Does finance need money/macrofoundations?

(I'm not 100% happy with this post. Too much emphasis on interest rates, for one thing. I sat on it for a few days, but have decided to post it anyway. Because I like my question better than I like my answer. So let's see your answers.)

David Glasner has a very good post: Does Macroeconomics need Financial Foundations? And Scott Sumner too on: Is finance an important part of macro? Now let's ask the reverse question.

Decades ago I read Graham and Dodd. I thought it was a great book. But one thing bugged me more and more as I read it. They talked a lot about Price/Earnings ratios. And about how some firms had P/E ratios that were overvalued compared to other firms. And about how some times might have P/E ratios that were overvalued compared to other times. But they said nothing at all about what determined P/E ratios on average, across firms and across times. They just assumed there was some 'normal' P/E ratio, but said nothing about what determined it. The book was partial equilibrium analysis. It lacked a macrofoundation. Ultimately, it lacked a theory of interest rates, because a P/E ratio is like (though not exactly like) the reciprocal of a rate of interest.

Given what Graham and Dodd were trying to do in that book (help Warren Buffett get rich by choosing the right stocks) it was perhaps unreasonable for a young macroeconomist to expect anything more. But I do expect more. How can you do finance without a theory of interest rates? And I don't just mean interest rate differentials.

Here's a very simple (and totally inadequate) theory of the rate of interest: it is set by the Bank of Canada. Add or subtract adjustments for risk, duration, liquidity, and earnings growth, and you get the equilibrium earnings yield on stocks. Take the reciprocal, and you get the P/E ratio. Done.

Why is that theory totally inadequate? Because the Bank of Canada does not set interest rates in a vacuum. It sets the rate of interest it thinks it needs to set to keep inflation at the 2% target. And that interest rate in turn depends on things like the demand for goods, and the Phillips Curve, and on the inflation target. And the demand for goods in turn depends on things like desired saving and investment, both in Canada and around the world. And those in turn depend on time-preference, and expectations of future income, and on the marginal rates of transformation of present goods into future goods, and whether there will be a demand for those future goods or a recession.

And the Bank of Canada is only able to set interest rates at all because its liabilities are used as money. And the liabilities of commercial banks that are also used as money are valued at par with Bank of Canada liabilities because those commercial banks peg their exchange rates with Bank of Canada liabilities. And Bank of Canada liabilities are used as the medium of account, as well as a medium of exchange, so if there is an excess supply of Bank of Canada liabilities the value of those liabilities will fall, which means the prices of other goods will rise. And if people expect prices to rise you need to distinguish between real and nominal interest rates, and ask how monetary policy affects both.

And those monetary liabilities are used as media of exchange, and that what makes media of exchange special is that they have no markets of their own, but are traded in all other markets, and so talking about "the money market" is nonsense, because all markets are money markets. The bond market is a money market; the stock market is a money market; the labour market is a money market; the supermarket is a money market. The foreign exchange market is a monies market.

And if the Bank of Canada tightens monetary policy, does that mean lower or higher interest rates? Well, it depends, on things like the slope of the IS curve, and how it affects people's expectations of future inflation and future real growth.

And are Ponzi schemes really unsustainable, and destined to burst like the bubbles they are? Well, not necessarily; if the rate of interest on Mr Ponzi's liabilities is less than the growth rate of the economy, it might be sustainable. Look in your pocket, and you will see an example of just such a financial asset. It's paper currency. There may be more.

If the first principle of finance is the "time value of money", aka the rate of interest, how can you even begin to understand finance without having a solid money/macrofoundation?

It is even possible for the "time value of money" to be negative, as Silvio Gesell showed.

Can you do finance while knowing nothing about any of that stuff? Well, I expect you can. But is it a good idea?

Comments

[Alex Godofsky]

And the Bank of Canada is only able to set interest rates at all because its liabilities are used as money.

A quibble: this isn't really true. Really anyone with sufficient wealth could set interest rates. Imagine I owned all the oil in the world. By trading oil for bonds (using money as an intermediary) I could in principle control interest rates through the same OMOs the central bank uses.

It is just a lot easier for the central bank to do this because they can just print the money they need.

[Nick Rowe]

Alex: If it came to a fight between me and the Bank of Canada, both trying to set interest rates on Canadian dollars, I think I would lose, no matter how much wealth I owned. Because I promise to redeem my liabilities for BoC liabilities (not vice versa), and the BoC can make the make its liabilities go from $0 to plus $infinity (as long as it has paper and ink).

[Akshay]

Unfortunately, the fundamental principle of finance is not time value of money but the fundamental theorem of asset pricing (the no-arbitrage principle, in essence) - given expectations of the future.

And you can do a lot without assuming any making any equilibrium assumptions at all (except for that of information-equilibrium).

[Akshay]

Also, it remains a good idea to do finance even without understanding where the equilibrium rate comes from. There are plenty of variables which have orthogonal components to interest rates - hazard rates, volatility etc. Finance is about determining the fair value of claims and uncertainty associated with that fair value. Macroeconomics provides just the expected time-evolution of one of the variables it deals with (albeit an extremely important variable).

[Nick Rowe]

Akshay: In a world with zero transactions costs, the price of one apple + the price of one banana = the price of a bundle with one apple and one banana. Etc. Or there would be arbitrage opportunities, for people to bundle or unbundle apples and bananas. But that doesn't seem to get you very far, in explaining the prices of apples and bananas.

[Akshay]

Nick: That's precisely the wrong variety of no-arbitrage example I am talking about.
No arbitrage talks about the relationship between risk and expected return. The financial crisis was entirely about being unable to find a single market price of risk to price assets off - which reduced liquidity drastically - the causative factors may have been macroeconomic - but not the mechanism.

[Akshay]

By the way, (the price of one apple + the price of one banana = the price of a bundle with one apple and one banana) is the kind of "theorem" FTAP warns you against. You are citing a very simple triangulation-arbitration example. FTAP does far more than that.

A bundle of banana+apple may have different risk characteristics as opposed to a banana and an apple held in isolation (diversification effects). They will be priced differently by different agents depending on their risk preferences.

Finance built on the foundations of FTAP gives you the fundamental insight that the relationship that holds between the bundle and the independent fruits in a risk-neutral world will continue to hold in some form or the other in a risk-averse or risk-loving world - and that relationship is the market-price of risk [1]. And it's when market participants are unable to agree upon a unique such price, that nominal shocks occur in the general economy.

It's not finance, at this point, which needs to learn from economics, I think - it's the other way round.

[1] - http://en.wikipedia.org/wiki/Fundamental_theorem_of_asset_pricing

[Nick Rowe]

Akshay: "A bundle of banana+apple may have different risk characteristics as opposed to a banana and an apple held in isolation (diversification effects). They will be priced differently by different agents depending on their risk preferences."

Suppose people like to eat apples and bananas together; they are complementary goods, and give you a balanced diet when eaten together. It is still true that Pa+Pb=P(a+b).

Even if some people like apples more than bananas, and others like bananas more than apples, it will still be true that they all face the same equilibrium price for apples, and price for bananas. All people who consume both goods will have the same ratio of Marginal Utility of apples/Marginal Utility for bananas.

What really matters is the covariance of the returns on an asset with the Marginal Utility of consumption. Done properly, CAPM is a macromodel, that has an underlying theory of business cycles.

[J.V. Dubois]

I would say that considering how finance people are getting involved more and more in the monetary policy I would say that getting some information about macro/money would be very beneficial. I would say that in many instance even basic micro course would not be wasted either. At least we would not have discussions where words with a very specific meaning like "demand", "inflation", "interest rates", "aggregate supply" etc. when they are thrown without notion what they actually mean in econ language whey they are ordinarily used. Just an example, there was a moment in a very good discussion with Cullen Roche where he said: "The whole point is that there really is no “supply of loans”. There is a bank’s willingness to make loans to creditworthy borrowers". Which is actually a pretty good and concise definition of supply of loans.

To me these discussions are a lot about what David Glasner said on comment section of his post:

"I am trying to understand why that might be the case. There should be some way of expressing the financial view in the language of macroeconomics, but I don’t think that I have yet figured out how to translate one language into the other."

And so far these translations were pretty poor. The fact that some people who seem to know a lot about both worlds like JP Koning do not seem to find finance view as particularly useful explanation of what is actually going on make me incline that maybe there may be no golden nugget hidden here. But I keep my mind open.

[Nick Rowe]

Take an example: suppose there are two types of apples trees. Hot trees give higher yields in hot summers, and cold trees give higher yields in cold summers. Which tree is worth more? If the marginal utility of an extra apple is greater in a hot summer than in a cold summer (either because people like eating apples when it is hot, or because there are fewer apples in total when it's hot, or because the banana crop fails when it's cold, or because the money supply shrinks in hot weather so you get a recession, or whatever) then hot trees are worth more. You need a macromodel to tell you which of the two assets is worth more.

