Question

You just received your annual performance statement from your investment advisor. The statement indicates that your portfolio return for the past year was up 12%. In addition, you noticed, within the statement, that the S&P 500 rose 10.5%. Also, the statement reflected that your portfolio had a beta 1.25. Further on, you noticed that the risk-free rate of return was 1.5%. To your dismay, the statement did not provide what the risk-adjusted rate of return was for the year. Therefore, you called your investment advisor for a clarification. The investment advisor provides you with the risk-adjusted rate of return. Are you happy with the risk-adjusted portfolio performance? Explain fully. What is the portfolio’s Risk-Adjusted Rate of Return and Jensen's Alpha Measure?

Answer 1

1.

Risk-adjusted rate of return refers to the rate of return that is computed as per the method given by Treynor ratio. In such ratio, difference between actual return and risk free rate is divided by the beta of stock or portfolio to compute the differential return on per unit of risk.

Following is the computation of Risk adjusted rate of return for portfolio:

Treynor Ratio (Risk Adjusted Rate of Return) = (Actual Return from Portfolio-Risk Free Rate)/Beta of Portfolio

=12%-1.5%/1.25

=8.4% per unit of Beta

Following is the computation of Risk adjusted rate of return for market (S&P 500):

Treynor Ratio (Risk Adjusted Rate of Return) = (Actual Return from Market-Risk Free Rate)/Beta of Market

=10.5%-1.5%/1

=9% per unit of Beta

Thus from above it can be seen that market provides return of 9% per unit of beta whereas portfolio provided return of 8.4% per unit of beta. Therefore, it can be concluded that an investor should not remain invested in the portfolio and must invest in the market portfolio. Marker portfolio means the stocks and securities comprised in a manner as same in the market.

Hence the investor will not be happy to remain invested in such a portfolio and must switch over to market portfolio.

2.

Jensen's alpha refers to the differential return earned by the stock or portfolio over its expected return computed by the CAPM model. In other words, it measures the performance of the security in comparison to its expected return.

Expected rate of return for portfolio= Risk Free rate+Beta(Market Return-Risk Free Rate)

= 1.5%+1.25(10.5%-1.5%)

=12.75%

Thus the expected return from the portfolio of investor is 12.75% as per the CAPM model.

Following is the computation of Jensen's Alpha:

Jensen's Alpha= Actual Return-Expected Return

=12%-12.75%

=0.75%

Therefore, jensen's alpha is negative showing that portfolio has not earned even the expected return of the portfolio. In other words, the portfolio has underperformed in comparison to market as well as its own expected return.

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