Question

You are trying to calculate the standard deviation of your portfolio that contains asset A, B and C. Consider the following:

Asset A: The current price of stock A is $10 per share. There is a 50% chance that at the end of the year (i.e., 1 year from today), the share price will be $11, and there is a 50% chance that at the end of the year, the share price will be $12. The probability that the stock will pay any dividend is zero.

Asset B: The standard deviation of stock B is 14%.

Asset C: The variance of asset C is zero.

The correlation between asset A and B is 0.7, while the correlation between asset B and C is zero, and the correlation between asset A and C is also zero. Your total investment in the portfolio is $400,000, out of which $200,000 has been invested in asset C. The remainder of the investment is equally distributed between asset A and B. What is the standard deviation of your portfolio?

Answer 1

Standard Deviation of Stock A:

Prob. Stock Price(X) (x-mean) p(x-mean)^2

0.5 11 -.5 .125

0.5 12 .5 .125

Mean= 11*.5+12*.5 = 11.5

Covaraince = .125+.125=.25 or 25%

Standard Deviation= 5%

Standard Devidation of Stock B= 14%

Standard Devidation of Stock C= 0%

Weights of Portfolio:- 0.25 - Stock A, 0.25 - Stock B, 0.5 - Stock C

Variance of Portfolio

Wa2*VARa+Wb2*VARb+Wc2*VARc+2*Wa*Wb*Rab*SDa*SDb+2*Wb*Wc*Rbc*SDb*SDc+2*Wa*Wc*Rac*SDa*SDc

(0.25)^2*25+ (0.25)^2*14*14+(0.5)^2*0+2*0.25*0.25*0.7*5*14+0+0

56.0625

SD of portfolio:- underroot of 56.0625= 7.49