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Written by Gregory Hight
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Friday, 20 February 2009 09:59 |
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Page 4 of 5
Comparing results in Figures 3 and 4, the new four-asset portfolio return practically adds no additional return or improvements in the Sharpe ratio, and beta rises. The new asset’s correlations with the other two equity assets (Figure 2) are high. Because of the higher correlation coefficients, the new DE is smaller than the three-asset DE, which means that the new four-asset portfolio delivers less diversification effect than the original three-asset portfolio. Because the new asset adds so much risk without a corresponding decline in the correlation coefficients, the four-asset portfolio standard deviation is higher than the standard deviation of the three-asset portfolio. Consequently, IDE is negative. We conclude that adding this new asset compromises DE.
Incremental Diversification Effect Illustration: Adding An Asset With Lower Correlations
If the investor decides the risk of adding IWM exceeds its benefits, the decision might be to replace IWM with an asset that co-varies less with existing portfolio assets. The Dow Jones – AIG Commodity TR Index (DJAIGTR) correlation coefficients range from +0.2526 to -0.0221. This near-zero range could yield a favorable IDE if we use it to replace IWM. Figure 5 illustrates results of replacing IWM with DJAIGTR.
In this scenario, compared to the original three-asset portfolio, the portfolio standard deviation falls, and because of the larger DE attributable to DJAIGTR’s near-zero correlations, IDE is positive. Beta drops and the Sharpe ratio increases. This portfolio is clearly superior to the three-asset portfolio and the IWM four-asset portfolio according to these measures.
The purposes of this illustration and the one before it are to show how DE and IDE can help evaluate portfolio risk in particular and, in general, how DE and IDE can be used with other portfolio statistics to make better-informed investment decisions.
These illustrations are not intended to advocate use of DJAIGTR-linked investments. In scenarios with different details, we would not necessarily realize favorable changes in returns, betas and the Sharpe ratios when we also realize an increase in DE or a positive IDE. Results for different time periods using these assets could be very different than the results obtained in the present illustrations.
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