a) | ||||||
Expected Return of Stock A | ||||||
State of Economy | Probability of State -[A] | Rate of Return [B] | [A] * [B] | ER-AR | (ER-AR)2 [C] | [A]*[C] |
Boom | 0.35 | 0.24 | 0.084 | 0.071 | 0.005041 | 0.001764 |
Normal | 0.5 | 0.17 | 0.085 | 0.001 | 0.000001 | 0.00 |
Bust | 0.15 | 0 | 0 | -0.169 | 0.028561 | 0.004284 |
Expected Return | 0.169 | 0.006049 | ||||
Standard Deviation | 0.078 | |||||
Expected Return of Stock B | ||||||
State of Economy | Probability of State -[A] | Rate of Return [B] | [A] * [B] | ER-AR | (ER-AR)2 [C] | [A]*[C] |
Boom | 0.35 | 0.36 | 0.126 | 0.211 | 0.044521 | 0.015582 |
Normal | 0.5 | 0.13 | 0.065 | -0.019 | 0.000361 | 0.00 |
Bust | 0.15 | -0.28 | -0.042 | -0.429 | 0.184041 | 0.027606 |
Expected Return | 0.149 | 0.043369 | ||||
Standard Deviation | 0.208 | |||||
Expected Return of Stock C | ||||||
State of Economy | Probability of State -[A] | Rate of Return [B] | [A] * [B] | ER-AR | (ER-AR)2 [C] | [A]*[C] |
Boom | 0.35 | 0.55 | 0.1925 | 0.38 | 0.1444 | 0.05054 |
Normal | 0.5 | 0.09 | 0.045 | -0.08 | 0.0064 | 0.00 |
Bust | 0.15 | -0.45 | -0.0675 | -0.62 | 0.3844 | 0.05766 |
Expected Return | 0.17 | 0.1114 | ||||
Standard Deviation | 0.334 | |||||
b) | Portfolio Expected Return | |||||
Stock | Percentage | Expected Return | Portfolio return | |||
A | 40% | 0.169 | 0.0676 | |||
B | 40% | 0.149 | 0.0596 | |||
C | 20% | 0.17 | 0.034 | |||
Portfolio Expected Return | 0.1612 | |||||
Stock | Percentage | Standard Deviation | Portfolio Standard Deviation | |||
A | 40% | 0.078 | 0.0311 | |||
B | 40% | 0.208 | 0.0833 | |||
C | 20% | 0.334 | 0.0668 | |||
Portfolio Standard Deviation | 0.1812 | |||||
c) Expected Return of Portfolio = 16.12% ( As calculated above)
Rf = 3.8%
B = 1.6
ER= Rf + B *( Market Risk Premium)
16.12% = 3.8% + (1.6*Rp)
12.32% = 1.6* Rp
Rp = 12.32%/ 1.6
= 7.7 %
Market Risk premium = 7.7 %
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