Question

There are three securities in the market. The following chart shows their possible payoffs: State .15 Probability Return on of Outcome Security 1 .192 142 .092 .042 Return on Security 2 .192 .092 142 35 Return on Security 3 .042 .092 .142 .192 WN .042 a-1. What is the expected return of each security? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16)) Expected return Security 1 Security 2 Security 3 a-2. What is the standard deviation of each security? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16)) Standard deviation Security 1 Security 2 Security 3 b-1. What is the covariances between the pairs of securities? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your final answer to 6 decimal places. (e.g., 32.161616)) Covariance Security 1 & 2 Security 1 & 3 Security 2 & 3

Answer 1

A-1

Expected Return of Security1:

= 0.15*0.192+0.35*0.142+0.35*0.092+0.15*0.042

= 0.117 =11.7%

Expected Return of Security2:

=0.15*0.192+0.35*0.092+0.35*0.142+0.15*0.042

=0.117 = 11.7%

Expected Return of Security3:

=0.15*0.042+0.35*0.092+0.35*0.142+0.15*0.192

=0.117 = 11.7%

A-2

Variance = Probability(Return-ExpectedReturn)^2

standard deviation = square root of variance

Variance of Security1

= 0.15(0.192-0.117)^2+0.35(0.142-0.117)^2+0.35(0.092-0.117)^2+0.15(0.042-0.117)^2

=0.002125

SD of security1 = $\sqrt{0.002125}$ = 0.0461 =4.61%

Variance of Security2

=0.15(0.192-0.117)^2+0.35(0.092-0.117)^2+0.35(.142-0.117)^2+0.15(0.042-0.117)^2

=0.002125

SD of security2 = $\sqrt{0.002125}$ = 0.0461 =4.61%

Varaince of Security3

=0.15(0.042-0.117)^2+0.35(0.092-0.117)^2+0.35(0.142-0.117)^2+0.15(0.192-0.117)^2

=0.002125

SD of security3 = $\sqrt{0.002125}$ = 0.0461 =4.61%

B1

covariance of 2 securities = Probability(Return1-Expected Return1)(Return2- Expected Return2)+......

cov(1,2)= 0.15(0.192-0.117)(0.192-0.117)+0.35(0.142-0.117)(0.092-0.117)+0.35(0.092-0.117)(0.142-0.117)+0.15(0.42-0.117)(0.42-0.117)

=0.014178

cov(1,3)=0.15(0.192-0.117)(0.042-0.117)+0.35(0.142-0.117)(0.092-0.117)+0.35(0.092-0.117)(0.142-0.117)+0.15(0.042-0.117)(0.192-0.117)

= -0.00213

cov(2,3)= 0.15(0.192-0.117)(0.042-0.117)+0.35(0.92-0.117)(0.92-0.117)+0.35(0.142-117)(0.142-0.117)+0.15(0.42-0.117)(0.192-0.117)

= -0.79426

Answer B-2

correlation between 2 securites = covariance(1,2)/$\sigma1\sigma2$

Correlation(1,2) = 0.014178/(0.0461*0.0461) =6.6712

correlation(1,3) = -0.00213/(0.0461*0.0461) = -0.9999

correlation (2,3) = -0.79426/(0.0461*0.0461)= -373.732

Hope this helps!!