Friday, January 28, 2011

Diversification Deja Vu

I've written before about life settlements.  Generally, I'm a fan of allowing the business.  More recently, I argued that people don't like unseemly parts of their investments when they draw too much attention.  It's really a matter of diversification.

This brings me to the latest controversy over the company Life Partners Holdings Inc., a seller of fractional interest in life insurance policies.  The company has just reduced their return expectations touted to customers, at least partially as a result of pressure from a WSJ story.  I know, this is a shocker: They could not deliver on their promised returns!!  Oh, and they're being investigated by the SEC.

Here's the idea: Think of a life insurance policy as a negative coupon bond with an unknown maturity.  Instead of receiving coupons, you pay coupons.  Instead of getting back your principle at a known future date, you get it back at a random date.  The longer the person lives, the lower your return, because you pay the coupon longer, and you get paid back your principle at a later date.  Variable maturity combined with negative coupons makes these bonds much riskier than typical bonds.  (Of course the upside can be huge if the insured falls short of life expectancy.)

How risky are they?  How many stories have you heard of people with months to live surviving years?  My understanding is that there's excellent medical evidence that the grumpier the old man, the longer he lives. 

The math isn't very difficult.  If you expect someone to die in three years, and they live for four, intuitively you're at least 30% worse off, right?  they lived 33% longer than expected, and you had to pay another year of premium.  (At least there's upside: The insured may live less than three years.)   

Many factors drive life expectancies, and they are just expectancies: Half of all people will live longer than expected. 

Moreover, those that are highly likely to live less than expected probably know this, and won't sell their policies.
Life actuaries will tell you your sample needs thousands of observed deaths to draw credible conclusions.  In other words, you need massive diversification to reduce risk.  Why is that?

In contrast, diversification in the stock market takes relatively few positions.  Twenty or thirty stocks in various sectors get you most of the way there.  A two or three thousand stock portfolio isn't going to deviate much from "the market" or our "expectations."

In it's history, LPHI has only sold 6,400 policies to 27,000 investors.  It seems unlikely many of those 27,000 investors hold even 1000 different lives.  They're undiversified and unrealistic about risk and return.

Frankly,  it doesn't matter if the doctor in Reno, NV who performs all their medical evaluations is any good.  He could be "perfect" at calculating expectancies, and results may be lousy for undiversified investors.  (However, giving him the benefit of the doubt is worse than giving credit rating agencies the benefit of the doubt when you buy mortgage backed securities!)

Think of it this way: Suppose the SEC were investigating an equity index mutual fund.  Rather than holding all 500 S&P stocks like Vanguard, it held 10 or 15.  Would you be surprised at the results when the fund underperformed the index?  (But your friend would still brag at the party that his IRA beat yours!)

1 comment:

  1. I'd have to disagree, actually -- suppose that you have ten-year LE's on a pure constant hazard rate model, working out to a 1% hazard rate per month (or thereabouts). If all the lives in a portfolio are genuinely independent, you only need about 400 lives to have a chance of only 1% of going any particular month without a maturity. I'd say at that point you're pretty well diversified, no?

    The real problem is correlation -- when your model is wrong, it tends to be wrong for everybody at once. The portfolios originated in the 90's were mostly for short-LE AIDS patients; when the triple cocktail was discovered and AIDS became survivable, the industry tanked hard. For the more recent spate of origination it looks to me like the moral hazard risk associated with secondary sales was just not modeled remotely adequately and that the entire industry (which depended on a small number of actuarial firms to compute LE's) got hit by it. Admittedly the guy who owns six policies is underdiversified, but even 100 is plenty for the law of large numbers to kick in.

    Relative to the equity markets, there's a confusion between (1) "get close to the market return, whatever that is" and (2) "have a portfolio that will return close to modeled expectations." In life settlements we're mostly interested in (2), in equities (1). Ironically, the reason you can get such a big chunk of the diversification in the stock market from 30 stocks is that there is a huge amount of correlation between equities -- there's just less diversification benefit to be had, which of course prevents you from being able to hold an equity portfolio that meets (2).