January 26, 2010
Why does this point seem to be lost on the vast majority of investors? Would any investor reject a strategy that is likely to net them an additional 30% in wealth accumulation over their working lifetimes? Further, it is worth noting that the incremental 1.3% per year over the last four years is relative to the original ETF portfolio, which was quite well diversified already.
When I wrote an article last year that examined whether diversification had failed in 2008, I got a nice note from William Bernstein, the author of the classic text The Intelligent Asset Allocator (among others), on the analysis. Dr. Bernstein reviewed the analysis I presented here, and he was kind enough to offer the following thoughts:
Any portfolio that is light on the S&P500 and heavier on more exotic, less orthodox investments is fine by me!
The only problem I have with these portfolios is that they use bond ETFs. In a particularly bad state of the world, when you are going to be expending a large part of your "safe" assets for living expenditures and rebalancing, their liquidity, because of the problems that the Authorized Participant (AP) process has with bonds, is poor. (Take a look, for example, at how bond ETFs performed in late 2008 on a day-to-day basis compared to their underlying indexes). Far better to buy Treasury bonds, and then use a corporate bond ETF, rebalancing in more placid times.
Did Modern Portfolio Theory fail to anticipate the 2008 fat tail?
One additional theme comes up in critiques of portfolio theory that have emerged in the wake of the crisis. Did portfolio simulation models underestimate the probability of losses on the order of what we experienced in recent years?
Certainly the models put a very low probability on losses on the scale of what we saw in 2008, but this question is ill-posed. The correct question is simply whether the models captured the possibility of the events that occurred – we have no way of assessing whether the probability assigned to such an event was correct. In the 12-month period through the end of February 2009, the modified ETF portfolio lost 29% (its worst rolling 12-month return over the four years). The Monte Carlo projections from my original article suggest that a loss at or below -24% should will occur with a probability of 0.15% in a single year (a three standard deviation event). At what probability would we say that the model was ‘correct’? If the model had suggested that there was a 2% chance of this level of loss, would it have been correct?
Furthermore, the probability assigned to any given outcome from a model is determined by both the model (whether it is Gaussian or not, for example) and the input parameters. Perhaps the ‘ideal’ model would simply have a time-varying volatility as input, and the underlying probability of returns at any point in time is, in fact, Gaussian. Market declines on the scale of what we experienced are very rare – so rare, in fact, that it is difficult to even assess a meaningful historical probability. Even if, by some chance, someone came upon the ‘perfect’ model of extreme events, it would be impossible to demonstrate that they had done so.
We can certainly create new models with ‘fat tails’ that will put higher probabilities on extreme events, but how could we have any confidence that these are better representations of reality? The best approach to dealing with the risks associated with major market dislocations is to stress-test models to ensure that the truly worst cases are survivable (see here).
I am not suggesting that the modified ETF portfolio is an optimal portfolio going forward, or even that it was optimal back in late 2005. The goal of my original analysis was to tune an existing ETF portfolio, without venturing too far afield in terms of asset classes. Furthermore, a number of factors have changed over the past four years with implications for the range of core asset allocations. When I run the two ETF portfolios through QPP as of the end of December 2009, the model expects the modified ETF portfolio to provide about 0.7% per year more return than the original. There are many portfolios that are more attractive on a going-forward basis at a range of risk levels.
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