[Nick Rowe]

JV: what you say there sounds right to me. But on the other hand, a lot of Finance people do seem to me to be really smart (like ones that comment here, for example), and a lot of stuff that happens in financial markets does sound really complicated, and I know I don't understand a lot of it, and I get a really uneasy feeling that I'm missing something there that they understand that would be important to me for macro if I understood it better.

I wish I understood shadow banking better.

I have a sense that a lot of it is really simple deep down, or could be simplified. It just needs a better way of thinking about it.

Must check in on David's post, to see if any of the finance guys answered my 3 simple questions about QE and safe assets.

[Akshay]

Nick: "It is still true that Pa+Pb=P(a+b)"

That's what I'm trying to refute. The "P"'s on the left side of the equation are *not* the same as the P on the right side of the equation.

The market will quote two different prices for the bundle and the independent assets (in isolation). And, in general,

P_a * q_a + P_b * q_b = P_bundle * q_bundle does NOT hold
(where P_a = price of apple, P_b = price of banana etc q's are quantities and q_bundle = q_a + q_b).

This is the reason an index future like one on the S&P500 does not trade at the same level as the weighted sum of prices of individual component-stock futures. The index-future enjoys a liquidity premium (or even a risk discount) as it is easier to hedge the index-future than a basket of individual stocks.

Also, CAPM is a very well-founded *micro*-model emanating directly from Arrow-Debreu general equilibrium and Black's theory for pricing contingent claims - it's a mathematical result of FTAP (under the assumption of VNM utilities for agents) - it's not a macro-model.

[Min]

Nick Rowe: "Suppose people like to eat apples and bananas together; they are complementary goods, and give you a balanced diet when eaten together. It is still true that Pa+Pb=P(a+b)."

But it will not be true in general that P(na) + P(mb) = P(na + mb).

[J.V. Dubois]

I know that there are a lot of smart finance people. But then I know a lot of smart people who believe some weird stuff especially if it is not something they are trained to deal with.

Look, the way I see it is that Krugman's babysitting co-op did not need complex shadowbanking dealing with derivatives and market plumbing to explain the gist of what is going on during recession according to modern macro. There are videos on youtube explaining the basic idea behind AD/AS model in less than 15 minutes. And I know that there were even some finance people who were quite impressed with explanatory power of your "simple" banking story.

So the fact that I did not see something similar in comming out of finance angle to macro makes me suspicious. And I have some history of studying heterodox ideas. I for instance have some experience with Austrian models of business cycles - at least as they are laid out by one Roger W. Garrison. I do not agree, but I do understand. I cannot say so about this finance stuff. But yeah, like I said I am still open minded.

[Nick Rowe]

Ashkay: If there are transactions costs (if some goods are illiquid) then I agree that Pa+Pb =/= Pa+b.

But, absent transactions costs, risk alone won't prevent Pa+Pb=Pa+b. Because people will just do the bundling or unbundling themselves, whichever is cheaper.

Yep, we normally say Arrow-Debreu is micro rather than macro, despite it's being *general* equilibrium. But macroeconomics, as a field, largely came into being because economists recognised that Arrow-Debreu and earlier Walrasian general equilibrium theory didn't seem to be able to explain the macroeconomic facts very well (some real business cycle theorists might disagree). Arrow-Debreu is an economy without money. It has one market, that opens at the beginning of time, where all goods are traded at the same time against all other goods. Then that market closes, and never reopens. If Arrow Debreu were true, there would never have been a financial crisis.

[Nick Rowe]

And all goods are perfectly liquid in that great Arrow-Debreu market that opens and closes again at the beginning of time.

[Akshay]

I should actually point out (before people jump on me) that the piece that we do use in financial economics is the concept of an Arrow-Debreu security (also used quite generously in the Arrow-Debreu GE model - which is generally known as a *macro* model). Black further enhanced it with his theory of replicating portfolios under uncertainty - and it was refined still further by a lot of quantitative finance experts to become what is now known as the fundamental theorem of asset pricing (with Fama et al providing fundamental empirical evidence to support arbitrage-pricing theory - where it works and where it doesn't).

[Frank Restly]

Nick,

"And the Bank of Canada is only able to set interest rates at all because its liabilities are used as money."

In the United States, the federal reserve was established in the 1913 Federal Reserve Act that gave federal reserve notes legal tender status. The ability of the federal open market committee to set bond market prices (the inverse of interest rates) didn't come until the banking act of 1933. And so interest rate setting and legal tender status are not joined at the hip.

A central bank can issue medium of exchange liabilities without setting interest rates and it could conceivably set bond market prices (inverse of interest rates) without having its liabilities used as a medium of exchange. For instance a central bank (or any bank) could offer equity in the bank for bonds sold by the government - in essence bartering one non-monetary liability for another.

[Akshay]

On a more philosophical note, the fundamental dichotomy I see between finance and economics arises from their treatment of risk. Econ models use rational expectations with mixed Nash equilibria etc or NK models with stochasticity thrown here and there (eg in DSGE models).

In finance, risk is a first-class citizen and the modelling and calibration of the parameters of the stochastic processes driving it forms the paycheck of many a quant on Wall Street. Risk is what drives prices of all financial assets and is fundamentally orthogonal to what the natural/equilibrium "risk-free" rate of interest in the economy is.

[Min]

OT: A complaint about a recent change in the site.

When I load a page, it seems to take 30 sec. to 1 min. to load (depending on network traffic, I guess). During that time I cannot do anything but wait. Clicking on the comments link, for instance, does nothing. Apparently what is happening after the first few seconds is that little images are loading for the buttons for Twitter, Google, Facebook, etc. As there are several of them per page, it takes a lot of time.

[Nick Rowe]

JV: I'm really pleased they liked my little banking story. There is really very little (nothing?) new there, though I am proud of making it simple.

The one thing I really wish I understood better about Finance is liquidity. I do tend to slip into a mode of thought in which "money" is perfectly liquid and all other goods are equally illiquid. And JP Koning keeps insisting that's not right, and he's right to do that. Though I still think there's something special about the *most* liquid good ("money"), and that it's a winner-take-all race, so that the winner of that liquidity race has a difference in kind and not just in degree.

I'm rambling.

I see David Glasner addressed my points on his post. The finance guys didn't.

[Akshay]

Nick:

"Arrow-Debreu is an economy without money. It has one market, that opens at the beginning of time, where all goods are traded at the same time against all other goods. Then that market closes, and never reopens. "

That's not true. Areow-Debreu models handle multi-period economies. It also has money (the risk-free numeraire and forms part of the allocation bundle).

"But, absent transactions costs, risk alone won't prevent Pa+Pb=Pa+b. Because people will just do the bundling or unbundling themselves, whichever is cheaper."

Again - not true. You are attributing the bifurcation of these prices to "transaction costs" whereas the bifurcation actually happens because of risk preferences of the agents in the economy - ie the uncertainty related to the future payout of an asset/bundle.

[Nick Rowe]

Ashkay: "Risk is what drives prices of all financial assets and is fundamentally orthogonal to what the natural/equilibrium "risk-free" rate of interest in the economy is."

Hmmm. I thought that one of the basic insights of CAPM is that the only risk that matters, in equilibrium, is undiversifiable risk. There is risk that is undiversifiable because of problems of asymmetric information (moral hazard/adverse selection). Aside from that, the only undiversifiable risk is macroeconomic risk. Booms and recessions. And that risk is not orthogonal to the natural rate, or to the rate of interest set by the Bank of Canada. It is no accident that real and nominal interest rates are very low in this recent recession.

[Akshay]

Actually I must qualify that statement. The canonical Arrow-Debreu model is a two-period economy with an inadequate treatment of money. Radner et al later formulated derivative models which do handle such deficiencies.

[Nick Rowe]

Frank: yep. I don't really believe that central banks really (let alone always must) set interest rates. But most people do believe that, so it seemed a good place to start. They certainly affect interest rates though.

Min: sorry to hear that. I'm having no problems getting WCI to load. Is anyone else?

[Akshay]

Nick: "I thought that one of the basic insights of CAPM is that the only risk that matters, in equilibrium, is undiversifiable risk. There is risk that is undiversifiable because of problems of asymmetric information (moral hazard/adverse selection)"

True. I would rather phrase it as "unreplicable" risk (via other assets) - which is where the orthogonality comes from. So, the return over the risk-free rate is proportional to the magnitude of unreplicable risk you're willing to take on (and the constant of proportionality is the market price of risk).

Most of *implied* macro-risk in advanced economies is completely diversifiable with financial derivatives. It's the *realized* risk that leads to realized above-normal returns (positive or negative). Financial assets are priced off implied-risk- not realized risk (although it feeds into the calibration of implied risk in some models).

