Longevity and Investment Risk

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1 Longevity and Investment Risk 15th Australian Colloquium of Superannuation Researchers A study into the individual impact and behaviour John Livanas UNSW Faculty of Business: 15th Colloquium of Superannuation Researchers : 19th and 20th July 2007

2 Abstract Interested in the interaction between longevity risk and investment risk The conventional wisdom is to plan for a target longevity and adjust risk accordingly However, given an investor risk profile, there is a question as to why risk should be reduced nearer retirement or expected death Paper looks at the impact on individuals of investment risk and longevity and comments that The aggregate of the effects on individual investors is different to the effects of the aggregate of investors due to investors asymmetric utility of gains versus losses If investors are Bayesian the response to these probabilities is to reduce risk, and the industry will offer lifestage funding There is an arbitrage opportunity for insurance against longevity and investment risk

3 Portfolio Choice Table 15 Investment choice by fund type Year end June 2006 Entities with more than four members Corporate Industry Public sector Retail a Total Number of entities with more than four members Number of entities offering investment choice Proportion of entities offering investment choice 36.9% 84.0% 65.9% 66.1% 49.1% Average number of investment choices offered per entity b Total assets ($m) 52, , , , ,333 Assets of entities offering investment choice ($m) 46, , , , ,799 Assets in entities offering investment choice 88.4% 99.0% 89.8% 85.8% 90.0% Assets in default investment strategy c ($m) 30, ,867 92,256 85, ,706 a Excluding approved deposit funds and eligible rollover funds, 75 per cent of retail superannuation funds offer investment choice. 49% in Default Investment Strategy: APRA Annual Superannuation Bulletin June 2007 b The average number of investment choices offered per entity refers to those entities that have investment choice. c Not all superannuation entities are required to have a default investment strategy. Where there is no default strategy, the strategy of the largest option is reported or the fund strategy as a whole.

4 Observations 50% is likely to be the upper limit Movement between funds; rebalancing; classification and other factors Questions: When choices are made between balanced funds, does the level and dispersion of fund returns mirror the risk? When choices are not made, what is the dispersion and returns of the default funds?

5 Dispersion of Returns : % Growth Assets % 5 Y ear : A n n ual R eturn s p.a % 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Proportion of portfolio allocated to 'Growth Assets'

6 Dispersion of Returns : Standard Deviation 5 Y ear : A n n u al % R etu r n s 25 Annual Returns versus Standard Deviation for Superannuation Funds over $200m As at 30 April 2007 TOTAL : $300bn 5 year annual returns vs 5 year annual standard deviation Risk Free (Cash) Portfolios % Linear (5 year annual returns vs 5 year annual standard deviation) Year % Annual Standard Deviation UNSW Faculty of Business : 15th Colloquium of Superannuation Researchers : 19th and 20th July

7 Default Funds Only SuperRatings Fund Crediting Rate Survey Default Options Fund Investment Option 5 Year Return 10 Year Return 5 Year Std Deviation 5 Year Sharpe Ratio Top Quartile Bottom Quartile All Fund Median Maximum Value Minimum Value

8 So.. Default funds represent roughly the centre of the funds dispersion and returns as expected Default funds on average have achieved a 5 year and 10 year return above the risk free rate (with a risk premium of around 4%) An average investor, knowing this, can readily plan for their retirement assuming an estimate of their own longevity or can they? This paper continues my interest in the effects of individual behaviour on aggregate observations

9 What is are the spread of effects on the individual investor Table 2 Comparison of Returns experienced by two investors, one of whom receives the top quartile of annual returns, the other who receives the bottom quartile of returns Top Quartile Apr 03 Apr 04 Apr 05 Apr 06 Apr 07 Opening Balance 30,000 44,104 59,655 76,802 95,708 Contributions Returns 4,104 5,551 7,147 8,906 10,846 Closing Balance 44,104 59,655 76,802 95, ,553 Bottom Quartile Apr 03 Apr 04 Apr 05 Apr 06 Apr 07 Opening Balance 30,000 43,392 57,920 73,679 90,775 Contributions Returns 3,392 4,528 5,760 7,096 8,546 Closing Balance 43,392 57,920 73,679 90, ,321

