A fund’s risk appetite is such that it wants to be 90% certain that it will not lose more than 20% in any one year. Using the performance of the S&P 500 between 1970 and 2016 (see Table 27.2), determine the beta the fund should have. Assume a risk-free rate of 3% per annum

Question

A fund’s risk appetite is such that it wants to be 90% certain that it will not lose more than 20% in any one year. Using the performance of the S&P 500 between 1970 and 2016 (see Table 27.2), determine the beta the fund should have. Assume a risk-free rate of 3% per annum.

Table 27.2 Return Statistics from S&P 500 Data in Table 27.1
Standard Deviation of Annual Returns (%)	Mean Annual Return (%)
Standard Deviation of Annual Returns (%)	Mean Annual Return (%)	Period
17.11	8.75	2007 to 2016
18.5	9.38	1997 to 2016
18.86	11.74	1970 to 2016

Accepted Answer

In equation (27.1), we set [latex]R = −0.2, R_F = 0.03, R_M = 0.1174, σ_M = 0.1886[/latex], and p = 0.9. The appropriate beta is 1.49.

[latex]β =\frac {R − R_F}{ R_M − R_F + N^{−1}(1 − p)σ_M}[/latex] (27.1)

Question 27.6: A fund’s risk appetite is such that it wants to be 90% certa...

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