ST. JOHN’S - International Actuarial Association · ST.JOHN’S COLLOQUIUM 29/06/2016 –JUNE...
Transcript of ST. JOHN’S - International Actuarial Association · ST.JOHN’S COLLOQUIUM 29/06/2016 –JUNE...
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ST. JOHN’SCOLLOQUIUM
Is one enough?An enquiry into default funds and risk preferences
Dave StrugnellHead of Research: Products & Solutions, MMI HoldingsAdjunct Senior Lecturer: Actuarial Science,
University of Cape Town
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The composition of defined contribution retirement outcomes
Retirement benefit
Level and duration of
savings
Investment returns
Preservation
Annuitisationand longevity
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The composition of defined contribution retirement outcomes
Retirement benefit
Level and duration of
savings
Investment returns
Preservation
Annuitisationand longevity
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Investment choice
Sanlam Benchmark survey 2016: 76% of schemes offer member investment choice.
Offering choice implies the need for a default fund.
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Default fund (trustee choice)
Sanlam Benchmark Survey (2016)
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The trustee’s environment
Fiduciary duty to act in the best interests of members, exercising “duecare” and acting in the “utmost good faith” (Du Toit, 2002).
Undersaving, non-preservation and optimistic annuitisation choices rampant, so investment strategy takes on great significance.
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Behavioural economics of investment choice
Framing effects
Overconfidence
Loss aversion Status quo bias
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So how is that choice used?
Sanlam Benchmark Survey (2016)
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Question for trustees
Members capable of exercising choice?
Irrelevant given an appropriate default?
But then, is the default appropriate for the members who end up in it?
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Investment strategy
Key question: is the price of life-stage protection (sacrifice of equity premium) worth it?
Asset allocation
Capital protection
close to retirement
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Critiques of life-stage
Industry:- Life-stage approaches prevail- But not without its critics
Literature:- Support in e.g. Hibbert & Mowbray (2002), Antolín, Payet & Yermo (2010)- High-equity strategies preferred by e.g. Booth & Yakoubov (2001), Blake,
Cairns & Dowd (2000, 2001), Byrne et al. (2007)- Low equity (inflation-linked bond strategy) proposed by Thomson (2011)
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Comparing strategies through the lens of risk preferences
Allocation and de-risking
strategyV (X)
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Elicitation of risk preferences for a South African population
Project carried out by UCT’s Research Unit in Behavioural Economics and Neuroeconomics, in association with Georgia State University’s Center for the Economic Analysis of Risk, for Allan Gray, using UCT staff members as subjects.
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Range of risk preferences
CRRA parameter estimates, n=181 (of 194)
Gamma
Fre
que
ncy
-100 -50 0 50 100 150
020
40
60
80
100
12
0
CRRA estimates in [-5,10], n=143
Gamma
Fre
que
ncy
-4 -2 0 2 4 6
020
40
60
80
γ CE (40, 100)
0 70
0.5 67
1 63
1.5 60
2 57
4 49
10 43
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Models of asset returns
Asset class returns from Feb 1976 (domestic equities, bonds, cash and property, and international equities and bonds) and from Feb 2000 (inflation-linked bonds).
Much modelling inspiration from Blake, Cairns and Dowd (2001).
Four classes of models considered:
1. Multivariate normal2. Multivariate t3. Mixture of independent multivariate normals4. Hidden Markov Model1
See e.g. Zucchini, MacDonald & Langrock. (2016). Hidden Markov Models for Time Series: An Introduction using R, CRC Press.
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Modelling
MLE of parameters due to shorter ILB history.
MV normal
Blake, Cairns & Dowd (2001): differing df for each class to capture kurtosis (not restricted to integers).
MV t
As for HMM, but states are independent rather than following a Markov chain.
MixtureHMM
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Model fits
Model States AIC BIC
Multivariate normal -13,324 -13,109
Multivariate t
Mixture of MV normals 2 -13,573 -13,138
3 -13,671 -13,015
Hidden Markov Model 2 -13,711 -13,270
3 -13,762 -13,082
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Adjusted means
0.0
00.0
20
.04
0.0
60
.08
0.1
0
Asset class
Retu
rn
Cash ILBs Bonds Int.Bonds Property Int.Equity Equities
Empirical
Projected
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Simulations of returns
25 65
Deterministic salary increases; contributions 12.5% of salary.
25,000 simulations for 480 months and 7 asset classes (in R).
Management fees in line with industry norms for medium to large scheme.Inflation-linked annuity secured at retirement (male, JL 50%); SA2001-04 mortality. ILB yieldsconsistent with simulated returns.CRRA utility; argument of function is replacement ratio.
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Investment strategies
Equity BalancedInflation-linked
bonds
Lifestage switch: 0,5,10 Threshold 50/75Compare certainty
equivalents assuming CRRA utility
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Results
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0.9 1
1.1
1.2
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1.9 2
2.5 3
3.5 4
4.5 5 6 7 8 9
10
Balanced threshold
Equity threshold
ILB throughout
Balanced 10 year switch
Balanced 5 year switch
Balanced 0 year switch
Equity 10 year switch
Equity 5 year switch
Equity 0 year switch
7 7 7 7 7 7 7 7 7 7 6 6 6 6 6 6 6 5 5 5 4 2 2 2 2 1 3 3 3 3 4 4
5 5 5 5 5 5 5 5 5 5 5 5 5 5 4 4 4 4 4 4 5 5 7 7 7 7 8 8 8 8 8 8
9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 7 6 5 5 3 2
8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 4 4 4 4 1 1 1 1 1 1
6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 6 3 3 3 3 3 2 2 2 2 2 3
4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 3 2 2 2 2 1 1 1 1 2 4 4 4 4 5 5
3 3 3 3 3 3 3 3 3 3 4 4 4 4 5 5 5 6 6 6 7 7 5 5 5 5 5 5 6 6 6 6
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 6 6 6 6 6 6 7 7 7 7 7
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 8 8 8 8 9 9 9 9 9 9
Preferred strategies
2 4 6 8 10
Value
Color Key
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Is a single default sufficient?
Results tentatively suggest that it may be, for moderate levels of risk aversion.But life-stage may not be the optimal solution.
Caveats:
- Subjective or historical nature of parameters- Appropriateness of utility functions and parameter estimates:
• Other forms of EU functions (e.g. displaying decreasing relative risk aversion)?• Other theories of choice (e.g. rank-dependent utility, prospect theory)?• Descriptive vs. normative/prescriptive estimates?• More risk-averse over retirement outcomes/near retirement age?
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Acknowledgements
Thanks to:
- BNP Paribas Cadiz for financial market data- Alexander Forbes for houseview salary increase assumptions- Iain MacDonald for guidance on Hidden Markov Models