[Nick Rowe]

Ashkay:

Arrow-Debreu has multiple periods, as many as you like, but the market only opens once, before time even begins.

"It also has money (the risk-free numeraire and forms part of the allocation bundle)."

That is absolutely not money. Money is the medium of exchange and medium of account. The Arrow-Debreu has no role for either. A "numeraire" is the good the *modeller* uses to measure prices. The medium of account is the good that *people* use to measure prices. And money is certainly not risk-free. Zimbabwe.

[Nick Rowe]

Ashkay: "You are attributing the bifurcation of these prices to "transaction costs" whereas the bifurcation actually happens because of risk preferences of the agents in the economy - ie the uncertainty related to the future payout of an asset/bundle."

I disagree. Can you give me a simple example, with zero transactions costs, so I can understand what you are saying.

[Akshay]

"And money is certainly not risk-free. Zimbabwe."

Money is totally risk-free (capital protected) in nominal terms. I hold a 100-dollar bill in my pocket. I will get a 100-dollar bill for it tomorrow from my friend regardless of what inflation/interest-rates are.

Bonds, on the other hand, are not risk-free - even in nominal terms.

[Nick Rowe]

Ashkay: Money is 100% risk-free, in terms of money. Copper is also 100% risk-free, in terms of copper. So is any durable good, in terms of itself.

[Akshay]

Example of why a bundle's market price differs from an equivalent combination of assets purchased in isolation:

E(r_bundle) = E(r_f) + m * risk_bundle
E(r_a) = E(r_f) + m * risk_apple
E(r_b) = E(r_f) + m * risk_banana

risk_bundle = sqrt(risk_banana^2 + risk_apple^2 + 2*cov(r_a, r_b))

m = market price of risk, r_x = stochastic return of asset X, risk = std-dev of returns of that asset, r_f = risk-free rate, E=expectation operator

Expected return on a bundle is different from the sum of expected returns on the individual assets. Why would the market pay the same price?

The only place it all adds up to be beautifully equal is where the market-price of risk is zero - ie a risk-neutral world. But the world is not risk-neutral.

[Akshay]

Nick: "Money is 100% risk-free, in terms of money. Copper is also 100% risk-free, in terms of copper."

Exactly. Why is a bond, which is just the discounted cashflows of "money" not risk free in terms of money? Do you now see what a risk-free asset is in terms of the numeraire?

[Nick Rowe]

Ashkay: cars would be worth less, if there was no gas. Gas would be worth less, if there were no cars. But that doesn't mean that a car with a full tank of gas sells for a higher price than a car with any empty tank plus the price of a tank of gas.

[Nick Rowe]

Akshay: sure. But the modeller can make any good he chooses the numeraire. The Arrow-Debreu model only determines relative prices. With n goods, there are only n-1 relative prices. The modeller can choose any good he likes, and set its price equal to 1.

Take the equilibrium. Now divide all prices by the price of copper. Copper is now the numeraire, and the price of copper = 1. But it makes no difference to the equilibrium. It doesn't make copper a "risk-free" good.

[Akshay]

Agreed - the numeraire need not be risk free (except in its own terms). In the Arrow-Debreu model, it is - and I totally agrre it's not a representation of reality.

However, financial asset risk can generally be broken down into two components - one due to the uncertainty in its "utility" in real terms and the uncertainty due to the choice of the numeraire.

[Sina Motamedi]

I was doing an MA last year and took several mathematical finance classes -- and this is exactly the kinda stuff I would think about. I can't remember exactly what I did, but as a starter I tried to adjust many of the models used there to have some sort of relation between inflation and interest rates, and the fact that the BoC is targetting 2%. I didn't have much success, unfortunately.

BUT, I definitely think it is important for macroeconomists to know financial mathematics, and vice versa. I can't explain why exactly, but it certainly helps with the intuition in understanding things. (Financial mathematicians, for example, don't understand monetary policy at all -- and it is very important that they do.)

[Akshay]

Nick: "cars would be worth less, if there was no gas. Gas would be worth less, if there were no cars. But that doesn't mean that a car with a full tank of gas sells for a higher price than a car with any empty tank plus the price of a tank of gas."

That's because you're risk neutral. Let's make you a bit risk-averse.

Say you're stuck in a desert with your car on an empty fuel-tank with the nearest gas station "half-a-tank" away - but the gas station may or may not be open. Your home is a "full-tank" away.

An angel comes down and offers you two choices: (money for half a tank of gas + half a tank of gas) OR (a full tank of gas).

Which one would you choose? If the angel turned out to be a mean businessperson, wouldn't s/he quote a higher price for the second portfolio (considering you're risk-averse)?

PS: You're spelling my name wrong :)

[Phil Koop]

Nick, I think you are using "finance" in a couple of different and incompatible ways.

As usually understood, finance is entirely about relative prices, partial equilibria, a glorified system of interpolation. I don't see how it could possibly inform macroeconomic theory.

What about the other way around? Sure, in principle a general equilibrium model could tell you the proper price of each individual asset. But to be arbitrage-free, such a model would have to be quantitatively very, very accurate. As a practical matter, that is an absurd proposition: the state of the art can't even produce a model with reasonable qualitative properties, in total.

The question of what is the "fundamental" value of an asset is not within the purview of finance. If macroeconomists could answer this question, then of course that would be of interest to investors. But if investors knew the fundamental value of all assets, they would have implicitly solved your G.E. model, would they not?

[Min]

Here is a thought experiment that may be pertinent. Suppose at time, T0, the price of an apple and a banana are each $1, and that people always consume them together, one apple and one banana. Suppose also that their prices are perfectly negatively correlated, so that at any time, T, the price of one apple plus the price of one banana = $2. (No inflation, but we could add it in.)

Consider two scenarios.

Scenario 1) At time, T0, each person has n apples and n bananas. They are otherwise employed keeping the economy humming along optimally. At time, T1, each person eats one apple and one banana.

Scenario 2) At time, T0, half the population has 2n apples and half has 2n bananas. They are otherwise employed keeping the economy humming along optimally. At time, T1, each person wishes to eat one apple and one banana. But now, because of the weather, each apple costs $1.50 and each banana costs $0.50. Say that the people with bananas now do extra work to pay $1 to each of the people with apples. By assumption, this extra work by half the population is suboptimal. There may also be an argument that the transfer of money is suboptimal. (See Bernoulli's Moral Value of Money.) There may also be an argument that, because of risk aversion on the part of the population, the loss in the price of bananas is worse than the gain in the price of apples.

[Min]

Hmmm. I think that we can tighten the risk aversion argument in scenario 2) by positing time, T2, when each apple costs $0.50 and each banana costs $1.50. (The shoe is on the other foot.) Even granting that we cannot compare subjective gain and loss across persons, each person will have gained less when the price of his or her fruit went up to $1.50 than he or she lost when the price went down to $0.50. The net result of the swings is a loss for each person.

[Lord]

I agree finance is all about relative prices and accepting interest rates as given, but when it looks at history, like Graham, there is an implicit assumption of a mean and reversion to it even without a restoring force or an indication of when or how it will. In this very long view, growth is constant, the real risk free rate is zero, the real risk adjusted bond rate is the growth rate, and that our best guess is the future will be similar to the past, since the industrial revolution, not any further back. I get a vague sense of a belief in Friedman's plucking model behind it.

[jt]

Akshay: "Most of *implied* macro-risk in advanced economies is completely diversifiable with financial derivatives."
Are you thinking just interest rates, CDS, ... but, what about operational risk (declining auto sales)? Companies do use interest rate swaps, FX forwards, but when I go through company financial reports, they are never material. Most companies "hedge" macro risk by maintaining liquidity and minimizing large fixed costs and long-dated liabilities.

Your answer may elucidate, why doesn't finance departments of the real economy do more macro hedging, if it was important?

[Akshay]

jt: I should have qualified that sentence with "financial risk arising directly out of the uncertainty in macro variables". You're right - operational risks are a separate and largely unhedgable with financial instruments.

The overall economic uncertainty can be broken down into uncertainty in the "operational"/"real" economy and the "nominal" economy. Transactions happen at nominal levels, investment and financing take place at nominal levels.

Operational decisions on the other hand are taken (or should be taken) based on the state of the real economy. But quite often they aren't - nominal variables serve as a proxy for the economy's performance. Now, ideally we'd want nominal variables to paint an accurate picture of the real economy - but sometimes, they don't.

Can we affect the real economy by adjusting risk and return levels in the nominal economy (via price/wage rigidities or some other channel - like term risk reduction/boosting money velocity by inflating collateral prices etc)?

That is the topic of the decade. So far, the effects of nominal policy-making have been undeniable - whether it be through QE or forward guidance or plain old short rate-cuts.

