Friday, January 10, 2014

Anther Application of Modern Portfolio Theory

Modern portfolio theory deals largely with the allocation of assets between asset classes in a portfolio. The field, grown predominantly from Markowitz's concept of the efficient frontier has been a hot topic among both investment professionals and more casual investors alike during my time in the workforce (no, that doesn't take us back to prehistoric times, just close).

Essentially, the most significant outgrowth of this concept is that there exists a continuum of allocations that maximize expected return for a given level of risk, or conversely, that minimize risk for a given expected return. All of this, of course, is based on a large set of assumptions, in this case, capital market assumptions. Oversimplifying somewhat, what Markowitz, and after him others, discovered was that you can reduce risk in a portfolio while sometime even increasing longer-term expected return.

That's pretty cool. Part of what we learned is the value of populating a portfolio with uncorrelated and inversely correlated assets. Okay, John, what does that mean?

Consider a two-holding portfolio. Suppose each holding has an expected return of 8% per year and that their returns are well correlated. In other words, when one goes up, the other is expected to go up by a similar percentage. And, when one goes down, the other is expected to go down by a similar percentage. Essentially, your diversification is not. You're not getting any additional benefit from the second holding.

Suppose instead, your tow holdings are somewhat inversely correlated. In other words, they are neither expected to perform particularly well nor particularly poorly at the same time as each other. The expected return of each holding doesn't change. But, by decreasing the overall risk of the portfolio, you are able to increase the long-term expected return of the total portfolio by decreasing volatility.

Now that we've got that straight, let's change our portfolio. Instead of looking at financial assets, let's consider the insured lives of a health insurance company. While less is known about correlations of costs among diverse populations, it seems clear to me that a homogeneous population carries with it a higher risk to the insurer than one that is not.

As an example, consider a population consisting of 100 insured lives, all of them men between the ages of 65 and 75. Without doing any research to get the correct percentage, my past reading tells me that a meaningful percentage of them are going to get prostate cancer over the next 10 years. That's a largely unavoidable occurrence, or so I read, and the claims could all come at the same time.

How would an insurer manage that risk (other than reinsuring or hedging in some other way)? Suppose they cut their population of insured age 65-75 males from 100 to 10 and added in 90 other insureds. Some of them might be of the type that represent a very low risk, say 20-30 year-old males. Some might be women in their 40s, mostly past the age that they will be in the maternity ward.

What it seems that we will find is that the more diversification that our insurer has in its portfolio, the less volatility in claims it will have over time. This is good for them.

Under the Affordable Care Act (ACA), again somewhat oversimplified, health insurers must pay out at least 85% of their premium dollars in medical claims. Suppose they develop a set of premiums whereby they expect to pay out, on average, 90% of their claims. Further suppose that the 90% average has a standard deviation of either 5% or 15%. If I am doing my math correctly, then in the case where the standard deviation is 5%, our insurer will only have to pay rebates in about 16% of all years. In the 15% standard deviation case, however, they will pay rebates in 37% of all years.

In a nutshell, here is what this means. Our hero, if you choose, the insurance company will keep its full profit in either 84% (100%-16%) of all years or in 63% of all years. Before rebates, their long-term profits will be identical, but managing their portfolio for lower risk allows them to actually keep more of their profits.

Another application of modern portfolio theory?

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