Question

A portfolio consists of Stock A and Stock B The summary statistics for these 2 stocks are as follow. Assume we place equal 90% weight in stock A. Calculate the portfolio risk? (10) b) Now replace stock B with a T–bill and calculate the portfolio risk again. A B Return (%) 12 20 Standard Deviation (%) 15.8 25.5 Covariance -120%

Answer 1

Answer : Part (a)

	Return	Standard Deviation
Stock A	12%	15.8%
Stock B	20%	25.5%

Corr_a,b = Cov._a,b/σ _{a X} σ _b

_{= -120/(15.8% X 25.5%)}

_{= -.2978}

_{Weight A = 90%}

Weight B = 100 - 90 = 10%

formula ->

σ_p = ((.9)² X ( .158)² + (.1)² X ( .255)² + 2 X (.9) X (.1) X (.158)X (.255) X (-.2978) )^1/2

σ_p = ( .81 X .024964 + .01 X .065025 - .002160 )^1/2

σ_p = ( .02022084 + .00065025 - .002160 )^1/2

σ_p = ( .01871109 )^1/2

σ_{p =} 13.68%

Answer Part (b)

If replace stock B with T bill( Risk Free)

σrisk free = 0

σa = 15.8%

Weight A = 90 %

Weight Risk Free = 10%

So, σ_p = ((.9)² X ( .158)² + (.1)² X ( 0)² + 2 X (.9) X (.1) X (.158)X (0) X (0) )^1/2

= ( .81 X .024964 + .01 X 0 - 0 )^1/2

= (.02022084)^1/2

= 14.22%