Question

1. An investor holds a portfolio which is expected to yield a rate of return of 18% with a standard deviation of 2.5%. The investor is considering buying a new share (investment being 5% of the total investment in the new portfolio). The share has the following distribution of return:

RETURN	PROBABILITIES
40%	0.30
30%	0.40
-10%	0.30

The correction coefficient between the new portfolio and the new security is 0.3; calculate the portfolio return and standard deviation of the portfolio.                                       [10 marks]

Answer 1

Let us first focus on the new share. Calculating the expected return for the new share,

Calculating the standard deviation for the new share,

Hence,

Hence,

Now, the new stock consists of 5% of the total portfolio. Hence, the expected return of the new portfolio can be calculated as 18.15%: -

Calculating the standard deviation of the new portfolio,

For this purpose, we need to find the correlation between the old portfolio and the new stock. We've:

On further simplifying,

Hence, on putting in the values, eq (1):

Moreover, using the formulae mentioned above,

Hence, on solving, eq. (2):

On equating the two equations,

On solving, using quadratic formulae,

On simplifying,

The first value will make eq. 1 negative. Hence, correlation between the old portfolio and new stock is -0.117. Putting in the value,

Hence, the standard deviation of the new portfolio is 2.477%