# Mean vs. Median — The Importance of Using the Mean

Recently, an asset manager asked me why the mean and median life expectancy (LE) figures in life expectancy reports seemed to have widened in recent years. The fact is we have changed nothing in our process to cause the effect this manager claimed to be observing. However, the population of insureds we underwrite is changing in that smaller policies tend to cover middle-income insureds, whose access to health care is different than the high net-worth segment of the population, and that is a likely cause of this effect. This change, however, is out of our control because it is the marketplace and whom it attracts that determines which insured lives we assess.

## Why might the difference between mean and median matter?

In the life settlement industry, it is standard market practice to use the mean (i.e., average) LE to value life settlements. Indeed, “LE” means *life* *expectancy*, which is defined in a famous actuarial text as “the average future lifetime.” If an asset manager was inclined to use median life expectancy figures to calculate values for their portfolio, they would likely overstate those values relative to other managers operating in the marketplace. Median life expectancy among a population of like-kind insureds tends to be shorter than the mean. Therefore, using median LEs to value life settlements generally increases the value of the policies involved...on paper.

The manager’s concern was that if the trend he believed he was observing continued, it could have an effect on his portfolio’s valuation and impact his business and his investors. In other words, since most life settlement asset managers use the mean life expectancy to value policies, a manager who uses the median would appear to have a more valuable portfolio than their competitors. If the median and mean converge, this advantage would diminish. Also, if mean LEs were really getting closer to median LEs for the same lives, the rate of increase in the value of the policies could slow, or in some cases, decreases in value could occur.

Most, if not all, life settlement-related mortality curves skew right, meaning the number of outcomes (i.e., deaths) among a given like-kind population tend to occur later or to the right side of the mortality curve, from the midpoint or median. Since the median is the point on the curve at which half of the population of insureds is expected to be dead, and the other half is still living, it does not provide the user with as good an indication of the curve’s “skewness” or the degree to which the data that makes up the curve “leans” to the right or long side of the mortality curve. In other words, the median does not capture those insureds who will live an extremely long time. They are on the “tail” of the probability distribution. In short, the median does not draw the maximum amount of information from the mortality curve.

## Life Settlements are Longevity Risk Instruments

This means that the primary risk of owning a life settlement is that the insured covered by the policy will live *longer *than expected. Since the mean LE on a mortality curve for a life settlement insured usually, though not always, is found to the right of (i.e., is greater than) the median, managers use the mean as the basis of their life settlement valuation calculations. The reason most managers use the mean LE to value policies is that it provides them with a better indication of the shape of the mortality curve that describes the way the population it is related to will die. Using the median is a less conservative approach to valuing policies, and ignores the huge financial costs (e.g., COI charges) of those policies running many years beyond expectations.

Related: Types of Life Settlement Transactions

Life settlement insureds were, at one time, insurable, meaning they were selected by an insurance company as being eligible to purchase life insurance. Therefore, the average life settlement insured is not the average person in the population. Mortality curves related to selected populations are different than general population curves, and again, most life settlement mortality curves skew right to reflect the longevity risk about which life settlement asset managers are concerned. As indicated above, using the median of such curves fails to reflect the “tail” risk.

So, the median tells you where the midpoint of the mortality curve is, but it doesn’t tell you anything about the shape of that curve. The difference between the median and the mean, on the other hand, tells you something about the slope of the curve and the degree of “skewness” involved in the insured being evaluated. If more of the members of the population can be expected to live longer than average (i.e., the mean), the difference between the median and the mean will be greater, and the inverse is true as well. It is important to note that some life expectancy underwriting firms do NOT provide a mortality curve, and several do not provide both a mean and median LE data point either. Without the curve, it is harder for managers to evaluate the longevity risk associated with life settlements. This is why ISC provides, and will continue to provide, a complete mortality curve in its reports. For more information on mean vs. median life expectancy figures, contact ISC Services.

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