[dlr]

Nick, I am an investment guy who came to money/macro for almost the precise reasons described in your post. My take is that the trenches of dealer and treasury desks create a brain fogging myopia that enlarges beyond reason the importance of things like liquidity constraints and collateral haircuts in informing a practical macro model of the world. I understand, for example, a lot of what Izabella Kaminska likes to dive into (and I think she does a very nice job of it), but I almost never think it leads her to say any useful (or entirely coherent) about the supposed macro implications. I also think a lot of smart Macro-centric guys like Tyler Cowen are a little too respectful of the putative import of these kinds of trading desk jargon filled reality checks. And although I don't share your "difference in kind not difference in degree" approach to thinking about the special liquidity characteristics of the medium of exchange (I think the only difference in degree that matters enough to be called a difference in kind is the MOA function), I still don't think a deep dive into the intricacies of tri-party repos, shadow banking, and relative liquidity would likely be useful to you. You won't ever wake up a New Monetarist. Even for very smart people, learning too much about finance is basically a prescription to intermittently forget about joint determination and underestimate the importance of expectational games.

But some of the most insightful stuff I've read works hard to combine a finance and macro view of the world. Like Cochrane's Money as Stock paper. The vast majority of letters from great, brilliant hedge fund managers commit major and basic macro malpractice. It would be great to see you write a bunch of posts on the macro foundations of finance. Brad Delong sometimes writes good stuff like this too.

[Akshay]

A rant (since I'm liking this post so much):

A few years years ago, when I was in college learning financial economics, the professor mentioned in class:
"One half of finance is about interest rates. The other half doesn't quite matter."

Some years of quantitative modelling of various asset classes in both the buy and sell side of finance in the backdrop of the biggest financial crisis my generation has seen has made me realize how true that statement was.

But the statement is not profound for what it says explicitly, but what it means implicitly.

The overt meaning might give economists much joy as validating their science as providing the fundamental input for all of finance (which is all about relative prices anyway, no?)

The implied meaning is much more powerful. It's the nominally risk-free yield curve (we call it the zero-curve - there are two other popular varieties - forward and par-swap - and a super-duper important one now - the OIS) and the interplay of the various risk-premia that play out on top of that is what drives the plumbing of the monetary system - both via signalling of macro behavior and by providing the incentives to set the wheels in motion - at least in a nominal economy.

No, you don't need to know how multi-curve discounting involving cost-of-tenor and cost-of-funding surfaces takes place in the modern world to price collateralized interest-rate swaps.

What you do need to know, however, are the fundamentals of financial economics. Why risk matters for the nominal world, how it affects the plumbing in the financial system etc.

I'd be accused of being a dweller of the concrete steppes for making such a statement - but any policy based on theory disregarding the institutional perspective (and hence nominal risks) of the macroeconomy and relying purely on equilibria assumptions - should come with a big "caveat emptor" sign pasted on it.

[JP Koning]

Good comment by dlr. As an "investment guy", I agree with a lot of what he says.

And a good discussion by Nick. I like to think that both sides can inform each other. Hopefully I can give a better comment when I have the time.

But for the time being, here's an interesting tidbit. Many people don't know that Ben Graham was also a macroeconomist/monetary economist. He was not formally trained, but he was good enough to get an article in the AER. Read Perry Mehrling:

http://economics.barnard.edu/sites/default/files/inline/monetary_economics_benjamin_graham_revised.pdf

Which speaks to the general point that perhaps there are ways to combine the finance and macro views.

[Roger Sparks]

Nick,

You are calling "money" a "liability", and in this post, a liability of the Bank of Canada. I certainly do not think of money as a liability of anyone. I do consider money to be "Evidence of Debt".

I only have green U.S. Dollars in my wallet but there is nothing on that bill to indicate it is a liability to anyone. It does say on it "THIS NOTE IS LEGAL TENDER FOR ALL DEBTS, PUBLIC AND PRIVATE" for what ever good that does.

Now I do know that when I take a loan or make a loan, I exchange these notes for a promise to repay. Banks do the same thing. Governments do the same thing. All the evidence is that these notes that we call "money" are nothing more than "Evidence of Debt".

I accept this "Evidence of Debt" because it is like receiving a gift certificate. In fact I rather like receiving money because I can buy just about anything with it, I just need enough.

Once in a while, I have more than enough money. I can lend a little. Nice! I will ask some interest rate, maybe negotiate a little, and trade my gift certificates for a promise to repay.

When I borrow, it is to accomplish with a large block of money, something that can not be accomplished with a small block. Yes, I am not doubt impatient and maybe anticipated inflation has something to do with my motivation. As an older gent, I have seen borrowers get badly burned, so inflation is not much of a impetus; it is much more important to be a able to cash flow a loan and maintain a fall-back position, all while cutting the bank into the deal with an interest carve-out that reduces loan attractiveness.

Do low interest rates help? Of course, but loan payback is the really important criteria.

[Too Much Fed]

test

[Too Much Fed]

If I can get Nick to take me seriously, I'll attempt an explanation.

"And the Bank of Canada is only able to set interest rates at all because its liabilities are used as money. And the liabilities of commercial banks that are also used as money are valued at par with Bank of Canada liabilities because those commercial banks peg their exchange rates with Bank of Canada liabilities. And Bank of Canada liabilities are used as the medium of account, as well as a medium of exchange, so if there is an excess supply of Bank of Canada liabilities the value of those liabilities will fall, which means the prices of other goods will rise."

I'm going to say that differently. It seems to me the central bank wants to keep demand deposits (DD's) and currency 1 to 1 convertible so currency is always available to be withdrawn from the commercial banks while still being able to set the overnight rate (fed funds rate in the USA). I call this 1 to 1 fixed convertibility (relative pricing). If demand deposits double, then currency should also be able to double.

With a fixed 1 to 1 convertibility, what is the MOA and MOE here? Currency = $800 billion, central bank reserves = $200 billion, & DD's = $6.2 trillion.

Let's also try this.

The capital requirement is 10% for computer loans and 100% for computers. The reserve requirement is 0%. Computers depreciate at 1% per month. Ignore interest. Start here:

A: $2 in treasuries and $20 in computer loans
L: $20 in DD
E: $2

$1 of the DD’s are saved (now not circulating in the real economy). The bank sells $1 more of bank stock (equity).

A: $2 in treasuries and $20 in computer loans
L: $19 in DD
E: $3

The bank now creates $10 in new (emphasis) DD’s to buy a new (emphasis) $10 computer loan. The $9 increase in DD's is needed.

A: $2 in treasuries and $30 in computer loans
L: $29 in DD
E: $3

Pay down $10 in computer loans for whatever reason.

A: $2 in treasuries and $20 in computer loans
L: $19 in DD
E: $3

Now there is a shortage of MOA/MOE (the demand deposits). Have the bank buy computers. It can only buy $1 (100% capital requirement).

A: $2 in treasuries, $20 in computer loans, and $1 in computers
L: $20 in DD
E: $3

There is still a shortage.

[Too Much Fed]

Comment in spam?

[Jon]

Nick writes: "If it came to a fight between me and the Bank of Canada, both trying to set interest rates on Canadian dollars, I think I would lose, no matter how much wealth I owned. Because I promise to redeem my liabilities for BoC liabilities (not vice versa), and the BoC can make the make its liabilities go from $0 to plus $infinity (as long as it has paper and ink)."

Well..... can the BoC defend a currency peg? Not in both directions. You see the "money market" does exist, and it is the only thing the BoC controls fully. Indeed, that is the definition of the money market.

When the other half of the market has a real good, BoC is in trouble. When there are two real goods the BoC is trying to control, it is completely in trouble.

[Nick Rowe]

Roger Sparks: "Is money a liability?" Not really.

"Only in the sense of an American put option on the CPI"

A couple of my old posts on this.

[Nick Rowe]

Reading back over these comments, they strike me as very strange.

Akshay (sorry about getting your name wrong) writes very clearly, and is smart, and has been well-educated in finance. And I can sort of see where he's coming from, because I can vaguely remember learning CAPM and stuff. But he says a number of things that, when I look at them from an economist's perspective, are just very obviously wrong. About prices of bundles not equalling the sums of the prices of the components in a world of zero transactions costs and where people can bundle and unbundle goods costlessly. And about what money is. And then Min joins in too, and says things that are wrong (Min: an A-D contract to deliver gas to me 200kms away is not the same good as an A-D contract to deliver gas to me here and now, in a world of positive transportation costs, and even more so if I don't know whether the first contract will actually be delivered.)

It's like we speak different languages.

But it's even more strange when you remember (I think this is right) that most/much finance theory was invented by people who were originally trained as economists.

[Peter N]

I'm not a finance guy, but I've spent enough time with them to catch the disease, I think. So:

1) "Can currency not be used as collateral?"

No. This is nonsense. Try translating it into operational terms. If my goal is to borrow currency, can I use the same currency as collateral? In the formal sense, you can always borrow money in exchange for the same amount of the same kind of money, but you don't need anybody else to play. Just do it with yourself in a mirror.

