Betting On One's Own Longevity

Bet on century wins £25,000:

A man who bet £100 a decade ago that he would live to be 100 is preparing to pick up his £25,000 winnings this morning.

In 1997 bookmaker William Hill offered Alec Holden odds of 250-1. But the retired engineer, born on April 24 1907, celebrates his century today, to the bookies' dismay. Mr Holden, from Epsom in Surrey, said: "I've been very careful about what I've been doing in recent months. If I saw any hooded groups from William Hill standing in the street, I avoided them."

Chris Dillow explains why the the bookmaker laid some really bad odds:

The bookies should be dismayed, as they underpriced the bet by a factor of around 10.

Government Actuaries tables show that back in 1997, the average 90 year-old had an 80% chance of seeing 91, a 91 year-old had a 78.4% chance of seeing 92, falling to a 63.4% chance of a 99-year-old getting his ton.
Multiplying these probabilities together shows that there was a 3.6% chance of an average 90-year-old getting to 100. William Hill should have offered less than 30-1.

Maybe much less. In staking £100, Mr Holden was revealing that his private information about his health suggested he had a better than average chance of seeing 100 than his contemporaries, who chose not to make the bet. William Hill should have cut the odds, on account of this asymmetric information.

Interesting that in the man's account, he consciously tried to avoid dangerous situations in his quest to hit the century mark.  I've always wondered whether lifespan can be elongated with the proper monetary incentives (e.g. does the estate tax discourage people from dying?).

Also, what kind of financial products could be developed using betting markets where people place wagers on their own longevity?  How about a form of life insurance that actually pays you, the purchaser, a big windfall upon hitting a certain age?  You'd still have the same asymmetric information problem, since purchasers in good health would be more likely to purchase these contracts, but asymmetric information alone hasn't prevented a number of other markets from happening. 

Also, what do you call it when the purchaser knows more information than the seller?  It's not a market for lemons; it's a market for limes.

Comments

[JD]

RE: What kind of financial products could be developed using betting markets where people place wagers on their own longevity?

It would seem that forward contracts would be the most appropriate product to make such wagers.. The enormous variance in health of individuals making such bets would make any standardized contract, such as a stand-alone option or other derivative, inefficient and very risky for speculators taking opposite sides.

A privately negotiated forward contract (non-standardized) between two individuals would seem fair IF there is complete transparency of information. Asymmetric information will make such a financial product inefficient, as you pointed out.

The example you gave regarding the life insurance policy is very interesting. It would behave as an insurance policy with an embedded option contract, with age performing the role of strike price. There is a dilemma, though.

Say you and I are the same age, and would like to place the same bet that we will reach the age of 100. Assume there is a standardized premium payment for such a bet. Contingent on reaching 100, a determined payout to you or I will occur (we can look at age 100 as being similar to an options strike price, and that this option behaves like a binary option with an all-or-nothing payout.)

However, I am a smoker and you are not. The odds of you reaching 100 are significantly greater, hence, the probability of a payout is greater in your case than mine. Bearing this in mind, the option SHOULD cost more for you to purchase than it would for me. If it doesnt, assuming full market liquidity for these products and the ability to take long or short positions, we could consider this a quasi-arbitrage opportunity.

If we remove the assumption of standardized price, such a policy would be quite interesting. Insurance companies would be able to collect additional premium “riders” to their policies, and individuals would be able to ‘bet’ on their longevity. If a fair pricing model based on complete and accurate information is put into place, this would address the “Adverse Selection” dilemma.

Financial engineering will never stop. I think we will see such contracts available, eventually...

[Lawrence]

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