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Consider two scenarios, w, with probability 1/4 and we with probability 3/4
Consider two scenarios, w, with probability 1/4 and we with probability 3/4. Suppose that the return on a certain security is K (wi) = -4% in the first scenario and K1(w2) = 10% in the second scenario. If the return on another security is K2(wi) = -6% in the first scenario, find the return K (W2) in the other scenario such that the two secu- rities have the same risk.
Expert Solution
Here given,
for security K1
| Scenario | Return(X) | Probability(P) | P*X |
| W1 | -4% | 1/4 | -1% |
| W2 | 10% | 3/4 | 7.5% |
| Total | PX= | 6.5% |
for security K2
| Scenario | Return(X) | Probability(P) | P*X |
| W1 | -6% | 1/4 | -1.5% |
| W2 | say"Y" | 3/4 | 0.75Y% |
| Total | PX= | -1.5% + 0.75Y% |
Now, equating the two returns,
6.5 = -1.5 + 0.75Y
or, 6.5 + 1.5 = 0.75Y
or, 8 = 0.75Y
Therefore, Y = 10.67%
Therefore, K2(W2) = 10.67%
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