"It's very hard to make predictions, particularly about the future" -- Yogi Berra
Consider this familiar Rorschach blot. It is a diagnostic tool most often used in the psychoanalysis of financial analysts:
(The above graph covers the 1973-94 period, with annual portfolio rebalancing.) What does this hieroglyph tell us about the optimal disposition of one's equity assets between foreign and domestic securities? Not much, unfortunately. Portfolio backtesters and mean variance optimizers will still sneer at home market bias, while grayer heads will still worry about currency and sovereign risk. Purveyors of "value added" asset management will still continue to tout their unique ability to translate economic and political variables into a more profitable asset disposition. This famous risk/return plot is of only marginal use to those few who are 100% equity exposed -- most investors are considerably exposed to nonequity assets, most often bonds or cash equivalents. A more complete perspective is gained by considering the combination of various S&P/EAFE mixes with fixed income assets. In the below graph I have used DFA's 1 year fixed income corporate index to leaven the return/risk characteristics of various mixes of S&P/EAFE:
It is apparent from the above graph that during the 1973-94 period the addition of EAFE to the stock portion of one's mix produced salutary return/risk behavior up to a level of about 60/40 S&P/EAFE, above which no significant further benefit was obtained. However, extrapolating this data into one's current allocation requires extreme caution. For starters, the shape of the above plot is dominated by the higer return of the EAFE over the 1973-94 period. The 2% return advantage of the EAFE can be explained entirely by currency effects. It is doubtful that this currency advantage will persist into the indefinite future. Also, in 1973 Europe and Japan were still suffering from the lingering economic damage suffered in World War II, with living standards far below that of the US. By 1994 this differential no longer remained to be closed. Let's assume that it is January 1, 1973, and we are faced with the choice of allocating our resources between equities A and B, which have unknown outcomes, but will in retrospect turn out to be the same as the S&P and the EAFE. The cowardly investor might hedge his or her bets by allocating 50% to each:
As you can see, this strategy worked quite well, with near optimal returns. Let's tweak the data further, and reduce the return of the EAFE to yield the same return as the S&P 500:
In this case, the "coward's portfolio" actually is significantly more efficient than either asset alone. The reason for this is simple: the annual returns on the EAFE and S&P 500 do not correlate perfectly, so addition of a small amount of EAFE results in both a decrease in risk as well as an increase in return (through rebalancing). It is important to understand that rebalancing is most effective when asset returns are similar, and that standard optimization techniques do not take rebalancing into account.
Over long time horizons small company stocks have provided higher returns than large company stocks. The below graph demonstrates that in fact for the 1973-94 period a 50/50 mix of US small stocks and international small stocks (one half each Japanese and UK) mixed with 1 year corporate bonds provided the most efficient portfolio mixes, yielding returns far higher than for S&P stocks alone, or S&P/EAFE mixes.There is no guarantee, of course, that small stocks will continue to outperform large stocks; most investors would be loathe to place all of their equity exposure in small stocks. A rational coward might split their equity exposure equally between S&P, EAFE, US small, and foreign small stocks. The below graph displays the plot for the 1973-94 period for the portfolio spectrum of this "coward's equity" mixed with 1 year corporates.
Once again, our coward did not do too badly -- risk adjusted returns are only slightly less than optimal, and much better than that obtained with the worst performing equity asset at each level of risk.
Optimizing a portfolio with historical returns, SDs, and correlations will never produce optimal future allocations. Similarly, the financial analytical equivalent of all of the king's horses and all the king's men will also fail to predict optimal future allocations, no matter how powerful the hardware, elegant the software, skilled the tailors, or impressive the verbal SAT scores. The best that can be hoped for is an allocation which will perform reasonably well under a wide variety of circumstances. The coward's approach seems to do this quite well.
3 and 5 year returns and SDs, as well as return for the 7.5 year period from inception are available for both the index as well as the S&P500. (All returns are annualized, and the SD is calculated as twice the SD of quarterly returns.) As you can see, the Coward's Indexes have provided comparable returns and SDs to the S&P500, even though during this recent period the S&P considerably outperformed foreign stocks, particularly foreign small stocks.
|3 Yr. Ret.||3 Yr SD||5 Yr. Ret.||5 Yr. SD||8 Yr. Ret.|
30%1 Yr. Corp.
30%1 Yr. Corp.
60% 1 Yr. Corp.
60%1 Yr. Corp.
The Coward's Equity Index (CEI) can be nearly duplicated by using both of the leading index fund providers; the Vanguard and DFA organizatons. (Only the MSCI Latin American Index lacks an easily available corresponding index fund -- an activlely managed fund must be used for this region.) With a $3000 fund minimum, Vanguard is not a problem for most investors. DFA is another story -- their current investment minimum is $2,000,000, plus an approved financial advisor.
The CEI can be closely approximated by the small investor with the following fund allocation, which is known as the "Small Investor's Coward's Equity Index, " or "SICEI":
The equity portion of the Small Investor's CEI (SICEI) can be diluted with Vanguard's Short Term Corporate Bond Fund. The regional distribution of the SCEI is nearly identical to that of the CEI. The Acorn and Tweedy Browne funds were chosen to represent the entire foreign small cap component because of their differing characteristics. Acorn International has a high emerging market exposure, growth orientation, and is currency unhedged, while Tweedy Browne has a low emerging market exposure, value orientation, and is currency hedged.
I have plotted the 3 year returns and annualized SDs for the portfolio spectrum between 100% equity and 100% bond for both the CEI and the SICEI below:
The solid lines represent the behavior of the spectrum of mixes from 100% CEI and 100% SICEI to 100% bond. The other data points represent the 105 "asset allocation" and "global multiple asset" funds listed by Morningstar for the 3 year period.
The 5 year results are also plotted for the CEI (The SICEI does not yet have a 5 year track record.) and the 67 Morningstar "asset allocation" and "global multiple asset" funds listed for the period:
I plan to make updates of the portfolio spectra for both the CEI and the SICEI a regular feature in Efficient Frontier. Stay tuned.
William J. Bernstein
copyright (c) 1996, William J. Bernstein