Question

Suppose each stock in Andre’s portfolio has a correlation coefficient of 0.40 (rho = 0.40) with each of the other stocks. The market’s average standard deviation is approximately 20%, and the weighted average of the risk of the individual securities in the partially diversified four-stock portfolio is 39%. If 40 additional, randomly selected stocks with a correlation coefficient of 0.30 with the other stocks in the portfolio were added to the portfolio, what effect would this have on the portfolio’s standard deviation?

Answer 1

Explained below.

Explanation:

The correlation coefficient for the portfolio with each of the other stocks is 0.40.

This correlation coefficient is less than 1. This implies that the portfolio’s assets are weakly correlated with each other.

The portfolio profits from modification. Randomly selected stocks are added to the portfolio.

The correlation coefficient of these stocks with the other stocks in the portfolio is about 0.30.

Therefore adding these randomly selected stocks will decrease the portfolio’s standard deviation.

Company-specific risk in portfolio can be reduced by this diversification but systematic or market risk can’t be eliminated. Thus the risk will (σ) decrease slowly until σp reaches to the average standard deviation of returns on the market i.e. about 20 %.