Question

9. Consider the following two stocks: State Normal Boom Probability 80% 20% Return on Stock A 26% 22% Return on Stock B 12% 44% Stock A has a beta of 0.4, and Stock B's beta is 3.8. The risk-free rate is 3.2% and the return on the market portfolio is 12.4%. Which has the least systematic risk: Stock A or Stock B, or a portfolio formed with 15% of Stock A and 85% of Stock B? Please show all of your work. 10. The recent history of stock prices is shown below for Dark Happiness Inc. (DHT). DIII's stock has a correlation with the market of 0.77. The variance of the market's returns is 0.0225. Calculate the beta of DHI's stock. Year 2013 2014 2015 2016 2017 Price at 12/31 ($) 62.13 77.24 62.41 74.53 86.03

Answer 1

Ans:- 9 Expected Return on Stock A is given by (0.80 * 0.26 + 0.20 * 0.22 ) = 0.252 =25.2%

Expected Return on Stock B is given by (0.80 * 0.12 + 0.20 * 0.44) = 0.184 =18.4%.

Now calculating the Expected return on the portfolio if Stock A is considered 15% and Stock B is considered 85%. Let the expected return for this portfolio be X.

The expected return of portfolio X will be (0.15 * 0.252 + 0.85 * 0.184) = 0.1942 = 19.42%.

Now the systematic risk is measured by Beta. More is the beta value higher is the risk since we know the beta of Stock A and Stock B as it is given in the question but we need to find the beta of Portfolio X. we find it easily by the CAPM model.

  Expected return = Rf + Beta(Rm - Rf) where Rf is risk-free rate and Rm is Market return which is given 3.2% and 12.4%

19.42 = 3.2 + Beta ( 12.4 - 3.2)

Beta = (19.42 - 3.2)/(12.4 - 3.2) = 1.76 is the beta for portfolio X.

Beta of Stock A is 0.4 Beta of Stock B is 3.8 and Beta for Market Portfolio is 1.76.

The beta which has the least value has the least systematic risk or is less risky as compared to other stocks and portfolio which is Beta of Stock A i.e 0.4. Therefore Stock A has the least systematic risk.

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