2) "Why not just spend the currency (or claims on currency in a 100% reserve bank) instead of going to the hassle of using the T-bill as collateral for getting a loan of money to spend?"

There are as many different answers to this as there are businesses dealing with collateral. It's a market where actors with different purpose find it convenient to use similar methods. This lowers transaction costs.

A quirk in bankruptcy law holds that a repo is a loan for tax purposes, but a sale and repurchase with regard to bankruptcy. That is, unlike other forms of loan collateral, repo collateral is not part of the bankruptcy estate. In the event of bankruptcy, the creditor can sell the collateral, rather than hire lawyers and wait a few years until the case is settled. The Lehman bankruptcy still hasn't been fully resolved.

As Akshay said above finance is concerned with risk. The effective removal of default risk translates to lower borrowing costs. If I own a bond and want to access its value, I could sell it to a dealer and later repurchase it in separate unrelated transactions, but the costs involve would be substantial. There are good reasons why it's a bad idea to have high turnover in a portfolio.

A short term repo of the same collateral (assuming the collateral has no unprotected market risk) is vastly cheaper. This allows financial institutions to take advantage of more opportunities and thus make more money. There's an increase in effective velocity.

Another example of collateral use is short sale covering. Using a reverse repo to borrow the security and then selling it, allows you to control the timing of coverage. This is particularly useful if you've shorted securities against holdings that you are temporarily unable to liquidate.

Another common use of repos is a dealer running a balanced book - trying to simultaneously buy and sell making a small profit without the market risk and capital opportunity cost of holding inventory.

Yet another example is the dealings between US money market funds and European banks, which have been huge.

Note that there is an important distinction to be made here between safe (low information) collateral and safe assets. With most reasonable collateral, market risk can be handled by over-collateralization (though at some point the transaction becomes unprofitable to the borrower), but the cost of diligence raises the cost of the loan and the time it takes to negotiate. Compare this with real estate, which is a model of high information collateral.

This lunch isn't entirely free. The lender can call for additional collateral, which subjects the borrower to a form of market risk. Short term repos with stably priced collateral reduce this risk, but if a form of collateral becomes repudiated (like subprime mortgage securities), collateral calls can produce illiquidity. Collateral calls took down Lehman and AIG.

It is, both in principal and practice, possible to have safe high information collateral. Unsafe low information collateral isn't very practical. You could have, theoretically, safely exchanged US dollars for Zimbabwe dollars, for a short time with a haircut and specialized knowledge. Black market currency dealers profitably managed to handle this sort of risk. You could could consider this an example of collateral with information that was low in that particular context.

3) "Do the finance people who make that argument understand that currency (plus other liabilities of the Fed like reserves) is the medium of account? If QE causes the supply of Fed liabilities to be too big, and the supply of T-bills to be too small, that would presumably make Fed liabilities worth less and T-bills worth more. But since Fed liabilities are the medium of account, if the medium of account is worth less, that is inflationary."

There's no such thing as "inflation", only relative prices. The question is which assets/goods would have how much long-term arbitrage with which others. Asset prices or groups of commodity prices can have large movements with relatively modest effects on deflators. Also, if the price of T-Bills goes up, interest rates on them go down. The inflationary consequences of this have been rather modest, at least so far.

[Nick Rowe]

Peter N: Your answer to my first question is the same as my second question.

You duck my second question. Suppose there were one of those tax law quirk reasons why someone wanted to borrow rather than just spend the currency they owned. Would currency work as well as bonds as colateral?

Your answer to my third question "There's no such thing as "inflation", only relative prices." makes no sense to me. Inflation means that the price of money is falling relative to other goods.

[Odie]

Could be the problem with the "different languages" that macro does most of the time not look at distributions? Take $1 million and 20 guys who want to buy a cars. Macro says the average price will be $50,000 per car. Now have 1 guy with the $1 million and 19 guys with $0. One car will actually be sold (maybe 2 or 3) but not 20. To look at financial instruments like bonds: Let's say you can buy bonds from Texas and NY. Same size, maturity, interest rate. Economists say it does not make a difference whether you buy 2 Texas bonds, 2 NY bonds or one each. Finance says to mitigate risk you should buy one each. It's like taking water samples out of a lake. There is a big difference whether you take 10 samples at the same spot or 1 sample at 10 different spots. The latter case is more likely to get a true average.

To the initial question: I think it never hurts for ANY profession to look beyond their little bubble. I am wondering though if macro has truly figured out all those things finance guys are supposed to know. It sounds like there is still quite a disagreement in the scientific community. Taken the Gesell paper as an example: Has that been widely accepted by now or is that still debated? Are there alternative theories? If yes, so what do you teach then?

[Akshay]

Nick: I think you're right in saying that we speak different language. What I talk about in finance is almost always related to transaction prices (or a two-agent partial equilibrium) - what you consider as a price is probably the equilibrium price - but I'm not quite sure what that equilibrium is or how that is reached. I can equally validly say that you're wrong - because that's simply not how transactions in the market play out (and if you're empirically wrong and "economically" right, you're wrong, in my book).

Now, you term the two contracts I proposed to you in the desert/car/gas example as being separate contracts because they have different utility propositions- whereas, to me - in nominal (or even legal) terms - they're the same contract. The reason they have a different utility is because of your risk preferences. The market recognizes that fact and hence quotes you a different price - there *is NO transaction cost* involved here at all - the difference in price arises purely due to the risk (ie the uncertainty about the gas station being open or not).

I will qualify that example even further: say I tell you there is 90% chance the gas station will be open. How much of a price difference between the two propositions from the angel will you tolerate?

What will be the magnitude of that difference if I told you the chance is 0%, 30%. Does your answer vary? Is your price now risk-dependent or not?

[Akshay]

And I'll definitely give you this - finance has zero predictive power - economics does have it. But finance play a huge role via redistribution of risk to make sure resource allocations do take place in the way economics predicts they should. It helps you price stuff in incomplete markets, with non-unique market prices of risk. Very few economists realize that interest rates are not traded in the market - they can't be traded, it's an incomplete market by definition.

Derivatives on rates, however, are traded - and their value depends not only on the shape of the rate-curve but the volatility (first, second, whatever order) of its components as well.

What the Fed does is provide some level of market-completion and reducing uncertainty about pricing by telling you what it's going to do - whether it's by signalling the projected size of its balance sheet or via the projected fed-funds rates in the future is immaterial. Both are risk-reduction and market-completion measures.

[J.V. Dubois]

Ashkay: "Now, you term the two contracts I proposed to you in the desert/car/gas example as being separate contracts because they have different utility propositions- whereas, to me - in nominal (or even legal) terms - they're the same contract. The reason they have a different utility is because of your risk preferences."

This does not sound right to me. First, according to Arrow-Debrou the same goods delivered at different place/time are actually different goods. And finance is supposedly based on this model.

Additionally what you describe as a "risk" seems more like transportation costs to me. If there was competitive market where people stranded in desert could purchase transportation of gas by angels the end price should be just price of gas + price of transportation regardless of the "risk" to which buyer is exposed to if he does not get his gas.

[Min]

Nick Rowe: "And then Min joins in too, and says things that are wrong (Min: an A-D contract to deliver gas to me 200kms away is not the same good as an A-D contract to deliver gas to me here and now, in a world of positive transportation costs, and even more so if I don't know whether the first contract will actually be delivered.)"

That was Akshay, pas moi. :)

[Min]

OK. I can tighten up scenario 2) some more, using expected value, and considering only risk aversion.

To recap, people prefer to eat apples and bananas together, at a a ratio of one apple to one banana. The price of bananas and apples are perfectly negatively correlated, such that P(a) + P(b) = $2. People are also risk averse. At time T0, P(a) = P(b) = $1.

Scenario 1. At time T0 each person has n apples and n bananas. At time T1 each person eats 1 apple and 1 banana. No problem.

Scenario 2. At time T0 half the population has 2n apples each and half has 2n bananas each. At time, T1, each person eats 1 apple and 1 banana, buying an apple or banana as needed.

Suppose that at time T0, whether P(a) = $1 + d and P(a) = $1 - d, for all d in range at time T1. OC, the same would hold true for P(b). Because of risk aversion, the expected gain from getting paid $1 + d at time T1 is less than the expected loss from getting paid $1 - d at time T1. Thus, holding n apples and n bananas is better than holding 2n apples or 2n bananas. People are better off under scenario 1). IOW, the value of holding one of each fruit is greater than the value of holding two of one or two of the other. V(a+b) > V(2a) and V(a+b) > V(2b).

It does not follow, however, that P(a+b) > P(2a) or P(a+b) > P(2b). Consider scenario 3).

