Question

Consider a 12 months two-security potential investment from the following three. The correlation coefficients between pairs of the stocks are as follows: Corr(A,B) = 0.85, Corr(A,C) = 0.60, Corr(A,D) = 0.45. Each stock has an expected return of 8% and a standard deviation of 20%.

Your entire portfolio is now composed of stock A and you can add some of only one stock to your portfolio.

Required:

1. Identify the stock to be added to Stock A and determine the optimum portfolio mix.                                                                                                                       [8 Marks]

2. If the overall rate of return on the LUSE is 9%, the risk-free rate is 4%, and the beta of 1.2, is it justifiable to invest in the new portfolio?             [5 Marks]

3. Discuss the assumption of keeping the correlations between stock returns constant in modern portfolio theory.                                                        [7 Marks]

Answer 1

A)

If we observe all the given three portfolio sets (i.e. A with B, A with C and A with D), we can conclude that A has the lowest correlation with that of D.

Correlation is a statistical tool which shows to what extent two factors are related. It is within the range of 1 to -1.

In a portfolio, we should ensure that no two assets should have high level of correlation because it can lead to a high risk portfolio, because a particular type of risk will heavily affect your portfolio.

Therefore, the next asset to be paired with A should be D.

Further, a 50:50 portfolio is the most optimum portfolio with the assets A and D as both the assets carry the same return and risk.

B)

As per the Capital asset pricing model, the return of equity should be

R_e = R_f + Beta x (R_m - R_f)

Therefore,

4% + 1.2 x (9%-4%)

= 10%

The required rate of return as per CAPM model is 10% while the return from the portfolio is 8%. Hence, it is not advisable.

C)

The Modern portfolio theory basically takes into assumption that the correlation between two or more assets will stay constant over the future duration of the portfolio. However, this assumption is highly flawed. In the real world, the correlation between different assets do not remain constant. That means that Modern Portfolio Theory becomes less useful during times of uncertainty, which is exactly when investors need the most protection from volatility.