Chapter 18, Problem 1PS

Summary Introduction

(A)

Case Summary:

The finance committee of an endowment fund decides to shift part of its investment in an index fund to a portfolio which is professionally managed. Upon investigation by a committee member, he proposes to choose a portfolio which has greater alpha value.

Characters in the case: A Committee member

Adequate Information: Alpha Value which is a performance ratio to help an investor evaluate risk-adjusted performance of a portfolio.

To determine if the proposed portfolio with greater alpha value should be chosen.

Explanation of Solution

Given Information:

The committee member proposes to choose an investment portfolio which has greater alpha value. Only this ratio will not help to determine the performance of the portfolio. Alpha along with Sharpe ratio is often used to rank the performance an investment portfolio.

Alpha is a ratio which reflects the performance of an investment relative to benchmark index which means that a positive alpha shows that the fund has beaten benchmark by 1% and so higher the alpha, better the fund. But alpha is just a number and expressed in percentage so alpha along with Sharpe ratio is used to determine the performance of the investment on risk-adjusted basis. Sharpe ratio helps to determine the real return on each unit of portfolio. Higher the ratio, better the return on investment and thus in turn better the investment.

Conclusion

Thus to conclude, a positive alpha alone cannot determine the performance of the investment portfolio to give the Sharpe measure higher than the benchmark.

Summary Introduction

(B)

To determine if positive alpha shows the performance of the portfolio is inferior.

Introduction: Alpha is a performance measure of an investment relative to benchmark index which means a positive alpha has beaten the benchmark index and so better the fund while Sharpe ratio along with alpha helps to determine the real performance of the portfolio.

Answer to Problem 1PS

A positive alpha can be associated with inferior performance of a portfolio if the Sharpe ratio has decreased.

Explanation of Solution

A positive alpha shows the performance of the portfolio relative to its benchmark while the Sharpe ratio shows the real return on each unit of investment. Thus it might be that the alpha is positive but Sharpe ratio has declined. This will in turn reflect inferior performance of the investment.

Conclusion

Therefore, yes it is true that a positive alpha may reflect inferior performance of the investment