Scenario 3). At time T0, some people have an equal number of apples and bananas, some have an excess of apples, some have an excess of bananas, and some have none of either. Looking ahead to times, when they will eat an apple and a banana together, people can buy apples or bananas or both. Those with excess apples can buy bananas for $1, and those with excess bananas can buy apples for $1, but what about those with none? They can buy an equal number of apples and bananas, or they can buy packages of one apple and one banana. As we have seen, the package is more valuable than two apples or two bananas, but if it costs more than $2, people will prefer to buy one apple for $1 and one banana for $1, instead of buying the package. Just because something is more valuable does not mean that it costs more. :)

[Vaidas]

"Does finance need money/macrofoundations?"
One way to avoid money in finance is to focus on long term value of stocks. For example, if you are forecasting 7 year stock returns, you can make an assumption that monetary factors on average will cancel out. Google "Ben Inker U.S. Equity Market Overvalued" for a good example (pdf, five pages, worth a read).

"If it came to a fight between me and the Bank of Canada, both trying to set interest rates on Canadian dollars, I think I would lose, no matter how much wealth I owned."

Remember Soros and BoE in 1992?

"Must check in on David's post, to see if any of the finance guys answered my 3 simple questions about QE and safe assets."

Let me try (my brief answer is that fortunately the Fed was very careful to increase the supply of safe assets when it designed QE).

1. "But QE (a silly new name for Open Market Operations) means swapping currency for TBills. Is currency not a safe asset? Can currency not be used as colateral? Is it not at least as good as Tbills for those purposes?"

Currency and reserves may be less convenient as a collateral. Collateralization works technologically and legally better with treasury securities. So QE may take a convenient form of money and replace it with a less convenient one, and so it is possible that you get a negative velocity shock.
But we have to test this empirically. If QE reduces the convenience of money, the central bank should on average get losses from QE. In my view, the Fed was very careful and loud in protecting the profitability of QE program, so I am convinced the direct effect of QE is inflationary (plus there are various signalling effects).

2. "Why not just spend the currency (or claims on currency in a 100% reserve bank) instead of going to the hassle of using the Tbill as colateral for getting a loan of money to spend?"
It is not a hassle. Opening an account at the Fed is a hassle (unless you are a bank). Monitoring the credit risk of your counterparties who are allowed to hold reserves at the central bank is a hassle. Tbills are safe, available and convenient. It is good thing that the Fed has sold Tbills long ago and is holding less liquid securities instead.

3. "Do the finance people who make that argument understand that currency (plus other liabilities of the Fed like reserves) is the medium of account? If QE causes the supply of Fed liabilities to be too big, and the supply of Tbills to be too small, that would presumably make Fed liabilities worth less and Tbills worth more. But since Fed liabilities are the medium of account, if the medium of account is worth less, that is inflationary."
Yes it makes Tbills worth more more than reserves. And reserves are worth less than Tbills. So what? I have never seen inflation defined as reserves being worth less than Tbills. We get more non-financial transactions. We get less financial transactions. The second effect is stronger, and we get deflation.

[Min]

Edit: For scenario 2 I meant to say this: "Suppose that at time T0, P(a) = $1 + d and P(a) = $1 - d are equiprobable, for all d in range at time T1."

[notsneaky]

"An angel comes down and offers you two choices: (money for half a tank of gas + half a tank of gas) OR (a full tank of gas)"

But isn't this exactly the problem of liquidity? In this example, for the purposes of the agent, it's money that is not liquid (it may not be possible to convert it into something useful) while the half a tank of gas is. There's no commodity more liquid than "exactly the bundle I want most" - which is of course what ends up getting trade in the moneyless Arrow-Debreau world. For Nick it seems "zero transaction costs = perfect liquidity". Likewise, forgetting about time discounting for a second, would the question of liquidity even make sense in a risk-neutral world? The reason I want to hold a liquid asset rather than an illiquid asset is because "something might happen". Liquidity is a hedge against risk, and I only care about that if I'm risk averse. I'm not sure there is a fundamental disagreement here, just semantics

(Arrow and Debreau would see "money for half a tank of gas" and "half a tank of gas" two different goods with some elasticity of substitution between'em. If that elasticity is one - they're perfect subs - then they are essentially the same good. But that's exactly the case of risk neutrality)

[Jeff]

Akshay,

Most of what you say is tantalizingly close to coherent. Unfortunately it is also liberally sprinkled with non-sequiturs and outright nonsense (always delivered with an air of perfect authority).

Just a sampling of vaguely suggestive yet probably meaningless words from the above:

"Also, CAPM is a very well-founded *micro*-model emanating directly from Arrow-Debreu general equilibrium and Black's theory for pricing contingent claims - it's a mathematical result of FTAP"

The CAPM is a trivial little portfolio optimization over some normally distributed single period assets. I’m not saying you can’t derive the CAPM using the full artillery of A-D, but I don’t see the relevance of the FTAP *at all*. Can you explain how CAPM *follows* from the FTAP? In detail?

"I would rather phrase it as "unreplicable" risk (via other assets) - which is where the orthogonality comes from."

What do you mean? Idiosynchratic risk doesn't disappear via replication in CAPM. It fades via diversification.

"the numeraire need not be risk free (except in its own terms). In the Arrow-Debreu model, it is"

With regard to the A-D framework, what does this mean?

“any policy based on theory disregarding the institutional perspective (and hence nominal risks) of the macroeconomy and relying purely on equilibria assumptions - should come with a big "caveat emptor" sign pasted on it.”

Because finance uses *disequilibrium* models??? What do you mean by “equilibrium?”

Nick,

“Akshay… writes very clearly”

No, he doesn’t…

“and has been well-educated in finance.”

Not very, IMO.

“It's like we speak different languages.”

Don’t blame finance.

[Phil Koop]

I think dlr has got it exactly right.

[Akshay]

JV: An Arrow-Debreu security describes state-contingent claims on the same portfolio. The price derived from backward-induction using state-prices attached to each state can be different depending on whether risk-aversion is present or not. [1]

"Additionally what you describe as a "risk" seems more like transportation costs to me"

It's not. Transportation costs are the same for both portfolios. The only unhedgable risk is the uncertainty regarding whether the gas station is closed or not. In a competitive market which is informationally efficient - all supplier agents are aware of this risk-premium. No-one will lower their price for the (full-tank) portfolio. The stranded person does not have the option of not making the transaction at all.

[1] http://en.wikipedia.org/wiki/State_prices

[Min]

Nick Rowe: "If it came to a fight between me and the Bank of Canada, both trying to set interest rates on Canadian dollars, I think I would lose, no matter how much wealth I owned."

Vaidas: "Remember Soros and BoE in 1992?"

But then the BoE was trying to maintain the exchange rate of the British Pound, something over which it had no control.

[Akshay]

Jeff: Thank you for your comments.

1. CAPM derived via FTAP with some utility assumptions and AD securities: http://dybfin.wustl.edu/research/papers/arbetc7.pdf

2. "With regard to the A-D framework, what does this mean?"
That the numeraire has the same payoff in all states of the world.

3. "What do you mean by “equilibrium?”
Of the IS-LM variety or anything else which may not be consistent in explaining a yield-curve that you see today (which ideally would be arbitrage-free with respect to the prices of financial instruments in the market).

4. "Idiosyncratic risk doesn't disappear via replication in CAPM. It fades via diversification."
I don't see what we're disagreeing on here.

[Jeff]

Akshay,

"Thank you for your comments"

You're welcome.

"CAPM derived via FTAP with some utility assumptions and AD securities: ..."

No it isn't. From the paper you link to: "Many applied results can be derived from the first-order conditions of the portfolio choice problem. The first-order conditions say that marginal utility in each state is proportional to a consistent state-price density, where the constant of proportionality is determined by the budget constraint...In the case of the CAPM, the first-order conditions link nicely to the traditional measures of portfolio performance."

It's the *first order pricing conditions*, i.e. standard AD that "link nicely to traditional measures of portfolio performance". Your paper is a fun overview of basic ideas in asset pricing from a modern perspective but there is no link from the FTAP to CAPM: they are separate and independent sections of the paper both viewed in the context of the AD framework. Why *would* there be a link from FTAP to CAPM? Can you explain in words?

"That the numeraire has the same payoff in all states of the world."

The numeraire divided by the numeraire is *one* and therefore it's risk-free??? You can't be serious! The numeraire is *the* risk free numeraire if *and only if* it is the argument of the utility function. That's why we call the bank account numeraire measure (and not the copper measure!) the "risk-neutral measure." It's because we assume (in finance) that utility is a function of money (and not copper).

