Trading Death: The Implications of Annuity. Speculation and Portfolios

Transcription

1 Trading Death: The Implications of Annuity Replicationfor the AnnuityPuzzle Puzzle, Arbitrage, Speculation and Portfolios Charles Sutcliffe The ICMA Centre, Henley Business School, University of Reading

2 Illiquidity and Annuities This analysis of annuities applies not only to annuities purchased in the market, but also to defined benefit and state pensions. In the 18 th and 19 th centuries it was possible to trade annuities on the lives of other people. However annuities can now only be purchased on the life of the annuitant, and cannot be surrendered back to the provider or traded. In addition annuitants cannot borrow using their annuity payments as collateral. This has led to a very widespread view that annuities are illiquid assets. Once purchased (or acquired) they cannot be liquidated.

3 Relationship Between Annuity and Life Insurance Prices With actuarially fair prices and no load factors there is a relationship between annuity and life insurance prices for the same person: a x* (y x* +r) = 1 (3) a x* is the actuarially fair cost today of an annuity of 1 for an annuitant aged x. y x* is the annual actuarially fair insurance premium for life insurance of 1 for an individual aged x. r is therateoft interest t for the lifeoff the annuitant t

4 Annuity Replication Given eqn (3), it is possible to replicate a short annuity position using life insurance and debt. Now Borrow a sum of money. Now Insure the life of the annuitant for the sum borrowed. Death Use the life insurance to repay py the loan.

5 Amount Borrowed The amount borrowed is chosen so that annual annuity income is equal to the interest on the loan and the life insurance premium. So each year until death the net cash flow is zero. A = X * r + Y * (4) X * is the sum insured A is the constant annual annuity payment Y is the annual life insurance premium the * superscript p denotes an actuarially fair price or amount

6 Collateral for the Loan The life insurance policy may provide security for the repayment of the loan if the beneficiary is also the guarantor of the loan. Alternativelyti l the annuitant t may have assets thatt can provide collateral.

7 Example of Offsetting an Annuity Two years ago at the age of 65 Orsino Thruston bought an annuity for 100,008, which yields an annuity payment of 8,628 per year until his death. At the age of 67 he now wishes to offset this annuity. The current actuarially fair price of an annuity of 8,628 p.a. for someone aged 67 is 93,641. He borrows 93,641 at 4%, which requires interest payments of 3,746per year. The remaining net cash inflow of 4,882 per year is used to pay the annual premiums on the life insurance policy on his life worth 93,641. For simplicity and brevity, it is assumed that Orsino dies at the end of the fourth year. So Orsino has effectively liquidated his annuity now for 93,641, its actuarially fair value.

8 Example of Offsetting an Annuity Year Transaction Undiscounted dcash hflows Discounted Cash hflows Inflows Outflows Inflows Outflows 0 Cost of annuity 100, ,008 1 Annuity 8,628 8,296 2 Annuity 8,628 7,977 2 Borrow 93,641 86,576 2 Insure life for 93,641 Mortality Credit 2,841 Totals 102, ,849 3 Annuity 8,628 7,670 3 Interest payments ( 93,641@4%) 3,746 3,330 3 Life insurance premia 4,882 4,340 4 Annuity 8,628 7,375 4 Interest payments ( 93,641@4%) 3,746 3,202 4 Life insurance premia 4,882 4,173 4 Life insurance claim 93,641 80,045 4 Repay loan 93,641 80,045 Totals 95,090 95,090

9 Load Factors for Annuities and Life Insurance p is the life insurance load factor w is the annuity load factor The profit (or loss) on annuity replication is given by * * * Ayx Y (1 w )( r yx (1 p )) (6) * * yx [ r yx (1 p)]

10 Applications Annuity Puzzle Arbitrage Longevity Speculation Portfolios

11 1. Annuity Puzzle One of the possible explanations for the annuity puzzle of under annuitization, is the illiquidity of annuities. The ability to offset long positions in annuities makes them reversible, and so reasonably liquid. If the replication of short positions in annuities is to reduce the annuity puzzle, and lead to an increase in the level of annuitization, it needs: 1 publicity of the offset procedure to individuals 2 money s worth ratios for annuities and life insurance that are not prohibitive Various authors has argued that annuitants would be willing to pay up to between 11% and 16% of the annuity price for the benefits of reversible annuities.

