January 26, 2010
My Monte Carlo simulation projected an average annual return of 8.3% per year for the S&P500 – a long-term expectation, based on the equity risk premium. The original ETF portfolio was projected to have an expected return of 9.1% per year (0.8% more than the S&P500) as well as lower risk than the S&P500, although not radically lower. The baseline projected risk level from QPP for the S&P500 is 15.1% per year vs. 13.6% for the original ETF portfolio. The modified ETF portfolio was projected to have an average annual return of 11.04% per year (1.94% more in annual return than the original ETF portfolio) while also being less risky than its predecessor.
The modified portfolio allocated 30% to bonds vs. 20% in the original, but that higher exposure is entirely in medium- and long-term bonds which are considerably more risky than short-term bonds which make up the majority of the allocation to bonds in the original portfolio. The risk reduction due to a higher allocation to bonds is partly offset by the substantial allocation to energy, a volatile asset class.
In the four years since my original analysis was published, the modified ETF portfolio has indeed out-performed the original ETF portfolio and the S&P500:
Both the original ETF portfolio and the modified ETF portfolio have soundly beaten the S&P500 in terms of increasing the average return and reducing the volatility of the portfolio relative to the S&P500. This should not be surprising. Unlike the S&P 500, both the original ETF portfolio and the modified ETF portfolio have allocations to bonds, and bonds out-performed stocks over this period.
Surprisingly, the modified portfolio generated both higher return and lower volatility than the original ETF portfolio, given that the new portfolio is very concentrated in energy and utilities and has twice the original’s allocation to REITs. Moreover, the modified portfolio has no allocation to emerging markets, which have been one of the few bright spots in terms of performance over the past four years.
For many investors, the improvement of 1.3% per year in average annual return and reduction of 1.6% per year in annualized volatility may not seem all that substantial, especially in the context of recent years’ huge market swings. When I run a basic Monte Carlo simulation for wealth accumulation over a 30-year period, however, missing out on 1.3% in return leads to a 35% reduction in wealth at the end of the period. This is generally consistent with analysis from the Department of Labor, which suggests that a 1% reduction in return per year leads to a 28% reduction in wealth accumulation over a working lifetime. The additional effect of lower volatility (which increases compounded return) reinforces the benefits of the more diversified portfolio.
Monte Carlo simulations can differ substantially between implementations, as discussed here. The adjustments to the portfolio from QPP may or may not agree with other models. A crucial element of effective Monte Carlo tools is parameters for expected risks and returns of various asset classes that are not simply equal to historical performance. It is well known that tuning portfolios with historical returns and risks invariably leads to bad outcomes, because you end up being massively overweight whatever asset class has out-performed in your historical sample.
The Intelligent Asset Allocator by Bill Bernstein provides a very nice study of this problem. QPP derives its parameters by combining recent history (three years is the standard) with long-term data on the relationship between risk and return in capital markets. An overview of the model is available here.
Reexamining the value of diversification
Let’s now circle back and examine the premise that asset allocation and diversification failed in the crash of 2007-2008. The first problem with this notion is that many investors simply do not understand the level of benefit that effective diversification is supposed to provide. In late 2005, I estimated that the original ETF portfolio (which many investors would have considered well diversified) was somewhat less risky than the S&P500, but not dramatically so. Even my tuned portfolio was hardly “low” risk. Diversification was expected to add on the order of 1-2% per year of return between the original ETF portfolio and the modified ETF portfolio, and it has done so over the past four years. In addition, the modified ETF portfolio has been somewhat less volatile than the original ETF portfolio. A key point, however, is that diversification was not expected to protect the portfolio from massive losses.
Portfolio theory suggests that effective diversification is perhaps the only ‘free lunch’ in investing. By combining asset classes effectively, you can add return and lower risk. Even over the past four years, during which the correlations between asset classes rose (thereby reducing the potential benefits), diversification has provided benefits that are remarkably close to what my Monte Carlo simulations projected four years ago.
Display article as PDF for printing.
Would you like to send this article to a friend?
Remember, if you have a question or comment, send it to .