10 What is the longevity risk for each investor Cumulative Probabilities of Survival at Age % 90.0% At Birth Age = 65 Age = 70 Age = 75 Age = 80 Age = % 70.0% % Probability 60.0% 50.0% 40.0% 30.0% 20.0% 10.0% 0.0% UNSW Faculty of Business : 15 Age th Colloquium of Superannuation Researchers : 19 th and 20 th July 2007

11 What is the investment risk for a retired investor? Modelled using Monte Carlo style simulation (Modelled once /year) Age at retirement = 65 Expected Age at Death =83 Amount at Retirement = $200,000 Bequest at age 83 =Nil Expected Return = 9.1% Expected Standard Deviation = 5.2% (gaussian) Consumption Inflation = 3% p.a. Assume an Investor wants to optimise consumption (i.e. leave no bequest at 83), the baseline model requires year 1 drawdown of $16,819, increasing by 3 % p.a. Achieve expected return each year 100 Runs, returns drawn from a sample randomly such that the average of returns equals expected return, and the standard deviation of returns equals expected standard deviation

12 Investor Problem : Baseline Case Assume at age 65, Opening Balance of $200,000, assume no bequest motive; no reliance on Age Pension and no reliance on additional income Mean Return Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8 Year 9 Year 10 Age = 65 Age = 66 Age = 67 Age = 68 Age = 69 Age = 70 Age = 71 Age = 72 Age = 73 Age = 74 Opening Balance $ 200,000 $ 199,850 $ 199,136 $ 197,790 $ 195,737 $ 192,896 $ 189,177 $ 184,482 $ 178,701 $ 171,718 Consumption $ 16,819 $ 17,324 $ 17,844 $ 18,379 $ 18,930 $ 19,498 $ 20,083 $ 20,686 $ 21,306 $ 21,945 Investment Return $ 16,669 $ 16,610 $ 16,498 $ 16,326 $ 16,089 $ 15,779 $ 15,388 $ 14,905 $ 14,323 $ 13,629 Closing Balance $ 199,850 $ 199,136 $ 197,790 $ 195,737 $ 192,896 $ 189,177 $ 184,482 $ 178,701 $ 171,718 $ 163,402 Annual Investment Return 9.10% 9.10% 9.10% 9.10% 9.10% 9.10% 9.10% 9.10% 9.10% 9.10% Assumptions: 1. Age at Retirement Achieving the fund mean return of 9.10% 3. Bequest (Terminal Value at Death) $0 4. Expected Age at death of No capacity to rely on age pension or additional income 6. Terminal value at age 83 is $0 7. Consumption inflation of 3% 8. Annualised Standard Deviation of 5.20% 9. Required Consumption to achieve bequest motive $16,819 Assume at age 65, Opening Balance of $200,000, assume no bequest motive; no reliance on Age Pension and no reliance on additional income Mean Return Year 11 Year 12 Year 13 Year 14 Year 15 Year 16 Year 17 Year 18 Year 19 Age = 75 Age = 76 Age = 77 Age = 78 Age = 79 Age = 80 Age = 81 Age = 82 Age = 83 Opening Balance $ 163,402 $ 153,610 $ 142,188 $ 128,965 $ 113,753 $ 96,349 $ 76,528 $ 54,046 $ 28,634 Consumption $ 22,604 $ 23,282 $ 23,980 $ 24,700 $ 25,441 $ 26,204 $ 26,990 $ 27,800 $ 28,634 Investment Return $ 12,813 $ 11,860 $ 10,757 $ 9,488 $ 8,036 $ 6,383 $ 4,508 $ 2,388 $ 0 Closing Balance $ 153,610 $ 142,188 $ 128,965 $ 113,753 $ 96,349 $ 76,528 $ 54,046 $ 28,634 $ 0 Annual Investment Return 9.10% 9.10% 9.10% 9.10% 9.10% 9.10% 9.10% 9.10% 9.10%

