Question

1. If the simple CAPM is valid, is the situation detailed below possible? Explain in a few short sentences

Portfolio	Expected Return	Std Dev
Risk-free	10%	0%
Market	21%	28%
A	18%	20%

Answer 1

Portfolio	Expected Return	Std Dev
Risk-free	10%	0%
Market	21%	28%
A	18%	20%

We will calculate the beta of the stock A and from beta we will calculate the correlation coefficient between stock A and the market.

CAPM Equation:

R_A = R_f + β_A*(R_M - R_f)

R_f = 10%

R_M = 21%

R_A = 18%

Putting the above values in CAPM Equation we get,

18% = 10% + β_A*(21% - 10%)

β_A = 0.727272

Now we know that,

Where, Cov(A,M) is the covariance between stock A and market which is again calculated using below formula:

Cov(A,M) = ρ*σ_A*σ_M

σ_A = 20%

σ_M = 28%

β_A = 8/11 = 0.727272(approx.)

therefore,

ρ = (0.727272*28%)/20% = 1.01818181818182

we know that the value of correlation coefficient lies between -1 and +1 and in this case the value of correlation coefficient is approximately 1.0182 which is greater than 1 and it is not possible. Hence, this situation is not possible because the correlation coefficient between stock A and the market is greater than 1.