Question 4
Olive King is an equity analyst at a large investment firm. He is analyzing the stock of HEY Corp. and gathered the following information:
- Expected return of HEY: 0.067
- Expected market return: 0.095
- Standard deviation of S&P 500 returns: 0.220
- Standard deviation of HEY returns: 0.326
- T-Bills rate: 0.045
- Correlation coefficient between HEY and market returns: 0.450
Based on the capital asset pricing model, King would most likely conclude that HEY is:
A. Overvalued and the investor should short the stock.
B. Undervalued and the investor should long the stock.
C. Overvalued and the investor should long the stock.
Solution
Answer is: A
We want to know whether the stock of HEY lies above or below the security market line (SML). If it lies above, HEY is undervalued. Conversely, if it lies below the security market line, we conclude it is overvalued.
Use the CAPM: E(R) = Rf +β * (RM-RF)
We have inputs for all unknown variables except for beta. Beta is a standardized measure of systematic risk that is, the covariance of an asset with the market:
Beta = (Correlation HEY & Market * SD of HEY) / SD of Market
= (0.450 * 0.326) / 0.22 = 0.667
Hence, the expected return of HEY is:
E(R) = Rf +β * (RM-RF) = 0.045 + 0.667 * (0.095 – 0.045) = 0.078
Since the expected return of HEY is lower than the required return of 0.078, we can conclude that HEY is overvalued. Put differently, HEY plots below the SML.
The investment recommendation based solely on CAPM is to sell (i.e. short) the stock.