Part (a)
State | Probability | Current price | Dividend | Exepcted price | Holding period return | ||
i | Pi = 1/3 | P0 | D1 | P1 | Ri = (P1 + D1 - P0)/ P0 | Pi x Ri | Pi x (Ri - 5.40%)^2 |
Boom | 0.33 | 50 | 3 | 58 | 0.22 | 7.33% | 0.00919 |
Normal | 0.33 | 50 | 1.4 | 52 | 0.068 | 2.27% | 0.00007 |
Recession | 0.33 | 50 | 0.7 | 43 | -0.126 | -4.20% | 0.01080 |
Total | 5.40% | 0.02005 |
Expected return = 5.40%
Standard deviation = (0.02005)0.5 = 0.1416 = 14.16%
Part (b)
Expected return = 0.5 x 3% + 0.5 x 5.40% = 4.20%
Standard deviation = 0.5 x 14.16% = 7.08%
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