# Evaluating the Risk Portfolio

Kallman, James, Risk Management

Since 1952, financial analysts have known that each risk must be understood relative to the entire portfolio of risks. The failure to take this holistic perspective (and instead focus on silos of risk) can result in the misallocation of scarce resources including money, people and time. Worse, the failure to adopt a portfolio perspective might be considered a breach of a risk manager's fiduciary duty.

The beauty of portfolio theory, like many other valuable management tools, is that it is surprisingly simple. Essentially, it states that adding non-correlated risks together decreases the portfolio's risk. In a previous RM 101 column ("Measuring Risk," July 2007), we discussed the concepts of a risk's expected value and standard deviation. The expected value is the arithmetic mean, or average. The standard deviation is the usual difference from that mean value. A financial manager will select investments for a portfolio such that two results are likely to occur. First, the expected return on the portfolio, E([r.sub.p]), is the sum of the weighted returns of the individual investments. Second, the standard deviation (risk) of the portfolio should go down.

Take this example. Let's say we have a portfolio, P, comprised of two stocks, A and B. Assume the expected return of stock A, E([r.sub.A]), is 6% and the expected return of stock B, E([r.sub.B]), is 10%. Further assume the standard deviation of stock As return, [S.sub.A], is 4% and the standard deviation of stock B's return, [S.sub.B], is 12%. Stock B has a greater return because it is riskier (it has a larger standard deviation relative to its mean; i.e., the coefficient of variation is larger).

[FIGURE 1 OMITTED]

Now let's assume we create a portfolio comprised of 60% of Stock A and 40% of Stock B. The weights, W, are .6 for A and .4 for B. We can then determine the expected portfolio return, E(re), with the following equation:

E([r.sub.p]) = the sum of [W.sub.i] x E([r.sub.i]), where i is the individual stock. (A or B)

= [[W.sub.A] x E([r.sub.A])] + [[W.sub.B] x E([r.sub.B])]

= [.60 x 6%] + [.40 x 10%]

= 3.6%+ 4.0%

= 7.6%

The portfolio's risk (as measured by the standard deviation) actually is less than the weighted average standard deviation of 7.2%.

But because of the interaction (correlation) between the two stocks the actual portfolio standard deviation is less than the above average. Assume the correlation between A and B is .8. I will spare you the math details and just say the actual portfolio standard deviation is 0.0687, or a little less than 7%. The important conclusion is that by combining the appropriate investments into a portfolio the financial manager can eliminate much of the portfolio's firm specific risk. This is referred to as portfolio diversification. A risk manager can also apply this same powerful concept to certain risks. In fact, portfolio theory is one of the important principles driving the adoption enterprise risk management.

For example, one of the first applications was at United Grain Growers when they integrated two independent risks: a property exposure plus a commodity exposure. …

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