12 2. Arbitrage If annuities are under priced, or life insurance is over priced, arbitrage is possible by buying annuities in the market and creating a synthetic annuity short position. This example shows arbitrage when annuities are underpriced by 6% and life insurance is overpriced by 5%. Buy an annuity 88,000 Insure his life 91,064 Borrow 91,064 Arbitrage profit ( 91,094 88,000) = 3,064 (eqn 6)

13 Arbitrage of an Annuity Underpricing with a Life Insurance Load Factor Year Transaction Undiscounted Cash Flows Discounted Cash Flows Inflows Outflows Inflows Outflows 0 Cost of annuity 88,000 88,000 0 Borrow 91,064 91,064 0 Insure life for 91,064 0 Profit 3,064 Ttl Totals 91,064 91,064 1 Annuity 8,628 8,296 1 Interest payments py ( 91,068@4%) 3,643 3,503 1 Life insurance premia 4,985 4,793 2 Annuity 8,628 7,977 2 Interest payments ( 91,068@4%) 3,643 3,368 2 Life insurance premia 4,985 4,609 2 Life insurance claim 91,064 84,194 2 Repay loan 91,064 84,194 Totals 100, ,467

14 Arbitrage Arbitrage isnot possible if annuities are over priced, p, or life insurance is under priced because individuals cannot sell annuities or life insurance. However there will be competition bt between rival insurance companies, tending to remove such arbitrage opportunities. An arbitrage opportunity exists if the actuarially fair annuity price exceeds the current annuity price plus the annuity and life insurance loadfactors.

15 Arbitrage Overpriced CB V AF Competitive Opportunities NAB Underpriced Arbitrage opportunities Time

16 Arbitrage opportunities are likely to be rare, but there is evidence to suggest they do exist. Money s Worth Ratios (MWR) Oregon Public Employees Retirement System has a median MWR of 1.45 (and over 1.60 in more recent years), which is an underpricing of (0.45/1.45) = 31% (and in some years over 38%) Singapore MWR of 1.37 for women and 1.34 for men Singapore MWR of 1.25 for both men and women Chile for almost all annuities had a MWR above one, with some annuities having MWR of 1.28 Switzerland MWR of 1.20 for jointlife annuities Israel MWR of 1.16 for men and 1.24 for women Germany MWR of 1.10 for men UK MWR were above 1.20 for men in 1971, 1990 and 1991 US MWR of 1.14 for Hispanic women

17 Arbitrage Opportunities In addition, there is considerable dispersion in the prices of similar annuities sold by different insurance companies, e.g. a 20% difference between the top and bottom quartile prices. In other markets arbitrage can be of unlimited scale, but this is not the case in annuity markets, which permits big deviations from the no arbitrage price to persist.

18 Effect of Load Factors on the Arbitrage Profit Life Insurance Load Factor (p) 0 5% 10% 15% 20% 25% 25% 23,410 20,834 18,395 16,084 13,890 11,805 Annuity 20% 18,728 16,152 13,713 11,402 9,208 7,123 Load 15% 14,046 11,470 9,031 6,720 4,526 2,441 Factor 10% 9,364 6,788 4,349 2, , (w) 5% 4,682 1, ,644 4,838 6, ,576 5,015 7,326 9,520 11,605

19 3. Longevity Speculation Information asymmetry Annuitants have better information about both their life expectancy, and changes in their life expectancy. Speculators can buy or sell (via replication) an annuity in the expectation that their life expectancy, as assessed by insurance companies, will rise or fall in the future. Insurers assess life expectancy using information such as: age, gender, post code, health status, occupation, size of pot, behavioural risks. A person s longevity, as assessed by an insurance company, may increase or decrease for a variety of reasons such as moving to a new post code or occupation, changing their behaviour, a change in their health status, etc.

20 Speculation on an Increase in Longevity Example Buy an annuity from the insurer with the lowest longevity expectations tti 100, Hedge the interest rate risk inherent in the annuity Receive annuity payments of 8,628for two years Expected longevity increases by 2 years Buy life insurance from the insurer with the highest longevity expectations for the current value of his annuity which is 100,008 Borrow 100, Close the interest rate hedge Profit with a present value of 5,887 (or 6,367 in year two, when it is available in cash)

21 Year Transaction Undiscounted Cash Flows Discounted Cash Flows Inflows Outflows Inflows Outflows 0 Cost of annuity 100, , Open an interest rate hedge 1 Annuity 8,628 8,296 2 Annuity 8,628 7,977 2 Borrow 100,008 92,463 2 Insure life for 100,008 2 Close the interest rate hedge Mortality Credit 2,841 Profit 5,887 Totals 108, ,736 3 Annuity 8,628 7,670 3 Interest payments ( 100,008@4%) 4,000 3,556 3 Life insurance premia 4,628 4,114 4 Annuity 8,628 7,375 4 Interest payments ( 100,008@4%) 4,000 3,419 4 Life insurance premia 4,628 3,956 4 Life insurance claim 100,008 85,487 4 Repay loan 100, ,487 Totals 100, ,532

22 4. Portfolios UK pension liabilities in 2010 were 7 tr. (almost 5 times UK GDP) and so form a major part of UK portfolios. The ability to offset annuities means they could be included in householdh portfoliomodels. dl However annuities seldom appear in such portfolio models. Incorporating them in portfolios leads to multi period life cycle models.

23 Conclusions Annuities can be offset, and so are liquid securities. This allows them to be incorporated in some standard finance models. Widespread use of annuity replication could reduce the annuity puzzle. The arbitrage of under priced annuities should help to increase the price efficiency ofthe annuity market. Speculation on the annuitant s own longevity should also increase price efficiency. Annuities should be incorporated in household portfolio models. Annuity replication undermines the UK government policy of compulsory annuitization.