Question

Here are the three scenarios of the state of the economy in a country A: State of Economy Probability Boom 0.2 Normal 0.6 Recession 0.2 Suppose the rates of return of the bond in three scenarios of the economy are 10% in a boom, 5% in a normal period, and -5% in a recession. The stock returns in the three scenarios are 20%, 10%, and -10%, respectively. Asset Allocation (Two-risky-assets Portfolio) Questions: 1. Compute the covariance between the two risky assets. 2. Compute the correlation coefficient and explain the correlation between these two risky assets. The Three Rules of Two-Risky-Assets Portfolio Based on the results of Question 1 and Question 2. If an investor plans to invest into a risky portfolio P which is composed of the stock and the bond, and he allocates 40% into the stock and the rest 60% into the bond. Apply Rules of Two-Risky-Assets Portfolio and compute: 3. The Expected Return of the risky portfolio P. 4. The Variance of the risky portfolio P.

Answer 1

State of economy	Probability	Rate of return of Bond	Rate of return of stock
Boom	0.2	10%	20%
Normal	0.6	5%	10%
Recession	0.2	-5%	-10%

Covariance between 2 of the risky assets= 1.167%. Calculation is given below:

Correlation coefficient is 1. Calculation is given below:

As the correlation coefficient is 1, so the bond and stock's return goes up or down by the same percentage i.e. if bond return goes up by 1%, stock's return will also go up by 1% and vice versa.

Now, Expected return of bond= 0.2*10%+0.6*5%+0.2*(-5%)=4%

Expected return of stock= 0.2*20%+0.6*10%+0.2*(-10%)=8%

Expected return of risky portfolio= 8%*0.4+4%*0.6=5.6%

Variance of the portfolio= 8%^2*0.4^2+0.6^2*4%+2*1*0.4*0.6*4%*8%=0.314%