividends. Nice when real estate and equities markets are booming. If one goes down you're in trouble, if they both go down, heaven help you.

The Tax Court of Canada and the SCC have never ruled directly on the Smith Manoeuvre itself. In tax cases the details are everything. Though the Singleton case attracted lots of attention and the Supreme Court's hearing room was packed that day. The court regulars who weren't financial junkies initially couldn't understand why, tax cases at the SCC are usually extremely dull and excruciatingly detail-oriented that they aren't anything like the general pronouncements that Charter cases frequently are.

Phil and Andrew F: Don't mix up risk free borrowing and short bond. Risk free borrowing is not an "asset" in standard portfolio theory; it's the numeraire. Going short bond (i.e. doing some or all of your mortgage fixed) is a separate decision which does, however, deserve an additional variable in the portfolio. But Andy's right not to designate leverage by "c".

Andy: I didn't mean to suggest that you did the wrong thing with your portfolio. I was just pointing out the consequences of a relatively simple version of CAPM. If you include asymmetric borrowing/lending, then there are indeed three distinct pieces of the capital-market "line": One from the lending point to the tangent on the EF, another from that point and up along the EF until you get to the tangent point of the borrowing-EF line, and then the last one following the borrowing-EF line out to infinity. You may have been on the middle section, and therefore changing your portfolio composition.

Nick: If there is a significant difference between risk-free borrowing and lending rates (and there is for consumers), then you don't begin to leverage until you have achieved an asset mix that is significantly more equity than bond (it's a portfolio that's way further to the right on the efficient frontier). Such a portfolio is unlikely to contain much bonds (as pointed out by Andrew F above). So to get back to your original question: For Garth Turner to be right, I suspect the market would have to be grossly underestimating the equity risk premium.

I have to give this one to Garth, as "variances and covariances and CAPM and stuff" generally support what he's saying (details on my blog). One cannot simply object that risk is increased without considering the associated gain in expected return. It's entirely possible that taking on the extra risk is fully justified.

"The Tax Court of Canada and the SCC have never ruled directly on the Smith Manoeuvre itself"

Yes, but think about why that is for a second. The CRA loves targeting marketed tax avoidance strategies (think of the various charitable donation schemes, RRSP strips, and offshore trust schemes that the CRA has targetted - often successfully - over the past decade). Moreover, the CRA takes some aggresive positions, often positions which are a stretch by any reasonable interpreation of the law (at least in the view of taxpayer's counsel), but even creative CRA auditors (and the DOJ lawyers who advise them) can only stretch the law so far, (and no one pursues a case when there is a SCC decision on point to the contrary).

If a common tax reduction strategy hasn't been brought before the tax court after a decade of marketing, that's suggestive. The basic point is that the legal principle, that you can repay non-deductible debt and then borrow new, tax-deductible, debt to invest with an income earning purpose, was decided in Singleton (and, seemingly affirmed in Lipson). What you describe as the "full" smith maneouvre is just a small scale, ongoing, version of the transaction in Singleton.

Now, the caveat to all this is that it has to be done right, which is, I think your point that details matter. There have been a number of cases over the past few years in which taxpayers could have done singleton-type transactions, but failed to do so properly (it seems because they didn't turn their mind to it. See Scragg v. R, Sherle v. R.). What is interesting about those cases, though, is the Courts (or, for that matter, the Crown) didn't dispute the possibility of implementing Singleton-type transactions, only the actual execution of the transactions.

You're point about the financial risks of the "Smith manoeuvre" are fair enough, though those are the risks inherent in any leveraged investment strategy.

