Question

You have been asked by the director of finance to put together a plan to invest in other companies. Your plan will manage a mutual fund with a $20 million portfolio with a beta of 1.50. Assume that the risk-free rate is 4.50%, and the market risk premium is 5.50%. You expect to receive an additional $5 million, which you plan to invest in a number of stocks. After investing the additional funds, you want the fund’s required return to be 13%. What must the average beta of the new stocks added to the portfolio be to achieve the desired required rate of return? Attach your Excel file showing your calculations. In a Word document, explain the steps you used to arrive at your answers. What does your calculated beta mean to UPC? Should UPC be concerned about the use of betas in making investment decisions?

Answer 1

As per CAPM model: expected return = risk free rate + (beta*market risk premium)

Or, 13% = 4.5% + (beta*5.5%)

Or 8.5% = beta*5.5%

or beta = 8.5%/5.5%

= 1.545455

We know that a fund's beta is weighted average of the betas of all individual investments and thus we can compute the required beta using the following formula:

1.545455 = 0.8*1.5 + 0.2*x

(Note that 20/(20+5) = 0.8 and 5/(20+5) = 0.2)

Thus 1.545455 = 1.2+0.2x

or x = (1.545455-1.2)/0.2

= 1.727272

Excel file's image:

The steps are already explained above.

The calculated beta means that the average beta of the new stocks is much higher than the beta of the portfolio and hence UPC should be concerned as higher beta of new stocks means higher level of risks and greater level of volatility in returns.