13 90 Simulation Runs Monte Carlo Simulation runs 88 Age at which money runs out Baseline AVERAGE OF ALL RUNS Age at Retirement Achieving the fund mean return of 9.10% 9.09% 3. Expected 72 Bequest (Terminal Value at Death) $0 $0 4. Expected Age at death of Expected Age at Death Age at which money runs out if the investment return equals the Risk Free Return 5. No capacity to rely on age pension or additional income 0 6. Actual 70 Terminal value at age 83 is $0 $9, Consumption 1 4 inflation 7 of % % Annualised Standard Deviation of 5.20% 5.19% 9. Required Consumption to achieve bequest motive $16,819 $16, Age at which money runs out Run Number

funds Numbers of people who, through normal fluctuations in investment

14 Distribution of Results around 83 Percentage of Simulation at which money runs out Numbers at age, who have sufficient funds Numbers of people who, through normal fluctuations in investment returns, will run out of money Age at which money runs out

Distribution of results vs Longevity Risk of people who have attained 65

and Probability of Running out of money Probability of not surviving to

money than anticipated through natural variation in returns Probability of

Numbers at age, who have sufficient funds Survival at age 65 Probability of

15 Distribution of results vs Longevity Risk of people who have attained 65 Percentage Probability of Survival at age 65 and Probability of Running out of money Probability of not surviving to anticipated age, and leaving an unintended bequest Probability of having more money than anticipated through natural variation in returns Probability of having less money than anticipated through natural variation in returns Numbers at age, who have sufficient funds Survival at age 65 Probability of surviving beyond the anticipated age, but not having enough money Age

16 4 Quadrants Live < Expected Live > Expected 9.0 Investments achieve < Expected (Risk : Unintended Bequest = 1) Live less than expected and perhaps out of money Live less than expected but run out of money early (Risk : Running out of money = 2) Live more than expected and run out of money early Live more than expected and run out of money early 9.2 (Risk : Running out of money = 2) Live less than expected and leave a bequest Live less than expected and perhaps run out of money Live more than expected and run out of money early Live more than expected and run out of money early 9.4 Investments Achieve > Expected Live less than expected and leave a bequest Live less than expected and leave a bequest Live more than expected and perhaps run out of money Live more than expected and run out of money early 9.6 (Risk : Unintended Bequest = 1) Live less than expected and leave a large bequest Live less than expected and leave a bequest Live more than expected and leave a bequest Live more than expected and perhaps run out of money

17 Investor s Utility A Unit losses reduces utility more than a unit gain EUi (Gains) + EUi (Losses) < EUt (Net of Gains and Losses) Bayesian inference revisited: If Longevity Risk is stated in terms of having sufficient money to sustain retirement, then assuming that the sufficiency of money is only dependant from the investment return, we can write Bayes: P(H o E) P (Having Enough Money Age) = P (Inv Age) P(Inv Age) = P (Age Inv) P(Inv) P(Age) As the person achieves an older age; and as the person sees the investment return deviate from expectations, person s opinion changes

18 Asymmetry and Insurance Bayes means that investors will re evaluate their outcomes as they age past 65, on the basis of investment returns and survivorship But where there is likely to be a unit of financial shortfall, there is a greater unit of utility loss, that is the case where there is a unit of financial excess. However on aggregate the sums match, so an arbitrage of individual risk is possible and insurance against longevity is viable

19 Summary 100 run Monte Carlo simulation of individual impact of investment risk and longevity risk Asymmetrical response leads to opportunities and explains aggregate risk aversion

LIFECYCLE INVESTING : DOES IT MAKE SENSE

Page 1 LIFECYCLE INVESTING : DOES IT MAKE SENSE TO REDUCE RISK AS RETIREMENT APPROACHES? John Livanas UNSW, School of Actuarial Sciences Lifecycle Investing, or the gradual reduction in the investment