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Source: Courtesy of Ibbotson Associates.

Source: Courtesy of Ibbotson Associates.

the period since 1985. In both periods, however, the risk of smaller stocks is substantially higher than that of large stocks. Statistics over the longer term are consistent with an equilibrium in which a higher investor risk is compensated by higher investor expected return. Statistics over the period of common observation, beginning in 1985, are inconsistent with the argument of expected reward for additional risk. Which set of inputs makes more sense as the basis for optimization? Are the differences due to poor estimation, due to the small amount of data or changes in economic conditions? How will these different sets of inputs affect the efficient frontier? Correlations for the two different periods are provided in Table 5.9—5.11. The reader is urged to calculate the two different efficient frontiers and examine the differences. Even without performing the two optimizations, however, the reader will note that the highest mean portfolio on the frontier differs, depending upon which set of inputs is used.

Correlations over Different Time Periods The entries to the right of 1.0 in Table 5.9 give the correlations calculated over the longest available period for both series. The entries to the left of 1.0 give the correlation over the period of common observation beginning in 1985.

Table 5.9 Correlation over Different Horizons

Top Triangle: All Periods

S&P 500

Small

Bonds

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