"Of the IS-LM variety or anything else which may not be consistent in explaining a yield-curve that you see today (which ideally would be arbitrage-free with respect to the prices of financial instruments in the market)"

But that's not a problem with "equilibrium" models, right? It's just a problem with some static "model" with insufficient degrees of freedom to fit the term structure. An NK model, on the other hand, can fit any term structure so obviously this has nothing to do with macro equilibrium (It's like using a vasicek short rate model instead of a Hull-White or other term structure consistent model). If, instead of a thousand confusing words, you had just said "IS-LM doesn't fit observed asset prices" that would have been clear (though still not very relevant).

Honestly, I feel a little bit bad picking on you, because you obviously want to contribute, but you talk so much and you don't stick to what you know. And people (like Nick) seem to be getting confused by it because they are trying to understand, and they don't have sufficient background in finance to separate the signal from the noise.

[Nick Rowe]

Phil: "I think dlr has got it exactly right."

I re-read dlr's comment a third time after you said that!

Min: my apologies. I got muddled. Your guys would swap apples and bananas before the shock hit, presumably, so each held one of each?

All: I'm still reading, but don't have much to contribute. Thanks for your comments!

[Min]

Nick Rowe: "Your guys would swap apples and bananas before the shock hit, presumably, so each held one of each?"

Yup. At time T0, when each costs $1. :)

That's in the latest scenario 3), which shows that V(A) > V(B) does not imply P(A) > P(B). ( No news, that, but I think that it is important here, because risk aversion shows that it is better to hold an apple and a banana than two of either.)

[Akshay]

Jeff:

"Why *would* there be a link from FTAP to CAPM? Can you explain in words?"

Using FTAP, you can use a normal diffusion process to derive that if the volatility of your asset returns is deterministic (like in CAPM), then under no-arbitrage the excess return of that asset (or its derivative) over the risk free rate is proportional to the volatility of returns of that asset (or its derivatives). The proportionality constant is exactly equal for all derivatives of the asset and is known as the market price of risk. The more well-known version (but not exactly the same) of this is called the Sharpe Ratio.

No utility assumptions have been used at all in this. All that's needed to arrive at the above result: (a) deterministic volatility (b) diffusion process for asset returns and (c) no-arbitrage.

The link between CAPM and FTAP for an asset such as the above is that the Sharpe ratio of asset = realized_correlation (asset return, index return) * Sharpe ratio of index.

The link arises from the fact that if you were to make your self-financed (asset+index) portfolio driftless, then *on average* you'd have to hold Beta (from CAPM) times more of the index than the asset.

"The numeraire divided by the numeraire is *one* and therefore it's risk-free??? You can't be serious! The numeraire is *the* risk free numeraire if *and only if* it is the argument of the utility function. That's why we call the bank account numeraire measure (and not the copper measure!) the "risk-neutral measure." It's because we assume (in finance) that utility is a function of money (and not copper)."

Risk-free means having same payoffs in all future states of the world. Absolutely nothing else.
Numeraire = what you measure prices in. That's it. You can measure prices in terms of coins and banknotes. You can measure prices in terms of bonds. No other meaning to my words. A numeraire may or may not be risk-free.
Also, the bank-account/money-market account is a *not* a universal risk-neutral measure as you're making it out to be. What the risk neutral measure depends on is the characteristics of the process driving the price of an asset. To price a swaption, for example, you'd use a forward par-swap as the risk-neutral measure - *not* a bank-account. The risk-neutral measure numeraire is simply the numeraire which makes the market-price of risk zero.

"An NK model, on the other hand, can fit any term structure so obviously this has nothing to do with macro equilibrium (It's like using a vasicek short rate model instead of a Hull-White or other term structure consistent model)."

Absolutely true. My point being there aren't any models in macro which do both bits consistently. And macro as a foundation for finance has relevance only if it can do both. I don't know how to build such a model but I think uncertainty ought to be a crucial part of it.

"Honestly, I feel a little bit bad picking on you"
You should feel bad not for picking on me (it's the Internet, come on!) but for being foggy about your fundamentals.

[JP Koning]

"Can currency not be used as colateral?"

Sure it can. The transactions we are referring to when we use the term "collateral" are swaps. Currency, reserves, and bank deposits are very useful as swap material. So are t-bills. Gold is also swappable. (A term deposit is not swappable.)

"Is it not at least as good as Tbills for those purposes?"

Cash almost always makes for a better medium of exchange than t-bills. For evidence, just take a look at the rate on a swap of cash for t-bills, or the repo rate, which is almost always positive. A positive rate indicates that the person who receives cash/provides t-bills must pay the person who receives t-bills/provides cash a fee to compensate them for foregoing cash's superior liquidity services, or its collateralizability. If the repo rate became negative, the receiver of cash would earn the fee, indicating that t-bills are more convenient than cash as exchange media. But even in recent years repo rates have almost always been above 0, so cash remains the most collateralizable and liquid asset.

Nick, one other thing. When you talk about people who "do finance", are you talking about finance professors, practitioners, or journalists/bloggers with a finance bent? They are not necessarily from the same tribe, nor do they speak the same language.

[Jeff]

Akshay,

"Using FTAP, you can use a normal diffusion process to derive that if the volatility of your asset returns is deterministic (like in CAPM), then under no-arbitrage the excess return of that asset (or its derivative) over the risk free rate is proportional to the volatility of returns of that asset (or its derivatives). The proportionality constant is exactly equal for all derivatives of the asset and is known as the market price of risk. The more well-known version (but not exactly the same) of this is called the Sharpe Ratio."

Apart from the fact that you are confusing the single period CAPM with a diffusion model, you are literally just stating the main results of the CAPM, and adding the words "using FTAP". No you didn't! You've got *huge* balls though. You had me reading that over about five teams looking for signs of meaning!

"The link arises from the fact that if you were to make your self-financed (asset+index) portfolio driftless, then *on average* you'd have to hold Beta (from CAPM) times more of the index than the asset."

On average? Or exactly? Or did you mean "on average driftless?" And "self-financed portfolio" is a big word for a one period model. And which part of the FTAP are you linking to? You make no reference to anything from the FTAP. I think I give up.

Akshay: "Agreed - the numeraire need not be risk free (except in its own terms). In the Arrow-Debreu model, it is - and I totally agrre it's not a representation of reality."
Me: "With regard to the A-D framework, what does this mean?"
Ashkay: "That the numeraire has the same payoff in all states of the world."
"Risk-free means having same payoffs in all future states of the world. Absolutely nothing else."

So to paraphrase: The numeraire may not be risk free, but in the Arrow-Debreu model it is (which is incorrect!), meaning that in A-D the numeraire has the same payoff always (but not apparently outside of A-D). However risk-free *always* means same payoff in all states in terms of the numeraire.

Did I get it?

"What the risk neutral measure depends on is the characteristics of the process driving the price of an asset. To price a swaption, for example, you'd use a forward par-swap as the risk-neutral measure - *not* a bank-account."

You'd use a forward par swap as a *measure*??? Or a numeraire? I can't read what you write!!! And if we do that, then I assume the swap becomes the "risk-free" asset because it has the "same payoffs in all future states of the world"? Nobody other than you, ever used those words with those meanings. The pricing measure with the swap numeraire is called the swap measure, not the risk neutral measure, just like the one with the forward bond numeraire is called the forward measure. And the risk-free asset is the bank account (assuming no inflation risk). And apart from using the correct meaning of words, the reason this stuff matters is because we are discussing the connection between finance and the real economy, and consumption (not swaps or copper!) is what you put in the utility function.

You can take this or leave it, but honestly, at the very best, your communication is really confusing. When you make up definitions as if they had no commonly accepted meaning, don't be surprised if people think you are confused.

[Peter N]

"You duck my second question. Suppose there were one of those tax law quirk reasons why someone wanted to borrow rather than just spend the currency they owned. Would currency work as well as bonds as collateral?"

Yes, such a thing is possible, but it requires rather peculiar circumstances that have rendered your money illiquid. Otherwise you couldn't increase its effective liquidity, since nothing could borrow using it as collateral would provide more liquidity services than the money you already had. In fact you'd be losing liquidity from having to take a small haircut on the loan and pay interest. You might have some kind if blocked funds like an unsettled estate (though you can argue that if it isn't liquid, it isn't really money, but some form of promissory note. Suppose the trustee institution filed for bankruptcy, and your funds got tied up in the bankruptcy estate - unlikely, but potentially ruinous).

What I'm not sure of is what point you're trying to make with the question. It doesn't have much practical relevance, since the required circumstances will almost never occur.

This is from Blackrock:

"The repurchase agreement market is one of the largest and most
actively traded sectors in the short term credit markets and an
important source of liquidity for money market funds and institutional
investors. Repurchase agreements (also commonly referred to as
Repo agreements) are short-term secured loans frequently obtained
by dealers (borrowers) to fund their securities portfolios, and by
institutional investors (lenders) such as money market funds and
securities lending firms, as sources of collateralized investment."

