Question-1 

Consider a company whose stock is expected to follow the following pattern under the different economic situations: 

Return (%) Probabilities -20 0.05 -10 0.10 10 0.20 15 0.25 20 0.20 25 0.15 30 0.05

Required: 

a) Calculate the expected rate of return of the company 

b) How risky is the company's share?

 

Question-2 

Consider a portfolio with assets which follow the probability distribution for the returns on stocks X and Y below:

State Probability Return on Stock X Return on Stock Y 1 20% 5% 50% 2 30% 10% 30% 3 30% 15% 10% 3 20% 20% -10% 

Required: Assuming the wealth of the investor can be shared between stock X and stock Y in the ratio 40%:60%; i) Calculate the expected return of a portfolio 

ii) Calculate the covariance of the returns of stocks X and Y 

iii) Calculate the correlation coefficient between the stocks X and Y iv) Calculate the portfolio risk 

 

Question-3 

An investor is interested in building a portfolio consisting of 3 securities with the following variance and covariance values; 

Variance Covariance Weights = 0.4 0.3 w1= 0.2 = 0.5 0.1 w2= 0.3 = 0.6 0.2 w3= 0.5 

Required: 

Compute the standard deviation of the portfolio 

 

Question-4 

A Kenyan investor is considering investing his funds in two different risky assets; the Kenyan (NSE) equity index and an index of the Japan's equity (Nikkei) which are expected to generate returns and risks as follows: Expected return Expected risk Kenya's NSE Equity Index 14% 11% Japan's Nikkei's Equity index 18% 13% Correlation coefficient (r) -0.38 If the weights of the investments in the two securities are Wkenya is 40% and Wjapan 60%. Required: 

Calculate the expected portfolio return 

Calculate the portfolio risk 

Calculate the portfolio weights that would give the lowest risk 

What would be the expected portfolio return at the weights in (c) above.

 

Question-5 

An investor has constructed a portfolio of two assets whose facts are as follows: 

Asset-X Asset-Y Expected return 22% 17% Risk 9% 6% The correlation coefficient is given as -0.4. 

Required:

Calculate the expected return for the minimum variance portfolio and the corresponding portfolio risk.