Question

The chairman provides you with the following data, covering one year, concerning the portfolios of two of the fund’s equity managers (manager A and manager B). Although the portfolios consist primarily of common stocks, cash reserves are included in the calculation of both portfolio betas and performance. By way of perspective, selected data for the financial markets are included in the following table.

a. Calculate and compare the alpha of the two managers relative to each other and to the S&P 500.

b. Explain two reasons the conclusions drawn from this calculation may be misleading.

Short answer

α_A= 3.0%

α_B= 4.5%

Step-by-step solution

Calculation and comparison of alphas

Formulae:

α_P = E(r_P) – {r_f + β_P [E(r_M) – r_f ]}

α_A = .24 – [ .12 + 1.0´( .21 – .12)] = 3.0%

α_B = .30 – [ .12 + 1.5 ´ ( .21 – .12)] = 4.5%

Explanation on the possibility of misleading conclusion

Two possible reasons:

(a) When managers would try to time the market, in that case the SCL of the portfolio could be linear.

(b) The sample size of a year’s data is too small.