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Compensation for Risk: ROE and Capital Seesaw!

by Stephen W. Philbrick

Several recent columns have focused on the following theme: given an opportunity to write an additional insured with above average risk, should the insurance company reflect the increased risk by allocating more capital, requiring a larger rate of return, or some combination of the two?

Mark Shapland added thoughts of his own. His words are in italics.

In the November issue, you ended with the "tentative conclusion that we should adjust for risk using a combination of higher equity and a higher required return." I have supported this conclusion for some time now and would like to add a few points in support of this option.

In my experience, the discussion of this topic often seems to focus on a question of "either/or," as if these two options should be mutually exclusive. Since required capital AND expected rate of return are BOTH related to risk, why wouldn't we relate both of them to risk? It may seem appealing to adjust only one variable instead of two, but this process would then require that (for whichever variable is being adjusted) the adjustment should account for the fact that the other variable is not being adjusted. For example, if we choose to only increase capital (for an increase in risk), then we would need to increase it further to compensate for the lack of increase in required rate of return. If there is a theoretically correct solution for both capital and expected return, then the process of balancing our capital and return requirements by overcompensation in one variable makes this issue more complex than it needs to be.

In the November issue, you pointed out that the two "either/or" approaches "will necessitate differing profit margins in the premium," which lead you to state that "we must determine which is correct."

I see now that my statement could be construed as asking how to choose one of two extremes. If I may clarify, I was attempting to head off a response such as "it doesn't matter, because either thought process leads to the same premium." My point was that the alternatives implied different premiums, thus we cannot avoid the issue.

Mr. Shapland then went on to construct an example to show what might happen if BOTH the capital requirements and the required rate-of-return were increased. He made an interesting observation that I wish I had thought of myself. Given a fixed capital requirement, if we wish to double the compensation for risk, we do not simply double the ROE value. A 15 percent return on equity value should be viewed as the sum of a risk-free component and a risk component. Thus, 15 percent may be a six percent risk-free return plus a nine percent return for risk. Doubling the risk should double the risk component, so that the resulting return with a compensation for risk is 6 percent + 2 x 9 percent = 24 percent (reemphasizing the assumption that we do not change the capital requirement.)

Mr. Shapland concludes:

The real value to this discussion is in understanding and applying adjustments for future variability to both capital and ROE.

I strongly concur that the proper response to virtually all realistic situations with an increase in risk is an adjustment to BOTH the capital and the required ROE. What is not clear to me, is how much of an adjustment to each element is appropriate.

I have been doing some thinking in this area, and have reached some tentative conclusions that I hope to clarify soon.

I believe that an increase in riskiness affects the insured and the investor in different ways. Suppose we postulate an aggregate loss distribution, then modify it in different ways. For example, we might add a single catastrophic spike to the extreme tail, or we might add losses to the "middle" of the distribution. I suspect that, in order to return to equilibrium, the relative increases in required capital versus ROE will differ. Increasing the losses in only those situations where the company is insolvent affects only the insured and not the investor. I hope to find that we can specify how changes to both capital and ROE "should" occur based upon the shape of the distribution (technically, the incremental change to the shape of the company's aggregate distribution).

If anyone has already solved this problem or can add insights, please let me know.