Portfolio Risk

Question 1(a)

Portfolio risk can be defined as the probability of failing to meet the financial objectives by a combination of financial assets within a group of investments. When choosing investments within a portfolio, each individual investment carries their own risk which may increase or decrease the overall risk of the portfolio. The risk of portfolio can be minimized with proper diversification. Diversification can be achieved, for example in a stock portfolio, by choosing different stocks that have minimum or no positive correlation. Securities that are less than perfectly positively correlated provide some diversification benefit to the overall portfolio.

One of the methods widely used to measure risk of an investment is by computing the variance or standard deviation of its expected returns. It is a statistical measure that measures the dispersion of return around the expected value. A high variance or standard deviation value indicates greater dispersion, hence higher risk due to greater uncertainty.

In an investment portfolio, the risk of the portfolio depends on a number of factors such as the standard deviation of each security, the covariance between securities in the portfolio, and the weights of each security in the portfolio. Instead of using the covariance value, investors usually compute a relative measure, the correlation coefficient, by using the covariance and standard deviation values. Correlation coefficient is more meaningful than using the covariance value as it is because correlation coefficient which can only vary between +1 and -1 allows investors to easily make comparisons between the values. +1 indicates the perfectly positively correlation between two securities. For example, when stock A increases by 10% stock B will also increase by 10%. Similarly, -1 indicates a perfect negative correlation between two securities. Using similar example, when stock A increases by 10%, stock B will decrease by 10%. Meanwhile, the return of the portfolio is a weighted average of the expected returns of these individual securities in the portfolio. The weight of a security is the proportion of total value for the investment.

By applying the above theories in portfolio management in the case of Hennessy, restricting him to construct a portfolio which comprised of only 20 stocks rather than 40 to 50 stocks would increase the risk of portfolio as diversification will be limited. However, the amount of risk increased may possibly be not as much as to the extent where it would become a huge concern for an investor.

To further explain this, we use an equally weighted portfolio as example and assume that the stocks in the portfolio hold the same standard deviation,, and the correlation coefficient between any two stocks, , is identical. The covariance between each pair of stocks would hence be. The variance of the portfolio can then be computed using the following equation:-[pic 1][pic 2][pic 3]