Question

a. As the Head of Business Development of Fidelity Venture Capital, a client has presented a business plan that has the following projected returns for your consideration;

Stock A Stock B

State of the Economy Returns / Prob Returns / Prob

Excellent 32% / 0.4 40% / 0.2

Worse -5% / 0.4 8% / 0.3

Normal 21. % / 0.2 25% /  0.5

Required:

i. Calculate the expected return for each stock

ii. Calculate the total risk of the client’s business for each stock

iii. If your client plans investing equally in each stock, with a correlation coefficient of -0.8, what is the portfolio return and portfolio risk?

iv. If the beta of the client’s business is 0.9 and the risk free rate is 22%, calculate the required rate of investment if the market risk premium is 4%.

Answer 1

i. Expected Return on Each Stock

Stock A = Return * Respective Probability

Stock A = 0.32 * 0.40 - 0.05 * 0.40 + 0.21 * 0.20

Stock A = 15%

Stock B = Return * Respective Probability

Stock B = 0.40 * 0.20 + 0.08 * 0.30 + 0.25 * 0.5

Stock B = 22.90%

ii. Total Risk of Each Stock

iii. Portfolio Return = Stock A Return * 0.50 + Stock B Return * 0.50

Portfolio Return = 0.15 * 0.50 + 0.229 * 0.50

Portfolio Return = 18.95%

Portfolio Risk = Squared Root (Weight A ^2 *Risk A ^2 + Weight B^2 * Risk B ^2 + 2 * Weight A * Weight B * Risk A * Risk B * Correlation)

Portfolio Risk = Squared Root (0.50 ^2 * 0.1682 ^2 + 0.50^2 * 0.1128^2 + 2 * 0.50 * 0.50 * 0.1682 * 0.1128 * - 0.80

Portfolio Risk = Squared Root (0.27%)

Portfolio Risk = 5.16%

iv. required rate of investment = Risk Free Rate + Beta * (Market risk Premium)

required rate of investment = 0.22 + 0.9 * 0.04

Required rate of investment = 25.60%