Question

a)         The assets of X, Y and Z have the following risk and return statistics.

                        Expected return Assets-X 16%       Standard Deviation-X 20%.

                                                     Assets-Y 20%      Standard Deviation-Y 25%.

                                                     Assets-Z 25%       Standard Deviation-Z 35%.

                        Correlation Coefficient between      X and Y   0.50

X and Z   0.75

Y and Z -1.00

            Required:

1. Determine the expected rate of return and risk of portfolio comprised on 25 percent X, 50 percent Y, and 25 percent Z.
2. Determine the expected rate of return and risk portfolio comprised equally weight age of Stock-X, Stock-Y and Stock-Z (1/3 each stock)

   b)         Mr. Ahmed established the following spread on the ABC company’s Stock.

1. Purchased Five 2-month call option with a premium of $3 and an exercise price of $ 50.
2. Purchased Five 2-month put option with a premium of $0.60 and an exercise price of $40.

The current price of ABC company’s stock is $45.

Required; Determine Ahmed’s profit or loss if ;               

1. The price of ABC Company stays at $45 after 2 months.
2. The price of ABC Company falls to $30 after 2 months.
3. The price of ABC Company rise to $55 after 2 months.

Answer 1

1).

Expected Return of a 3 stock portfolio is a weighted average of individual returns. It is calculated as (w1*r1)+(w2*r2)+(w3*r3)

Standard deviation of a 3 stock portfolio is calculated as sqrt((w1^2*sd1^2)+(w2^2*sd2^2)+(w3^2*sd3^2)+(2*w1*w2*c12*sd1*sd2)+(2*w2*w3*c23*sd2*sd3)+(2*w3*w1*c31*sd3*sd1)); where w is weight of the stock, sd is standard deviation of the stock and cxy is the correlation between stock x and stock y.

a).

For the portfolio with 25% stock x, 50% stock y and 25% stock z,

Expected return= (0.25*16%)+(0.5*20%)+(0.25*25%)= 20.25%

Standard deviation= sqrt((0.25^2*0.20^2)+(0.5^2*0.25^2)+(0.25^2*0.35^2)+(2*0.25*0.5*0.5*0.2*0.25)+(2*0.5*0.25*-1*0.25*0.35)+(2*0.25*0.25*0.75*0.35*0.2))= 12.93%.

b).

For the portfolio with 1/3 stock x, 1/3 stock y and 1/3 stock z,

Expected return= ((1/3)*16%)+((1/3)*20%)+((1/3)*25%)= 20.33%

Standard deviation= sqrt(((1/3)^2*0.20^2)+((1/3)^2*0.25^2)+((1/3)^2*0.35^2)+(2*(1/3)*(1/3)*0.5*0.2*0.25)+(2*(1/3)*(1/3)*-1*0.25*0.35)+(2*(1/3)*(1/3)*0.75*0.35*0.2))= 15.09%

2).

Given that Exercise price of call option is $50 and Excercise price of put option is $40.
Total Invested amount to buy five 2-month call options and five 2-month put options is (5*3)+(5*0.6)= $18

a). When Stock price is at $45, both options will be worthless. So, Ahmed's Loss will be $18

b). When Stock price is at $30, call option will be worthless and put option's value will be $10. So, Ahmed's Profit will be (5*10)-18= $32.

c). When Stock price is at $55, put option will be worthless and call option's value will be $5. So, Ahmed's Profit will be (5*5)-18= $7.