Pension fund asset allocationin a low interest rate environment

Dennis Bams, Peter Schotman and Mukul Tyagi

(Maastricht University)

How do low interest rates affect asset allocation?

Peter Dennis Rogier Mukul Schotman Bams Quaedvlieg Tyagi

What pension funds do and should do

• What does portfolio theory tell us about adjusting portfolios?

– Strategic asset alllocation

• What did funds do?

– Average holdings before and after 2008

– Active rebalancing

• Additional work

– Dynamics of portfolio adjustments: strategic versus actual holdings, active rebalancing

– Hedging interest rate risk: separate paper sponsored by GRI

Own research

Long-term strategic asset allocation: an out-of-sample evaluation,Management Science 2015 (with Bart Diris and Franz Palm)

Strategic asset allocation for long-term investors: parameteruncertainty and prior information, Journal of Applied Econometrics2014 (with Roy Hoevenaars, Roderick Molenaar and TomSteenkamp)

Strategic asset allocation with liabilities: beyond stocks and bonds,Journal of Economic Dynamics and Control 2008 (with RoyHoevenaars, Roderick Molenaar and Tom Steenkamp)

Long memory and the term structure of risk, Journal of FinancialEconometrics 2008 (with Rolf Tschernig and Jan Budek)

HIDDEN SLIDE

Pension fund portfolio holdings

• Data from CEM Benchmarking (Toronto)

– actual and strategic holdings of pension funds

– international, half of funds US

– annual since 1990, close to 1000 funds

• Pros

– Information is highly disaggregated in asset classes

– Both actual and strategic holdings

– Details on benchmarks and their returns

– Details on fund characteristics

• Cons

– Self reported

– Data is only annual

Descriptive statistics

• The average (and median) allocation to risky assets is 63%

– Equity 54%; alternatives 9%

– Cross-sectonal average has increased by 10% in 20 years

• Stategic means are the same

– Strategic weights are constant for about 25% of included funds

• Many more observations towards the end of the sample

– 89 funds in 1990

– 362 funds in 2011

Portfolios before/after 2008Difference in average allocation between 2009-2011 and 2005-2007

Aggregate -7.0*** 2.4 *** 4.4 ***

US -8.9 3.5 5.1

Non-US -4.0 *** 0.7 *** 3.4 **

Public -4.9 -1.8 6.4

Non-public -8.0 *** 4.7 *** 3.3 ***

DB -7.5 3.0 4.4

Non-DB -4.3 ** -0.8 *** 4.8

Large -7.2 1.0 5.9

Small -6.7 3.7 *** 3.0 ***

Old -8.7 4.7 4.0

Young -6.6 ** 1.2 *** 5.2 *

Equity Bonds Alternatives

Portfolios before/after 2008Difference in average equity allocation between 2009-2011 and 2005-2007

Strategic asset allocation

• Optimal portfolio choice for long-term investors

– Textbook treatment in Campbell and Viceira(2002).

– Much of theory based on seminal contributions by Merton.

– Extensions to pension setting with liabilities

• Optimal portfolio weights change in response to changes in investment opportunity set

– Changes in risk and expected returns

• Optimal adjustment may depend on investment horizon and preferences (risk aversion)

Changing investment opportunities

• State variables predict changes in expected returns

– Term premium

– Default premium

– Dividend yield (price-earnings ratio)

– Interest rate level

• Investment asset menu

– Equity

– Long-term nominal bonds

– Short-term bonds

• Alternative assets can make a difference: commodities, inflation linked bonds, private equity, hedge funds, real estate

Expected adjustments

EQUITY BONDS

Asset only Asset-Liability

Asset only

Asset-Liability

Interest rate - - + +

Dividend yield + + - -

Credit spread + ? - ?

Yield spread - - + +

Strategic allocation and state variables

Dividend yield explains equity allocation, but with the wrong sign?!

• fixed effects: focus on explaining time series variation

• strategic weights reported by funds

• Residual asset class is Cash

Actual allocations

• Active investment decisions:

• Explain active allocations using variables that signal investment opportunities

portfolio return

asset class return

Active allocation

Dividend yield is powerful predictor with the expected positive sign

Conclusions

• Funds have responded to change macroeconomic conditions

– reduce equity holdings

– substantial heterogeneity

• Strategic asset allocation models suggest opposite response

• Discrepancy between actual active allocation decisions and strategic benchmarks

– active decisions in line with portfolio allocation models

• NEXT: what determines the difference between active and strategic portfolios?

How do pension funds adjust their portfolios?

• Pension funds response to bad market conditions of 2001 and 2008 could go in different directions:

– Decrease risk, motivated by regulatory pressure when funding ratio is low, or because of increasing risk aversion

– Keep the same, being a long-term institutional investor

– Increase risk, due to belief in mean reversion, or driven by liabilities

• On top there are tactical effects like momentum strategies.

