Question

Considering the world economic outlook for the coming year and estimates of sales and earnings, we expect the rate of return for the stocks ABC and SGF with the following probabilities: Probability 0.35 0.4 SGF 10% ABC 36% 14% 0% 8% 0.25 4% 1. For each stock, calculate the expected return and the standard deviation: 2. Calculate the covariance and the correlation coefficient between the rates of return; 3. If you invest 80% in ABC and 20 % in SGF, what are the expected return and the standard deviation of your portfolio P1;

Answer 1

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 / (0.0201^0.5*0.0005^0.5) = 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)