Question

Problem #5 (12 Marks) You have a portfolio with a standard deviation of 30% and an expected return of 18%. You are considering adding one of the two stocks in the table below to your portfolio. After adding the stock, you will have 20% of your money in the new stock and 80% of your money in your existing portfolio. A) Calculate the risk and return of a new portfolio with 20% invested in stock A and 80% in your original portfolio. (5 marks) B) Calculate the risk and return of a new portfolio with 20% invested in stock B and 80% in your original portfolio. (5 marks) C) Which stock should you add and why? (2 marks) Correlation with Your Portfolio Stock Expected Return Standard Deviation Returns 02 0.6 15% 25% в 15% 20% Problem #6 ( 34 Marks) As part of an investment team at a large Canadian investment company, you are analyzing the returns of two stocks: MFC and BCE. You consider five possible scenarios for the stocks' returns depending on how good the economy will be over the coming year. MFC has a 0.9 correlation with the market portfolio. BCE has a 0.5 correlation with the market portfolio. The market portfolio has a standard deviation of 10%. The risk-free rate is equal to 4%. Economy scenario ProbabilityReturn on MFcReturn on BCE Boom 0.3 30% Above average 0.2 20% Average Below average Recession 0.2 10% 10% 0.2 12% 0.1 -20% 15% a) Calculate the expected returns for each stock. (4 marks) b) Calculate the standard deviation for each stock. (8 marks) c) Calculate the correlation between the two stocks. (5 marks) d) Assume you have a portfolio with $8,000 invested in MFC and $20,000 invested in BCE. Calculate the expected return and standard deviation of returns for this portfolio. (9 marks) e) Calculate the beta of each stock. (4 marks) f) What is the beta of your portfolio in (d)? (2 marks) g) Suppose the return on Government of Canada T-Bills = 2% and the return on the market portfolio is 6%, what is your required return of your portfolio in (d)? (2 Marks)

Answer 1

A Let i will be the existing portha. on-30% Rn - 18) WAN- 80% Stock A, GA-25%. RA= 15%. Wr-20% Correlation - 0.2 Return - (Pnawn) + (RAXWA). - 189. x 0-60)+t = 0.18xo.so] + 10.1580. 20. Co. 1447 +0.03] - 0.194 WR 17.4% Rish = nown) + ( x w y)2 + 2ax W x WA x loir XA. al 10.30x0.80)+10.25x0.20) + CV 2 x 0.30x0.25% 0.20 0.20 x 0.2 No.0576 +0.0025 +0.0048 = 0.25 Cor) 25),

corr. o.b. GB -20% ; RB-15% Wt. Ba 20%. Retwin Raewrn) + (RB X WB). To 180.so]+ (0.15*0.20]. 1704% - Risha Y (0.30x0.80) ² (0.20x0.20) 27 2 x0.30XD 20x0.80 x 0 2020.6- - Vo.0576+ 0.0016+ 0.01152 -0-26 CoR) 26% option A option B Reterrn 174% 17.47. Rish 25% 26% rista have to game return so low be chovsen, ophyh A 1 рак.