Question

1. Explain what diversification is. How is diversification different from hedging? Mathematically, by looking at the composition of portfolio variance, considering the relationship between beta and covariance, how does the effect of diversification change according to the change of the number of securities in the portfolio? Is this relationship between the reduction of portfolio variance and the increase of security numbers linear? If not, is it concave or convex? Why?

Answer 1

Diversification: It is a risk management strategy that mixes a wide variety of investments within a portfolio. It strives to smooth out unsystematic risk events in a portfolio so the positive performance of some investments neutralizes the negative performance of others. The benefits of diversification hold only if the securities in the portfolio are not perfectly correlated—that is, they respond differently (often in opposing ways) to influences that drive the markets.

How is diversification different from hedging: Diversification is a portfolio management strategy that investors use to smooth out specific risk in one investment, while hedging helps to decrease one's losses by taking an offsetting position. If an investor wants to reduce his overall risk, the investor shouldn't put all of his money into one investment. Investors can spread out their money into multiple investments to reduce risk.

Relationship between reduction in portfolio variance and increase in number of securities: This relation is not linear. It is Convex in shape. As the no. of securities increases, the probability of correlation between the securities being uncorrelated increases, which tend to reduce the portfolio variance. Portfolio with 30 securities tend to have 90% lower portfolio variance compared to single security portfolio.