The Sharpe Ratio, Part III: Comparison of current portfolio allocations

The Sharpe Ratio, Part III: Comparison of current portfolio allocations

This is the final installment of our discussion of the Sharpe Ratio. Today we’ll see some representative Sharpe Ratios of portfolios allocated according to Modern Portfolio Theory (MPT) using traditional asset classes, that is, stocks and bonds (as opposed to futures or derivative instruments). We’ll also see how adding the element of market timing to classic Modern Portfolio Theory greatly increases the Sharpe Ratio by dramatically reducing overall portfolio risk.

Current Optimally Allocated Portfolios and the Sharpe Ratio
Let’s look at some current (through September 2009) classic MPT allocated portfolios and their Sharpe Ratios. The table below lists the best allocations among a set of nine diversified asset classes. Target returns shown are for the range of possible achievable returns derived from monthly data since 1928. The data reflects compounded annualized returns.

Classic MPT Allocation Table 11-10-09

This table was computed by the SMC Analyzer software available for user subscription on the StockMarketCookBook.com web site. As you can see, the Sharpe Ratios are highest for the lower risk portfolios  predominantly made up of Treasury Bills.  This is rather misleading because as T-Bills have historically averaged those returns, they’re not producing close to the same today. This is one reason to be cautious when evaluating the Sharpe Ratio as the contributing investment return term is backward looking, i.e. what the investment has produced in the past, while the riskless investment return is forward looking, i.e. what U.S. Treasury Bills will pay over the next few months. With this caveat in mind, one can still fairly compare the Sharpe Ratios in the above table since they are all calculated in the same way and over the same time frame.

Note that higher portfolio returns come at the cost of much higher risk (as defined by the standard deviation). By definition, an increase in risk lowers the value of the Sharpe Ratio revealing the declining compensation received for assuming the risks entailed with higher targeted returns.

Market timing improves Sharpe ratio values
Let’s now look at the table for MPT allocated portfolios using the conservative Long/T-Bills strategy enhancement to MPT. In this strategy, the percentage allocated to a particular asset class (equity asset classes only) is normally held Long when that asset class is in a bullish trend. When the trend reverses, the percentage of the portfolio allocated to that particular asset class is transferred into the safety of T-bills. (Trend reversals are determined by an oscillator that is optimized according to a robust and proprietary optimization method.)

The following table was produced using the SMC Analyzer software. In the table, Long/Long is equivalent to the classic MPT approach and is always applied to the bond asset classes.

SMC Allocation Table 11-10-09

The remarkable thing to notice is that it is possible to achieve a long-term rate of return of 10% with a Sharpe Ratio greater than 1.0. Compare that with the meager 0.44 Sharpe Ratio obtained with the classic MPT strategy!

Summary
The Sharpe Ratio can be a useful tool for financial decision making when properly understood and properly applied. As mentioned in Part I, the Sharpe Ratio is not a particularly reliable measure of non-traditional hedge fund comparison because of the non-Gaussian nature of the underlying instruments. What the investor has hopefully learned here is that when properly understood and applied, the Sharpe Ratio can be a legitimate tool for fund comparison but it shouldn’t be the only tool.

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