Monday, December 14, 2009

Nagging Questions About Investment Theory

At the recent IBM STG (Systems and Technologies) Group analyst briefing, I heard Helene Armitage assert that a primary cause of the failure of financial-services models to detect the problems with the mortgage-backed securities that were the proximate cause of our economic-system seize-up was “firms’ failure to examine the models’ assumptions adequately.” I think this is flat wrong.

I think that the root cause of analysis failure was the mind-set behind the models themselves. I believe that analysts and firms failed to challenge the models because of a mindset that said – and continues to say – “a security is a security is a security.” More specifically, I think that firms look at investments with the notion that all investments are fundamentally alike, and can be represented in terms of return and risk, strictly defined. But as, over the last thirty years, this notion has been steadily extended from stocks to bonds, commodities, private equity, derivatives, and mortgages, no one has exhaustively examined the ways in which, beneath the surface of alpha and beta, risk and return for these investment types differ from those of stocks.

What follows is a couple of things that have bothered me about this mindset as I look at capital market pricing theory (CAPM) and the like. This is not an argument about whether CAPM is accurate – my impression is that, accurate or not, it shares these “bothersome” assumptions with other alternative proposed theories. It simply provides a well-defined way to examine these assumptions.

The first thing that bothers me is the notion of diversification. Let’s suppose I have two equally weighted stocks with exact -1 correlation (or an index and costless shorting of that index). If I understand the theory, this is the ultimate in diversification: no matter what, I earn zero. There is no unsystematic risk; in fact (conceptually), there is no systematic risk. I never earn money; the only way I lose money is if the United States collapses.

Now suppose I invest the same amount of money in the “risk-free investment” (U.S. bond, let’s say). This contains the systematic risk I’ve eliminated; also, I always (conceptually) earn at least as much money as in index-and-short, and (practically) always earn more money than index-and-short. In other words, despite the fact that I am more fully diversified, there is no justification for me ever to do index-and-short. I have not reduced the “real” risk of losing money; in fact, after inflation, I have increased it. I have not increased my return, compared to the risk-free asset; I have reduced it. So diversification, for certain types of investments, appears to be worse than useless.

Now apply this same notion to commodities – that is, not ownership of companies producing commodities, but ownership of the commodities themselves. Economics suggests that over the long run, due to technology applied to the commodity or its substitutes, prices fall. Either the commodity is seen as a store of value (gold as money) or not. If it is a store of value, over the long run it will track inflation (like the risk-free investment). If it is not, over the long run it will do worse than inflation. So, by this logic, commodities behave much like index-and-short: in the long run, they always do as badly as, or worse than, the risk-free investment.

So why, in a recent study of the best investments to preserve an annuity after retirement, is there a recommendation to invest in commodities for “diversification”? Well, it turns out that there was a particular point at which commodities performed better than the risk-free asset or anything else, conceptually allowing 5% yearly withdrawals rather than 4%. Translation: 1% more if I assume that I have to keep my “principal” at 100% or more of its initial value. But if I know that on average I will earn 1% more from the risk-free asset than from commodities, then it really doesn’t matter if my principal (when I substitute the risk-free asset for commodities) goes down in one of those years, and stays down; I can still withdraw the same dollar amount as if commodities were in the mix – in effect, I will get a 1% additional return on lower principal, and I can start withdrawing a greater percentage of the entire investment. I realize that this is very crude math, but you get the point.

So, to summarize, my first problem with “a security is a security” is that for certain types of investments, both risk and return are almost always negative compared to the risk-free investment, and therefore diversification does not seem to work.

My second problem is with the notion that risk – defined as variance – is effectively stable over time, for a particular asset type. Take the example of mortgages. It is very easy to think that mortgage failure rates are a creature of the business cycle alone, just like company or bond default rates. In that case, mortgage-backed securities will behave just like other securities, with a large body of historical data allowing a reasonable approximation of failure rates, and well-established procedures for handling them. Because actuaries have long experience with establishing the “risks” of individual mortgages, it seems a natural assumption that the actuarial “risk of failure” of an individual mortgage translates straightforwardly into the variance-type “security is a security” risk of a mortgage-backed security.

I would suggest that a mortgage differs from the usual investment in two key ways: it is more “sticky”, and there is a power imbalance between borrower and lender. It is more “sticky” because, even when you have adjustable rates, changing the terms of the contract is a matter of changing millions of individual policies, so that the outcome is more typically complete failure rather than part payment. There is a greater imbalance in favor of the lender than in the typical investment, because the bank or other lender has economies of scale compared to the individual borrower. The result of both differences, I would argue, is that there are incentives in the system to increase the likelihood of failure over time, across multiple business cycles, and therefore past data tends to underestimate the rates and effects of failures and the increased failure-type risk of the next business-cycle downturn or excess investment.

I think of it this way: suppose, to finance a house, an individual sold a $250,000, 5% coupon, sinking-fund bond. The security would be the bond itself. If interest rates/inflation changed, the price of the bond would change. If credit risk increased, the price of the bond would decrease. The investor who bought the bond would assume this risk, and the bond issuer – the borrower – would have a market to handle increases in credit risk normal to the business cycle. Does anyone really think that this describes the way mortgages work? And if not, why would you think that devices appropriate for bonds, like stripping, matching, and hedging, would be appropriate for mortgages? But because people did, risks were underestimated in formulating derivatives, demand for securities drove demand for mortgages, and unnecessary failures with little yield to the investor drove banks and hedge funds to their knees, with horrendous spill-over effects.

To summarize: sorry, Helene, I think that the real cause of financial-firm model failure is not a failure to examine assumptions, but a failure in the mindset that produced the models: the assumption that “a security is a security.” I question the mindset that thinks diversification handles risk for every investment type, and I question the mindset that thinks that variance-type risk is stable across business cycles for every investment type. I am not the right person to suggest a better mindset. But I sure hope someone does, instead of accepting the half-solutions that seem to me to be implicit not just in Helene’s critique, but those of most commentators.

Parenthetical note: it seems to me that we are seeing two types of “extreme” risks in today’s world, and only two. There is the risk of country collapse, in which case it doesn’t matter if you invested your money in your mattress or in gold or in a risk-free investment or whatever; it’s all worthless anyway. Then there’s the bank-seize-up/Great Depression type of risk, which we have seen at least twice in the last 100 years. While the jury is still out, it appears that this doesn’t distort the relative risk/return of stocks, bonds, and the risk-free asset over periods of 15-20 years. So why, as investors and investment theorists, are we living in fear that it will?