Question

Problem 7 (10 points): Consider an economy where only the following two stocks exist. Expected Return (u) Standard Deviation (a) Stock A 10% 10% Stock B 5% 5% Based on these two stocks, Tony Cirillo constructs a portfolio with an expected return (portfolio) of 8% and a standard deviation (portfolio) of 6%. What is the correlation (PAB) between the returns of stocks A and B?

Answer 1

Firstly calculate the weight of portfolio:

Expected return of portfolio (rp) = 8%

Expected return of stock A (rA) = 10%

Expected return of stock B (rB) = 5%

Weight of stock A = wA

Weight of Stock B = (1-wA)

rp=wA*TA + (1 - WA) *18

0.08 = WA * 0.10+ (1 - WA) 0.05

0.08 – 0.05 = WA* 0.10 – WA*0.05

0.03 = UA * 0.05

0.03 WA 0,05

WA = 0.6

thus,

wp=1 – 0.6 = 0.4

Now, we can compute the correlation between A and B with variance equation.

Standard deviation of Portfolio = 6%

Variance of Portfolio = 0.06^2 = 0.0036

Standard deviation of A = 10%

Standard deviation of B = 5%

o = (WA*A)+ (WB*OB)2 + 2 *WA*WB*A*O* PAB

where,

$\sigma ^2_P=$ variance of Portfolio

$\sigma =$ Standard deviation

  Correlation between A and B

PAB

Putting the values:

0.0036 = (0.6 * 0.1)? + (0.4 * 0.05)2 + 2*0.6 *0.4 * 0.10 * 0.05* PA.B

0.0036 = 0.0036 +0.0004 + 0.0024 * ρΑ.Β

-0.0024 * PA.B = 0.0036 +0.0004 - 0.0036

-0.0024 * PA,B = 0.0004

PAB = -0.0004 0.0024

PAB = -0.16666666

PA.B = -0.1667

Hope it will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.