Asset Allocation - Part III
Comparison to Traditional Asset Allocation
Traditional portfolio selection approaches build on an observation first proven by Tobin in 1958 ["Liquidity Preference as Behavior Towards Risk", Review of Economic Studies]. Investors can select their portfolios solely on the basis of expected return and variance if either (1) the investor's Utility Function for the value of his portfolio is quadratic, or (2) portfolio returns are normally distributed.
Based on this powerful truth, the investment community has a solid theoretical basis for defining variance of return as risk, developing a score of approaches to balance expected return by calculated risk, including the Capital Asset Pricing Model, the Arbitrage Pricing Model, and a myriad of others.
Recall how I often call out for the importance of the investor being concerned with downside possibilities prior to "investing big" in a company. Consider this theoretical fact, taken from Markowitz' classical book entitled Portfolio Selection: "If an investor chooses among portfolios solely on the basis of expected return and maximum loss, insisting on a minimum loss for any given value of return, then the investor's actions could not be based on a single stage utility function." That is, such an investor is acting irrational unless he has some kind of exotic excuse.
The asset allocation theory presented in Part I, and illustrated in the case studies presented Part II, result in rational actions that obviously are diametrically opposed to anything that might be served up using any traditional techniques for portfolio selection or asset allocation. Moreover, there appears to be a focus on downside possibilities, which we know can be irrational. Since both techniques claim they derive results from the same axioms governing rational investment behavior, how can they be so different?
Confused? Let's try to straighten things out.
To begin with, the fact that the investor has theoretical justification, under broad but not totally inclusive real-world conditions, to concern himself strictly with expectation and variance of return, does not limit him to those concerns. I just happen to find it convenient, and in my mind much more relevant, to caste major investment decisions in a variant of the Gambler's Ruin problem, which focuses on probabilities. I afford the irrationality pitfall reserved for any investor obsessed with worst possible outcomes, by treating the downside probabilistically. Investors can rationally focus on the downside, but only if they put everything into proper perspective. Finally, there are no restricted assumptions required to use my approach. It works with any utility function, however, the formulas were presented only for specific forms, including the quadratic form that gets so much attention in traditional models.
Why do I prefer the Gambler's Ruin approach over a selection from a basket of expected returns with variances (and co-variances)? For the very simple reason that there is no acceptable source for accurate expected returns and variances. Garbage in with the best of theory equals garbage out by any definition.
Expectations and variances of past performance of all companies are readily available to investors, with as many significant digits of accuracy as wanted. The problem is that past results are not a guarantee of future performance - as every mutual fund prospectus is so fond of warning investors. Not only is past performance not a guarantee of future performance, it is rarely even a statistically significant predictor of future performance. (This is a practical fact and a theoretical result of efficient market theory.)
The good news is that by enforcing diversification, a persistent outcome of using traditional techniques, investors pretending to optimize their portfolio selections using these techniques will always achieve returns approximating market returns. This means advisors don't get fired, and on average most such investors do as well as they would with any other approach.
But most rich, successful investors eschew traditional approaches. I think they do this because they know with certainty how useless are computer estimates of expectations and variances of returns. Further, they realize that variances poorly describe their concerns as they set about to invest big in a company and management they have come to know well, and in which they now have much confidence. They expect ups and downs, but they also expect better-than-market performance over the long term, and they are obsessed with downside "likelihoods".
Nevertheless, all successful investors fully understand that, all things being equal, diversification is desirable. The only problem is that things are never equal.
Allen |
