In: Finance
What is the variance of the returns on a portfolio comprised of $4,200 of Stock G and $5,300 of Stock H?
State of Economy |
Probability of State of Economy |
Rate of Return if State Occurs |
|||||||
Stock G |
Stock H |
||||||||
Boom |
.18 |
.18 |
.08 |
||||||
Normal |
.82 |
.14 |
.11 |
.001324
.000000
.000209
.000248
please show work
Total Portfolio P value = Value of Stock G + Value of Stock H |
=4200+5300 |
=9500 |
Weight of Stock G = Value of Stock G/Total Portfolio P Value |
= 4200/9500 |
=0.4421 |
Weight of Stock H = Value of Stock H/Total Portfolio P Value |
= 5300/9500 |
=0.5579 |
Stock G | |||||
Scenario | Probability | Return% | =rate of return% * probability | Actual return -expected return(A)% | (A)^2* probability |
Boom | 0.18 | 18 | 3.24 | 3.28 | 0.000193651 |
Normal | 0.82 | 14 | 11.48 | -0.72 | 4.25088E-05 |
Expected return %= | sum of weighted return = | 14.72 | Sum=Variance Stock G= | 0.00024 | |
Standard deviation of Stock G% | =(Variance)^(1/2) | 1.54 | |||
Stock H | |||||
Scenario | Probability | Return% | =rate of return% * probability | Actual return -expected return(A)% | (B)^2* probability |
Boom | 0.18 | 8 | 1.44 | -2.46 | 0.000108929 |
Normal | 0.82 | 11 | 9.02 | 0.54 | 2.39112E-05 |
Expected return %= | sum of weighted return = | 10.46 | Sum=Variance Stock H= | 0.00013 | |
Standard deviation of Stock H% | =(Variance)^(1/2) | 1.15 | |||
Covariance Stock G Stock H: | |||||
Scenario | Probability | Actual return% -expected return% for A(A) | Actual return% -expected return% For B(B) | (A)*(B)*probability | |
Boom | 0.18 | 3.28 | -2.46 | -0.000145238 | |
Normal | 0.82 | -0.72 | 0.54 | -3.18816E-05 | |
Covariance=sum= | -0.00017712 | ||||
Correlation A&B= | Covariance/(std devA*std devB)= | -1 | |||
Variance | =( w2A*σ2(RA) + w2B*σ2(RB) + 2*(wA)*(wB)*Cor(RA, RB)*σ(RA)*σ(RB)) | ||||
Variance | =0.4421^2*0.01537^2+0.5579^2*0.01153^2+2*0.4421*0.5579*0.01537*0.01153*-1 | ||||
Variance | 0.000000 |