As HOMEWORKLIB's policy, only the first four sub-parts are answered below:
Part 1:
E(R) = prob * observed value
E(ABC) = 0.35*36% +0.4*14% +0.25*0 = 0.182
Similarly,
E(SGF) = 0.35*10% +0.4*8% +0.25*4 = 0.077
Variance = [R-E(R) ]2 * probability
V(ABC) = 0.35*(0.36-0.182)2 + 0.4*(0.14-0.182)2 +0.25*(0-0.182)2 = 0.0201
V(SGF) = 0.35*(0.10-0.077)2 + 0.4*(0.08-0.077)2 +0.25*(0.04-0.077)2 = 0.0005
Part 2:
Cov(ABC, SGF) = probability * [ ABC - E(ABC) ] * [ SGF - E(SGF) ] =
= 0.35*(0.36-0.182)(0.10-0.077) + 0.4*(0.14-0.182)(0.08-0.077) +0.25*(0-0.182)(0.04-0.077) = 0.0031
Correlation = Cov (ABC, SGF) / [Std dev (ABC) * Std dev (SGF)]
= 0.0031 / (0.02010.5*0.00050.5) = 0.9390
Please refer to excel calculation below for the values calculated till now:
Probability | ABC | SGF | ABC*prob | SGF*prob | ABC - E(ABC) | SGF - E(SGF) | [ABC - E(ABC)]^2*prob | [SGF - E(SGF)]^2*prob | (ABC - E(ABC))*(SGF - E(SGF))*prob |
0.35 | 36% | 10% | 0.126 | 0.035 | 0.1780 | 0.0230 | 0.0111 | 0.0002 | 0.0014329 |
0.4 | 14% | 8% | 0.056 | 0.032 | -0.0420 | 0.0030 | 0.0007 | 0.0000 | -0.0000504 |
0.25 | 0% | 4% | 0 | 0.01 | -0.1820 | -0.0370 | 0.0083 | 0.0003 | 0.0016835 |
0.182 | 0.077 | 0.0201 | 0.0005 | 0.0031 | |||||
E(ABC) | E(SGF) | V(ABC) | V(SGF) | Cov(ABC, SGF) |
Part 3:
Expected return = 80%*E(ABC) + 20%*E(SGF) = 0.8*0.182 + 0.2*0.077 = 0.161
Standard deviation = 0.82 * V(ABC) + 0.22 *V(SGF) + 2 *0.8*0.2*Cov(ABC,SGF) ]0.5 = 0.1177
Part 4:
Efficient frontier for 2 stocks ABC and SGF is drawn by plotting the portfolio returns versus standard deviation by taking various values of weight distribution. The weight (w) is increased for one stock from 0 to 1 in increments of 0.1. Since the total weight is 1, the weight of the other stock is (1-w)
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