Beta coefficients

EIFM Seminar 9 – week commencing Dec 7th 2021

Question 1: The FTSE100 has a return of 11% and the risk-free rate is 3%. The Beta coefficients of the two shares X and Y are 0.5 and 1.5, respectively. Calculate the expected return for both shares and draw the security market line. Assume that the risk-free rate rises to 4% but the market risk premium remains the same. Show how this affects the SML.

According to CAPM,

SML (security market line) plots the fair value of asset expected return against its risk measured by beta. Its vertical intercept represents the risk-free asset whose beta is zero. The beta of market portfolio is one.

If the risk-free rate increases to 4% and the market risk premium is unchanged, then SML would shift upwards. The expected return of market portfolio would rise by 1% to 12%. Both X and Y would have higher expected return.

Original SML

Risk-free rate ↑

Market RP constant

Question 2: Wilson is evaluating the expected performance of two common stocks, Furhman Labs Inc. and Garten Testing Inc. He has gathered the following information:

The risk-free rate is 5%.

The expected return on the market portfolio is 11.5%.

The beta of Furhman stock is 1.5.

The beta of Garten stock is 0.8.

Based on his own analysis, Wilson’s forecasts of the returns on the two stocks are 13.25% for Furhman stock and 11.25% for Garten stock. Calculate the required rate of return for Furhman Labs stock and for Garten Testing stock. Indicate whether each stock is undervalued, fairly valued, or overvalued.

E(r) = rf + β × [E(r M ) − rf ]

Furhman Labs: E(r) = .05 + 1.5 × [.115 − .05] = 14.75%

Garten Testing: E(r) = .05 + 0.8 × [.115 − .05] = 10.20%

If the forecast rate of return is less than (greater than) the required rate of return, then the security is overvalued (undervalued).

Furhman Labs: Forecast return – Required return = 13.25% − 14.75% = −1.50%

Garten Testing: Forecast return – Required return = 11.25% − 10.20% = 1.05%

Therefore, Furhman Labs is overvalued and Garten Testing is undervalued.

Question 3: Fidelity provides data on the risk and return of its funds at www.fidelity.com. Click on the “News & Research” icon. Then choose “Mutual Funds” from the drop-down menu. In he “Quick Criteria” section, choose “Fund Type” “by Class/Category”. For “Asset Class”, choose “Sector Equity”. Click “see results”. Select three funds from the resulting list and click Compare. Click “Risk” and compare the funds using the two risk measures: standard deviation and beta. If you are not holding any asset, which fund would you choose to hold along with risk-free asset? Which fund does offer the highest expected return according to the CAPM?

If you are not holding any asset now, you should invest in the fund with the highest Sharpe ratio and decide the proportion of investment in this fund and that in a risk-free asset to suit your taste for risk.

The fund with the highest beta offers the highest expected return, according to beta. However, it might not be suitable to you because it doesn’t fit your risk profile or it has too much idiosyncratic risk.

Question 4: Compute the price of a share of stock that pays a \$1 per year dividend and that you expect to be able to sell in one year from \$20, assuming you require a 15% return.

Question 5: After careful analysis, you have determined that a firm’s dividends should grow at 7%, on average, in the foreseeable future. The firm’s last dividend was \$3. Compute the current price of this stock, assuming the required return is 18%.