Question

A hedge fund manager wishes to calculate the SML formula for his portfolio of stocks. In May the beta of the portfolio was determined to be 1.25 and gave a return of 14.5%. In August the portfolio had a beta of 1.35 and a return of 15.7%. Calculate the formula for the SML line for this portfolio. Then determine what the expected return would be for a beta value of 1.45. Finally, determine the beta value of the portfolio if the return is 10.5%.

Answer 1

We have:

Beta = 1.25

Month	Beta	Return
May	1.25	14.50%
August	1.35	15.70%

Rm – Rf = ( R2- R1)/ (B2- B1)

               = (.1570-.1450)/ (1.35-1.25)

               = 12%

Using, CAPM equation for May, we have:

Er = Rf + (Rm- rf) x beta

14.50% = Rf + 12% x 1.25

Rf = 14.50% - 15%

Rf = -0.50%

Expected return for beta 1.45

We know CAPM equation is:

Er = Rf + (Rm- rf) x beta

Plugging the values in the formula:

Er = -0.50% + 12% x 1.45

     = 16.90%

Beta for Er of 10.5%

We know CAPM equation is:

Er = Rf + (Rm- rf) x beta

Plugging the values in the formula:

10.5% = -0.50% + 12% x beta

Beta = 11%/12%

         = 0.9167