Question

Suppose that the Nasdaq, with beta of 1, has an expected return of 12 percent and Treasury Bills provide a risk-free return of 3 percent. a. (1 mark) Construct a portfolio from these two assets with an expected rate of return of 10 percent. b. (2 marks) Calculate the beta of the portfoliol. C. (2 marks) Construct a portfolio from these two assets with beta of 0.5, what are the weights? What is the portfolio's expected return?

Answer 1

Question a

Expected return of the portfolio=weighted average of individual return of securities

Let weight ofNASADQ be x, then weight of Treasury=1-x

so, x*12+(1-x)*3=10

or,9x=7, x=7/9

Hence the portfolio consists of securities in the following weights

weight of NASDAQ=7/9, of treasury=1-7/9=2/9

Question b

Beta of the portfolio=weighted average of individual beta of securities

And beta of treasury=0

so, 7/9*1+2/9*0=7/9=0.7777=0.78.

Question c

Beta of the portfolio=weighted average of individual beta of securities

and beta of treasury=0

So let the weight of NASDAQ be y,

so, 1*y+0*(1-y)=0.5

or, y=0.5

Hence the portfolio consists of securities in the following weights

weight of NASDAQ=weight of treasury=0.5

Expected return=0.5*12+0.5*3=7.5%