(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?
Worthwhile Canadian Initiative 
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.
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.
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.
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.
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.
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?
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?
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.
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.
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. 🙂
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. 🙂
“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.
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.”
“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)
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.
I think dlr has got it exactly right.
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
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.
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.
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.
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!
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.)
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.
“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.
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.
“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.
“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.
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).
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.
” 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.
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.
“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.
JP Koning,
nobody is doing banknote – T-bill swaps. Why are you ignoring the fact that reserves are paying 25bps?
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.)
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.
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?
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.
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.
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.
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.
Oops! I obviously meant “debtor,” not “creditor”
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”.
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