Question

State of Economy Probability Returns for X Returns for Y GDP growth of 8% GDP growth of 4% GDP growth of 1% 0.23 0.12 0.3 0.5 0.06 0.05 0.2 0.09 -0.02

Using the information provided,

a. Calculate the correlation between rates of return of X and Y using the above information.

b. Construct a portfolio, with X and Y, which has an expected return of 7.8%. What is the portfolio’s standard deviation?

c. If your portfolio invests 65% in X and 35% in Y,

i. Calculate its return when GDP growth is 8%.

ii. Calculate its return when GDP growth is 4%.

iii. Calculate its return when GDP growth is 1%.

iv. Calculate its expected return and standard deviation.

Answer 1

Correlation between X and Y is 0.7714.Calculation given below:

A B C D Return for X Return for Y 0.23 0.12 0.06 0.05 0.09 -0.02 Correlation coefficientCORREL(A2:A4,B2:B4) CORREL(array1, array2)

A B Return for X Return for Y 0.23 0.12 0.06 0.05 0.09 0.02 Correlation coefficient 0.771454

b. Expected return of X= 0.3*0.23+0.5*0.06+0.2*0.09=11.70%

Expected return of Y=0.3*0.12+0.5*0.05+0.2*(-0.02)=5.70%

Say, we need to put x into X and (1-x)% into y to get return of 7.8%

So, x*11.70%+(1-x)*5.70%=7.8%

or, 0.117x+0.057-0.057x=0.078

or, 0.06x=0.021

or, x=35%

So, you need to invest 35% into x and (1-35%) or 65% into Y

Standard deviation of the portfolio= (0.35^2*0.117^2+0.65^2*0.057^2+2*0.7714*0.35*0.65*0.117*0.057)^(1/2)=7.34%

c)

i. When GDP growth rate is 8%, then return= 65%*0.23+35%*0.12=19.15%

ii. When GDP growth rate is 4%, then return= 65%*0.06+35%*0.05=5.65%

iii. When GDP growth rate is 4%, then return= 65%*0.09+35%*(-0.02)=5.15%

iv. Expected return of the portfolio=65%*11.7%+35%*5.7%=9.60%

Standard deviation= (0.65^2*0.117^2+0.35^2*0.057^2+2*0.7714*0.35*0.65*0.117*0.057)^(1/2)=9.23%