Question

Observe the following returns over time:

Year:                     Stock A:                Market:

2014                     18%                      14%

2015                     6%                         8%

2016                     23%                      12%

Assume that the risk-free rate is 6% and the market risk premium is 5%.

a)     What are the expected rates of return on Stock A and the market?

b)     What is the standard deviation on Stock A and the market?

c)     What is the Beta for Stock X given a correlation to the market of 0.8117? Is Stock A more or less risky than the market?  

d)     What is the rate of return on a portfolio with 80% Stock A and 20% of Stock B (where Stock B has a Beta of 1.5)?

Answer 1

a. Expected Return of Stock A = (18 + 6 + 23) / 3 = 15.67%

Expected Return of Market = (14 + 8 + 12) / 3 = 11.33%

b. Standard deviation of Stock

Standard deviation of Stock = 7.13%

Standard Deviation of Market

Standard Deviation of Market = 2.49%

c. Beta of Stock X = Standard deviation of Stock * Correlation / Standard deviation of Market

Beta of Stock X = 7.13 * 0.8117 / 2.49

Beta of Stock X = 2.32

The Beta of market is always 1 and the beta of stock x is 2.32 which is very risky when compared with marrket.

d. Return of Stock B = 1.5 * 5 + 6 = 13.5 %

Rate of return on a portfolio = 13.5% * 0.2 + 15.67% * 0.8

Rate of return on a portfolio = 15.24%