Risk-return tradeoff and the U.S. treasury

In our last post devoted to the mathematics of finance, we mentioned that the standard deviation of a bell curve showing the range of possible returns from an asset can be employed as a surrogate for its risk. I'd like to pursue that point a bit.

It is the chanciest corporations, the ones that do have significant risk, that have to bribe you into buying their bonds with a higher return than their safer brethren need offer: thus, a trade-off.

One way of looking at the trade-off is this: suppose I come into your neighborhood and offer to play a simple game. You will roll a pair of dice I provide and I will give you $1,000 times the number shown on the dice when they come to rest. I require only that you pay me $1,000 before we begin.
The lowest possible score is 2, so the lowest possible pay-out is twice what you’ll pay me up front. This, then, (if I am honest and actually have the money I’m offering to pay) is a can’t-lose proposition for you. The worst outcome is you gain $1,000. The best outcome is that you gain $11,000 [(12x1,000) - $1,000.] In this case, the variance among the outcomes doesn’t amount to risk in the intuitive sense of the word at all.

But in finance (as in life generally) such no-lose propositions are rare and fleeting. Suppose I start offering to let you and your neighbors bid on who will play the game next. Wouldn’t you, or someone else in the group, be likely to bid something higher than $1,000?  Something higher, even, than $2,000? If the winner bidder agrees to pay $2,001, then he has agreed to risk $1. It is possible, after all, that he will roll snake eyes, and collect only $2,000 back from me after paying that $2,001.

Eventually, I will be playing only with those in the neighborhood who are most tolerant of risk, and my operation, which began as so blatant a money-losing extravagance, may even start turning me a profit. The possibility of that big $12,000 return is what is drawing people to my auctions, rendering them willing to take some risk: and in such cases the variance of results is, as Markowitz noted, a convenient way to quantify that risk.

In order to give some formal elegance to the idea of a risk-return trade-off, economists often talk about the risk-free rate of return, which is called r.  Until quite recently, and throughout the period when economists were busily formulating the key notions of modern finance theory, the return on U.S. Treasury bills served as an empirically-observable proof of r. In a formula that contains that letter, simply plug in that return as r and carry on.
 

In 2011, though, the world changed. After a months-long political deadlock brought the U.S. close to default, and produced a debt-ceiling deal promising further work on fiscal issues in a way that seemed to many observers just … not credible, one of the big three credit rating companies downgraded U.S. Treasuries, from AAA to AA+.

Through simple inertia, T-bills are still often used for r, but when this is done explicitly, it is done almost apologetically. Howard Marks, co-founder of Oaktree Capital, told me soon thereafter (“speaking as a non-quant”) that there may be no riskless place in the world, but that short T-bills are still “essentially” riskless.
 

Irene Aldridge, managing partner at ABLE Alpha Trading, has said that she would lean toward the use of a basket of the bonds of the most secure U.S. municipalities as the better risk-free benchmark.  

But let’s get back to the question with which we began: what moves stock prices. The trade-off we’ve discussed worked among asset classes and within any asset class. Thus, on the one hand,  the world of stocks is (in accord with the ideas we’ve outlined thus far) both higher risk and higher return than the world of sovereign or corporate bonds. Within stocks as an asset class, there is again a wide variation as to both risk and return. 

If ECMH is valid, then one would expect that the price of a stock will reflect its risk, both its historical volatility and all publicly available information that bears on that risk. We should accordingly redefine alpha. We defined it above at a first approximation as the excess (or deficit) of an actively managed performance beyond what an investor could get from a passively managed investment. We should add here that alpha as a technical term also includes a risk premium. So it is the risk adjusted excess (or deficit) return that an investor can get in reference to a passive benchmark.  

ECMH is only valid (indeed, it is only even plausible) for highly liquid, high-volume markets. We can see this if we state the argument in its favor carefully.