Homework Answers
| X | Y | P | X*P | Y*P | Dx | Dy | P*Dx^2 | P*Dy^2 | P*Dx*Dy |
| 0 | 10 | 0.1 | 0 | 1 | -14.8 | 7.4 | 21.904 | 5.476 | -10.952 |
| 4 | 8 | 0.1 | 0.4 | 0.8 | -10.8 | 5.4 | 11.664 | 2.916 | -5.832 |
| 10 | 5 | 0.2 | 2 | 1 | -4.8 | 2.4 | 4.608 | 1.152 | -2.304 |
| 20 | 0 | 0.4 | 8 | 0 | 5.2 | -2.6 | 10.816 | 2.704 | -5.408 |
| 22 | -1 | 0.2 | 4.4 | -0.2 | 7.2 | -3.6 | 10.368 | 2.592 | -5.184 |
| 14.8 | 2.6 | 59.36 | 14.84 | -29.68 |
In the above table ........ X denotes returns from security - 1 and Y denotes returns from security - 2
Question - (a)
The total of X * P column will give the expected return on security - 1 = 14.80 %
The total of X * P column will give the expected return on security - 2 = 2.60 %
Question - (b)
Dx = X - 14.80. That means subtract 14.80 from each of the given returns of stock - 1
P* Dx^2 = Probability * square of Dx = P * Dx * Dx
The total of P * Dx^2 = Variance of stock - 1 = 59.36
Standard deviation = Square root of ( variance ) = Square root ( 59.36) = 7.70
Dy = Y - 2.60. That means subtract 2.60 from each of the given returns of stock - 2
P* Dy^2 = Probability * square of Dy = P * Dy * Dy
Variance of stock - 2 .......... = Total of (P * Dy^2 ) = 14.84
Standard deviation = Square root ( 14.84) = 3.85
Question - (c)
Cov(X,Y) = Total of P * Dx * Dy = - 29.68
Correlation = Cov / (σx * σy) = - 29.68 / ( 7.70 * 3.85 ) = - 1
Question - (d)
Expected return on portfolio = 1/3 * 14.8 + 2/3 * 2.60 = 6.67 %
Standard deviation of the portfolio = √ [ (W1)2 * (σx)2 + (W2)2 * (σx)2 + 2 * W1 * W2 * COV(x,y) ]
= √ [ (1/3)2 * 59.36 * (2/3)2 * 14.84 + 2 * (1/3) * (2/3) * ( - 29.68 ) ]
= √ [ 6.60 + 6.60 - 13.19 ]
= √ (0.01)
= 0.10 %
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