Question

You are an investment manager considering two mutual funds. The first is an equity fund and the second is a long-term corporate bond fund. It is possible to borrow or to lend limitless sums safely at 1.25%pa. The data on the risky funds are as follows:

Fund	Expected return	Expected standard deviation
Equity Fund	8%	16%
Bond Fund	3%	5%

The correlation coefficient between the fund returns is 0.10

a You form a risky portfolio P that is equally weighted between the bond fund and the equity fund. Calculate the forecast expected return and the estimated risk of your portfolio.  Show your working.

b Your client wants to invest a proportion of his total investment budget in your risky portfolio identified in part (a) to provide an expected rate of return on his complete portfolio equal to 8%.

1. What proportion should he invest in the risky portfolio and how should this be funded?

2. What is the risk of his combined portfolio?

3. Mark this portfolio onto your portfolio’s CAL.      Show your working.

Answer 1

a) The return of a portfolio is the weighted return of the two stocks

So Return of this portfolio = 0.5 * 8% +0.5 *3% = 5.50%

The standard deviation of a portfolio is given by

Where Wi is the weight of the security i,

is the standard deviation of returns of security i.

and is the correlation coefficient between returns of security i and security j

So, standard deviation of portfolio =sqrt (0.52*0.162+0.52*0.052+2*0.5*0.5*0.16*0.05*0.10)

=sqrt(0.007425)

=0.086168 =8.6168% (estimated risk)

b)

1. To invest a part in the above portfolio to expect a return of 8%, one has to lever the portfolio by borrowing at 1.25% and investing in the above portfolio

Let W be the weight of Risky portfolio and (1-W) be the weight of Riskfree asset

Then W*5.5%+ (1-W)*1.25% = 8%

=> W =6.75%/4.25% =1.5882

So, 1-W =-0.5882

So , one has to borrow an amount equal to 58.82% of own amount and invest own as well as borrowed amount in the risky portfolio to  get a return of 8%

2 . The standard deviation of the combined portfolio = 1.588 * 8.6168% (as risk of Riskfree asset is 0)

=13.6856%