Question

Brandon Stark is the Investment Manager at Redwood Investment Management and is currently considering whether to make an investment in the stocks of Bravos Inc. (BRA) and Dragonstone Ltd. (DGS). During his research, he noted that the performance of the two companies will hinge greatly on how the national economy performs in the coming year. Specifically, he is studying the following possible outcomes: State of the Economy Probability of Occurrence Expected Return (%) BRA DGS Expansion 45% 15% 25% Normal 20% 10% 20% Recession 1% Brandon is considering investing a total of $4 million, with an investment of $2,500,000 in DGS stocks and the remainder in BRA stocks. He knows that the two stocks tend to earn high returns and low returns at about the same times in the business cycle and as such has assigned a correlation coefficient of 0.80. Required: (1) Define systematic and unsystematic risk. (5 marks) Define and briefly discuss the value of diversification for investors. (4 marks) (1) (iii) Calculate the expected retum and standard deviation of each stock and state which stock has the highest risk and why. (8 marks) (iv) If Brandon invests in the two stocks as planned, calculate the expected return on his portfolio as well as the standard deviation. (8 marks)

Answer 1

i)Systematic Risk is the risk which affects the entire economy and all industries and such risk cannot be diversifies. Beta of firm is representation of the systematic risk of firm. Example of Systematc risks are Interest rate, inflation,etc
Unsystematic risk is the risk which is specific to a particular company or industry. This risk can be minimised through diversification. CAPM method doesnot provide return for unsystematic risk. Examples of unystematic risks are
Strikes in a particular company, machine failure in a factory, accident in a factory etc,

ii) Diversification means adding securities with lower correlation or increasing number of securities .This reduces the unsystematic risk of the investment.
Value of diversification of stocks means reduction in the standard deviation of overall stock without affecting average returns. This means there is reduction of risk.Lower the standard deviation, lower is the risk.

iii) Probability of recession =100%-45%-20% =35%
Expected Return of BRA=45%*15%+20%*10%+35%*2% =9.45%
Standard Deviation of BRA=(45%*(15%-9.45%)^2+20%*(10%-9.45%)+35%*(2%-9.45%)^2)^0.5 =6.65%
Expected Return of DGS=45%*25%+20%*20%+35%*1% =15.60%
Standard Deviation of DGS=(45%*(25%-15.60%)^2+20%*(20%-15.60%)+35%*(1%-15.60%)^2)^0.5 =14.23%

iv) Weight of investment by Brandon in BRA =2500000/4000000=62.5%
Weight of investment by Brandon in DGS =1500000/4000000=37.5%
Expected Return in case of Expansion =62.5%*15%+37.5%*25% =18.75%
Expected Return in case of Normal =62.5%*10%+37.5%*20% =13.75%
Expected Return in case of Recession =62.5%*2%+37.5%*1% =1.625%
Expected Return of Portfolio =Probability of Expansion*Expected Return in case of Expansion +Probability of Normal*Expected Return in case of Normal+Probability of Recession*Expected Return in case of Recession
=45%*18.75%+20%*13.75%+35%*1.625% =11.76%
Standard Deviation =(45%*(18.75%-11.76%)^2+20%*(13.75%-11.76%)^2+35%*(1.625%-11.76%)^2)^0.5 =7.66%