Money market funds in particular have (or used to have before the zero lower bound period) huge volumes of money that they needed to invest safely but reclaim immediately to cover customer withdrawals. We're talking about hundreds of billions of dollars. They didn't make much on the money, but then they didn't pay customers much either and had very low costs.

"Your answer to my third question "There's no such thing as "inflation", only relative prices." makes no sense to me. Inflation means that the price of money is falling relative to other goods."

Inflation is an synthetic economic aggregate construct. Its not directly observable. Any actual value for it depends on how you choose to measure it. When you have a situation where some prices are unusually elevated and others are low or stable, it's hard to draw conclusions about the effect something might have on inflation in the abstract, particularly through a mechanism such as you propose, where it's not clear where the effects would be felt. It depends on what people buy. If they run up the prices of financial assets, while the CPI rate stays around 1% is that inflation?

So far the massive bull market in treasuries hasn't seemed to have much effect other than pumping up other financial assets. There the results have been dramatic and a bit disturbing. Certainly it can't go too much farther before Stein's law intervenes. If and when that happens I'd expect to see the specter of deflation make an encore appearance. The fat lady hasn't sung yet.

[Peter N]

"Sure it can. The transactions we are referring to when we use the term "collateral" are swaps. Currency, reserves, and bank deposits are very useful as swap material. So are t-bills. Gold is also swappable. (A term deposit is not swappable.) "

It's a question of convention, like which direction you call a repo and which you call a reverse repo. The collateral is usually the good on the non-cash side. It's the less liquid good that is securing the loan. The side paying the interest is the one posting the collateral. The collateral is the security for the rental of the superior liquidity. Thus:

"In lending agreements, collateral is a borrower's pledge of specific property to a lender, to secure repayment of a loan"

or

"Property or other assets that a borrower offers a lender to secure a loan. If the borrower stops making the promised loan payments, the lender can seize the collateral to recoup its losses. Because collateral offers some security to the lender in case the borrower fails to pay back the loan, loans that are secured by collateral typically have lower interest rates than unsecured loans."

To call the money lent collateral is terminology abuse, the traditional punishment for this being the dreaded "death of a thousand trolls".

I'll emphasize again that it's important to distinguish between safe assets and low information collateral. Calling them both safe assets or safe collateral interchangeably will (and does) cause confusion. In the case of safe assets the goal is to shelter wealth. In the case of low information collateral, it's increased liquidity with reduced costs. A safe asset can be illiquid as long as the owner has otherwise adequate liquidity.

[Akshay]

Jeff:

1. Do yourself a favor. Read a financial economics book such as Rebonato/Bjork/Neftci/Shrieve.

2. Read them once again

3. Read them over and over for about 5 years (at least)

And then come talk to me. Because clearly you've done a one-semester course somewhere and think you know these things when clearly you don't. I can't even begin to tell how deeply unaware a person would be if they can't understand that a diffusion process can be modelled in discrete time as well continuous time - over a single-period or a multi-period setting. That the results of FTAP hold in a single-period and a multi-period setting. Who doesn't know the difference between quadratic variation and variance and is arguing with me about "exactly" or "on average"?

"I can't read what you write!!! And if we do that, then I assume the swap becomes the "risk-free" asset because it has the "same payoffs in all future states of the world"?"

How on earth did you draw this implication? I have explained things very clearly, in my opinion.

Don't start a flame war by being exceedingly rude on Nick's blog - go read a book and get some experience dealing with stuff (and get to know the terminology people use).

[Nick Rowe]

JP: "Nick, one other thing. When you talk about people who "do finance", are you talking about finance professors, practitioners, or journalists/bloggers with a finance bent? They are not necessarily from the same tribe, nor do they speak the same language."

I don't know. I can't tell them apart. All I know is that there are those "others" out there, who talk different from my tribe. So I lump them all together into the "Finance" tribe.

Thanks for the nice clear answer to my colateral question. Your answer makes sense to me.

[Jeff]

" I can't even begin to tell how deeply unaware a person would be if they can't understand that a diffusion process can be modelled in discrete time as well continuous time - over a single-period or a multi-period setting. "

Yes, increments of Brownian motion are normal. I didn't say otherwise. I just said you are turning a trivial thing into something more complicated (implying, for example, that we need to worry about a continuous trading strategy). Not that the Brownian motion idea is very complicated, but it does require a much more involved mathematical framework than the little CAPM with lots of big words that we don't need in this discussion and only serve to confuse people.

But I do apologize for my words. It was late, I thought you were deliberately obfuscating and I lost it, but no excuse. So I apologize to Nick, but mostly you are the one who are owed an apology. I'm sorry.

[Vaidas]

JP Koning, Nick,

Cash vs T-bills comparison is irrelevant. The relevant comparison is reserves vs T-bills. As T-bill rate is lower than interest on reserves, it is clear that T-bills are better collateral than reserves.

[JP Koning]

"To call the money lent collateral is terminology abuse."

Of course it's an abuse. But let's not get bogged down in terminological debate and focus on the underlying ideas. What Nick is really asking about is relative swappability (or exchangeability, liquidity, marketability, re-hypothecatability, etc). And the way to measure an asset's liquidity/swappability is by observing the rate at which it can be swapped against some other asset. Whoever foregos the most liquidity services over the term of the swap receives compensation. And given the currently positive repo rate, we can surmise that cash still yields more liquidity services than t-bills.

[Vaidas]

JP Koning,
nobody is doing banknote - T-bill swaps. Why are you ignoring the fact that reserves are paying 25bps?

[JP Koning]

Vaidas, good point. You're right that Fed reserves pay 0.25% whereas t-bills yield 0.05% or so, which would imply that on the margin t-bills are considered to be more liquid than reserves. However, Fed paper notes yield 0% whereas t-bills yield 0.05%, indicating that paper notes are still on the margin considered to be more liquid than reserves. Only if t-bill rates were to fall below 0% would they be more liquid than paper notes. (The fact that only banks can hold reserves whereas paper notes and t-bills are non-exclusive markets probably explains this discrepancy.)

[Vaidas]

JP Koning,
Sorry, but you have to compare marginal units on both sides of comparison. Marginal unit of monetary base yields 25bps which is more than T-bill rate.

[Nick Rowe]

Vaidas and JP: If the interest on reserves (US equivalent of the Canadian deposit rate) were reduced to 0%, like currency, that would presumably make a difference though?

[Vaidas]

Nick, if interest on reserves were reduced to zero, we would get negative T-bill rates in the US.

However, the Fed is preparing a overnight, fixed-rate full allotment RRP program, where the Fed would create a new class of liabilities that are almost as convenient as T-bills. If RRP is launched, T-bill rates would be very close to zero, maybe slightly negative, maybe slightly positive. Proponents of deflationary QE thesis have called the RRP "The greatest trick the Fed ever pulled", which of course it is not. It is more like reintroducing a 10000 USD banknote - interesting, but not macroeconomically important.

[Vaidas]

To sum up, the Fed is taking a sensible middle-of-the-road position in the deflationary QE debate. The Fed recognizes that its liabilities is not the most liquid thing around (it has sold T-bills long ago). It also recognizes that the range of assets it is permitted to acquire is limited, and these assets are quite liquid, and the risk exists that they will get more liquid than reserves as QE progresses. QE has not reached that point yet, but early this year they have started considering that possibility and have quite sensibly shifted to forward guidance instead. Of course, the discussion above ignores QE signalling effects, but you get these effects with forward guidance too.

[Jeff]

Vaidas, JP Koning, and Nick,

First, Vaidas is right that reserves yield more than t-bills and there is no reason why that would change if IOR was still zero. But I don't think it has anything to do with liquidity. The reason that t-bills are better collateral is that they are segregated from other assets in case of bankruptcy, whereas cash is commingled, meaning that it is considered an asset of the creditor like everything else on the creditor balance sheet. This is why banks and dealers almost always post securities as collateral for OTC derivatives trades, futures margins, etc.

The yield difference is due to credit, not liquidity.

[Vaidas Urba]

Jeff, in my first comment here in this thread, I have referred to legal and technical reasons on why T-bills are a better collateral than cash, so in a sense I agree with you. On the other hand, we can say that these features of T-bills facilitate financial transactions, and ability to facilitate transactions is liquidity.

[Jeff]

Oops! I obviously meant "debtor," not "creditor"

[Jeff]

Vaidas,

But then what word are we going to use to describe the ability to buy and sell t-bills? Besides, lots of things, like telephones and credit ratings, facilitate transactions. That doesn't make them "liquid".

[carsjam]

Late to this (just back from the tropics) - but I would point you to Penman "Accounting for Growth" for a nice bridge between P/E's and "residual earnings growth" (over and above required rates of return), along with data showing nice fit with long-term GDP growth rates. The book also considers the impact of leverage and other non-value-added activities on P/E and P/B. Penman refers to Graham and Dodd in a similar way as was done in the original post above^n

J