In: Finance
Consider the following information: |
Rate of Return if State Occurs | ||||
State of Economy | Probability of State of Economy |
Stock A | Stock B | Stock C |
Boom | 0.76 | 0.23 | 0.21 | 0.31 |
Bust | 0.24 | 0.09 | 0.15 | 0.07 |
a. What is the expected return on an equally weighted portfolio of these three stocks? |
b. What is the variance of a portfolio invested 10 percent each in A and B and 80 percent in C? |
Ans a) 21.48%
Stock | Probability (i) | Stock A (ii) | Stock A Return (i)* (ii) | Stock B (iii) | Stock B Return (i)* (iii) | Stock C (iv) | Stock C Return (i)* (iv) |
Boom | 76.00% | 23.00% | 17.48% | 21.00% | 15.96% | 31.00% | 23.56% |
Bust | 24.00% | 9.00% | 2.16% | 15.00% | 3.60% | 7.00% | 1.68% |
Total | 19.64% | Total | 19.56% | Total | 25.24% | ||
Stock | Investment (i) | Return (ii) | Investment* Return (i)* (ii) | ||||
A | 33.33% | 19.64% | 6.55% | ||||
B | 33.33% | 19.56% | 6.52% | ||||
C | 33.33% | 25.24% | 8.41% | ||||
Total | 21.48% | ||||||
Ans b) 5.0899
Stock | Probability (P) | RETURN (Y) | (P * Y ) | P * (Y -Average Return of Y)^2 |
A | 10.00% | 19.64 | 1.96 | 2.00 |
B | 10.00% | 19.56 | 1.96 | 2.07 |
C | 80.00% | 25.24 | 20.19 | 1.02 |
TOTAL | 24.11 | 5.09 | ||
Expected Return = | (P * Y) | |||
24.11% | ||||
VARIANCE = | P * (Y -Average Return of Y)^2 | |||
5.0899 |