I think I've got some results, Nick. Ignoring CAPM for the moment, I decided to work out the impact on the Sharpe ratio of adding a leveraged position to a house asset. But rather than adding a lot, I decided just to do a first order calculation, to see if adding a tiny amount could even be justified. So following Andy, let x be the house, y be the additional asset (stock, bond or other portfolio), s denotes a volatility (sigma), rho a correlation, and r the risk free rate. The initial Sharpe ratio is

( r_x-r)/s_x

Lets assume we have a unit amount of x, to which we add an amount b of the the asset y funded by borrowing at the rate R. For the new portfolio p:

r_p = r_x + b(r_y-R)
s_p^2 = s_x^2 + 2b*rho_xy*s_x*s_y +b_2*s_y^2
~= s_x^2(1+2b*rho_xy*s_x*s_y)

where I have dropped terms O(b^2), and the sharpe ratio is:

(r_p-r)/s_p = (r_x + b(r_y-R) -r) (1-b*rho*s_y/s_x)/s_x

where I have Taylor expanded 1/s_p around b=0 and dropped terms O(b^2) and higher. To see when the Sharpe ratio is improved by the addition of y, we set this expression greater than the initial Sharpe ratio of x alone. For b not equal to zero, and with a small amount of algebra, I get

(r_y-R) > rho_xy*(s_y/s_x)*(r_x-r)

Go ahead and make your own interpretations. Here are a few to start with:

1) r_y has to beat R, by some multiple of the amount by which r_x beats r. If r_x = r, or x and y are uncorrelated, r_y must be greater than R.
2) y can't be bonds. Bonds are basically uncorrelated with real estate, so the right side is close to zero. The expected return on bonds will not beat the cost of an investment loan. [Note that we are not comparing the *yield* on bonds to R. That yield currently comes from the back end of curve, a point in time when the short rate is expected to be much higher. The expected return on bonds is just the short rate, plus a bit of risk premium of the order of the long-run typical steepness of the curve]
3) Equity vol is *much* higher than housing. So if y is stocks, I would guess s_y/s_x is 3 and rho_xy is around 0.7, so s_y must exceed R by about twice the amount r_x exceeds r . Make your own guesses for the equity risk premium and the housing risk premium. The investment doesn't look like a no brainer to me.
4) You can reexpress r_x and r_y in terms of CAPM:

R-r < (rho_ym - rho_xy*rho_xm)(s_y/s_m)(r_m-r)

where m is the market portfolio. I don't find it very illuminating, for the usual reason that I have no idea how to define the market (Roll's critique). Maybe someone else can make something of it.

Just a comment on Nicks update at the end of his post above (and to see if I can get some attention for my last comment): Andy points out that risk goes up even if covariance is zero. But it doesn't address the point that risk rises quadratically, ie zero derivative for small added positions. My point addresses the general case.

Ping. :-(

In case people are put off by the math, the only equation that mattered was:

(r_y-R) > rho_xy*(s_y/s_x)*(r_x-r)

That was my last comment. Promise.

K: Sorry, I missed seeing your comments till you added the last one. (I was away from the blog for a bit).

I think I'm getting it, roughly. The Sharpe ratio is a return/risk ratio, right? And I think I see your point: you are wanting to see whether a *small* amount of doing what Garth recommends could increase the return/risk ratio. And it doesn't under reasonable assumptions.

Now I think Garth would say that house prices will fall, so r_x is strongly negative. And stocks will rise, so r_y is positive. And he may be right, of course. But if he is right the optimum strategy would be to sell the house, rent, and invest the money in stocks and bonds. What I objected to is the idea that by borrowing against the house, and investing in other assets, you diversify and so reduce risk. Which you don't, no matter how small a loan you get, unless rho_xy is negative. Right?

That's exactly how I see it, Nick. The Sharpe ratio is the relevant return/risk measure in CAPM. If leverage is permitted, then a portfolio dominates any other that has a lower Sharpe ratio. If r_x is inconsistent with CAPM, you should arbitrage it, as you should propose. So Garth's strategy is dom as very dubious assumptions and 2) no matter what, is dominated by a better strategy. Not great advice.

K: thanks.

Oops: second last sentence got mangled: So Garth's strategy 1) has very dubious assumptions that are totally inconsistent with historical correlations and 2) no matter what, is dominated by a better strategy. Not great advice.

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