Question

Your friend wants to invest in two securities in transportation industry: KLM and DELTA. KLM has a standard deviation of returns of 47% and DELTA has a standard deviation of 33%. These securities have a correlation of +1. Your friend cannot decide how much to invest in KLM and DELTA so that the portfolio standard deviation is minimized. Help him

Answer 1

Solution:

The standard deviation of a portfolio of two securities is given by the formula:

where = standard deviation of the portfolio

= proportion to be invetsed in KLM

= standard deviation of KLM's returns = 47% or 0.47

= proportion to be invetsed in DELTA

= standard deviation of DELTA's returns = 33% or 0.33

and = correlation coefficient between returns of KLM and DELTA = +1

Our friend wants to minimize the standard deviation of the portfolio of both securities but we need to know which of these securities he needs to maximize his investment in order to minimize the standard deviation of the portfolio.

Let's say he has $100 to invest and he invests in 1 share of KLM that costs $10 and the remaining $90 in some number of shares (depending on current market price, but doesn't matter!) of DELTA.

The weights of his investments would be 0.1 and 0.9 respectively.

Substituting in the above equation:

or 34.40%

Now let's say he has $100 to invest and he invests in 1 share of DELTA that costs $10 and the remaining $90 in some number of shares of KLM.

Substituting in the above equation:

or 45.60%

Thus the standard deviation is lowest and closest to 34.40% when he invests maximum in DELTA and minimum in KLM

We can see that when investing in a portfolio of both the securities, he can minimize his portfolio standard deviation by investing maximum amount in DELTA and a minimum amount in KLM.