st. john’s - international actuarial association · st.john’s colloquium 29/06/2016 –june...

29/06/2016 1ST. JOHN’S COLLOQUIUM – JUNE 2016

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

29/06/2016 2ST. JOHN’S COLLOQUIUM – JUNE 2016

The composition of defined contribution retirement outcomes

Retirement benefit

Level and duration of

savings

Investment returns

Preservation

Annuitisationand longevity

29/06/2016 3ST. JOHN’S COLLOQUIUM – JUNE 2016

The composition of defined contribution retirement outcomes

Retirement benefit

Level and duration of

savings

Investment returns

Preservation

Annuitisationand longevity

29/06/2016 4ST. JOHN’S COLLOQUIUM – JUNE 2016

Investment choice

Sanlam Benchmark survey 2016: 76% of schemes offer member investment choice.

Offering choice implies the need for a default fund.

29/06/2016 5ST. JOHN’S COLLOQUIUM – JUNE 2016

Default fund (trustee choice)

Sanlam Benchmark Survey (2016)

29/06/2016 6ST. JOHN’S COLLOQUIUM – JUNE 2016

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.

29/06/2016 7ST. JOHN’S COLLOQUIUM – JUNE 2016

Behavioural economics of investment choice

Framing effects

Overconfidence

Loss aversion Status quo bias

29/06/2016 8ST. JOHN’S COLLOQUIUM – JUNE 2016

So how is that choice used?

Sanlam Benchmark Survey (2016)

29/06/2016 9ST. JOHN’S COLLOQUIUM – JUNE 2016

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?

29/06/2016 10ST. JOHN’S COLLOQUIUM – JUNE 2016

Investment strategy

Key question: is the price of life-stage protection (sacrifice of equity premium) worth it?

Asset allocation

Capital protection

close to retirement

29/06/2016 11ST. JOHN’S COLLOQUIUM – JUNE 2016

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)

29/06/2016 12ST. JOHN’S COLLOQUIUM – JUNE 2016

Comparing strategies through the lens of risk preferences

Allocation and de-risking

strategyV (X)

29/06/2016 13ST. JOHN’S COLLOQUIUM – JUNE 2016

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.

29/06/2016 14ST. JOHN’S COLLOQUIUM – JUNE 2016

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

29/06/2016 15ST. JOHN’S COLLOQUIUM – JUNE 2016

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.

29/06/2016 16ST. JOHN’S COLLOQUIUM – JUNE 2016

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

29/06/2016 17ST. JOHN’S COLLOQUIUM – JUNE 2016

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

29/06/2016 18ST. JOHN’S COLLOQUIUM – JUNE 2016

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

29/06/2016 19ST. JOHN’S COLLOQUIUM – JUNE 2016

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.

29/06/2016 20ST. JOHN’S COLLOQUIUM – JUNE 2016

Investment strategies

Equity BalancedInflation-linked

bonds

Lifestage switch: 0,5,10 Threshold 50/75Compare certainty

equivalents assuming CRRA utility

29/06/2016 21ST. JOHN’S COLLOQUIUM – JUNE 2016

Results

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9 1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

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

29/06/2016 22ST. JOHN’S COLLOQUIUM – JUNE 2016

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?

29/06/2016 23ST. JOHN’S COLLOQUIUM – JUNE 2016

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