• Answer may depend on fund characteristics

Literature (1)

• Rauh (RFS 2009) examines incentives for risk shifting versus risk management.– better funded plans have riskier portfolio– strong positive effect of lagged investment returns

• Mohan and Zhang (JBF 2014) find that pubic plans take more risk than corporate plans– risk taking increases after bad returns

• Pennacchi and Rastad (JPEF 2011) find that US public pension funds increase risk after poor performance.

• According to Papaioannou et al (IMF 2013) US pension funds were net sellers of equities in the crisis of 2008-09, reflecting a move towards a more conservative asset allocation.

Literature (2)

• Blake, Lehmann and Timmermann (JB 1999) find slow adjustment of UK funds towards a strategic portfolio

• Bikker, Broeders and Dedreu (IJCB 2010) consider rebalancing towards a strategic portfolio for Dutch pension funds

Cross-sectional stdev in actual minus strategic

CEM data, all funds

Basic regression model

Hypotheses

ββββ1111 = 0= 0= 0= 0 Portfolio change cannot be attributed to passive change (past returns)

ββββ2222 = 1= 1= 1= 1 Actual change fully reflects strategic change

ββββ3333 = 1= 1= 1= 1 Full adjustment to target

• Coefficients do not depend on fund characteristics and past returns

Extensions

1. Parameters dependent on past returns

– Returns implicit in passive change

– Asymmetry with dummy for MSCI<0

2. Parameters dependent on fund characteristics

– Fund size, proportion retired, public dummy, DB dummy, US dummy

3. Disaggregate risky assets in equity and alternatives

– rebalancing models slower for alternatives due to liquidity

Basic model

Dependent variable: actual change

Passive change 0.18 0.20 0.06 0.09

(t-stat) 9.0 10.9 1.5 2.2

Strategic change 0.45 0.46 0.43 0.44

15.0 13.9 14.3 13.0

Adjustment 0.43 0.52 0.40 0.50

14.3 18.7 13.3 17.7

Fund FE N Y N Y

Year FE N N Y Y

R 2 0.41 0.46 0.45 0.46

Asymmetry (1)

Dependent variable: actual change

Passive change 0.09 0.25 0.07 0.25

(t-stat) 2.2 4.2 1.1 3.8

Strategic change 0.44 0.43

13.0 14.3

Adjustment 0.50 0.50 0.39 0.39

17.7 16.7 14.2 14.1

(MSCI<0)*Passive -0.30 -0.36

-3.3 -3.2

Fund FE Y Y Y Y

Year FE Y Y Y Y

R 2 0.46 0.46 0.28 0.28

Asymmetry (2)

Dependent variable: actual change

Passive change 0.20 0.30 0.23 0.32

(t-stat) 10.9 8.0 10.8 8.0

Strategic change 0.46 0.46 0.00 0.00

13.9 13.9 0.0 0.0

Adjustment 0.52 0.52 0.42 0.42

18.7 18.8 15.2 15.2

(MSCI<0)*Passive -0.15 -0.15

-2.7 -2.4

Fund FE Y Y Y Y

Year FE N N N N

R 2 0.46 0.41 0.45 0.21

Fund characteristics (1)

ββββ1111 ββββ2222 ββββ3333

Passive Strategic Adjustment

Constant 0.12 0.82 0.55

log(size) 0.00 -0.02 -0.13

% Retired -0.06 0.02 0.15

PUBLIC 0.01 -0.11 0.00

DB 0.02 -0.16 0.09

US 0.12 0.01 -0.05

Fund FE Y

Year FE N

R 2 0.43

Fund characteristics (2)

ββββ1111 ββββ2222 ββββ3333

Passive Strategic Adjustment

Constant -0.07 0.70 0.33

log(size) 0.00 -0.02 0.01

% Retired 0.02 0.03 0.13

PUBLIC 0.02 -0.13 -0.01

DB 0.06 -0.09 0.01

US 0.07 -0.02 -0.09

Fund FE N

Year FE Y

R 2 0.48

Alternative assets

Risky Equity Alternatives

Passive 0.09 0.15 0.94

t-stat 2.2 2.4 21.1

Strategic 0.44 0.35 0.09

13.0 12.9 3.2

Adjustment 0.50 0.42 0.08

17.7 14.5 3.7

Fund FE Y Y Y

Year FE Y Y Y

R 2 0.647 0.605 0.138

Main results

• A significant proportion of the change in the weight in risky assets is related to a passive change (procyclical)

– asymmetry: lagged return has positive effect when positive, but almost zero when negative

• Actual changes only partially reflect strategic changes (< 50%)

– Part of rebalancing is moving towards last year’s strategic weight

• Cross-sectionally, Public and DB funds significantly slower in incorporating changes in strategic weights – US funds are more subject to passive change

• Disaggregating, within all risky assets the slowest rebalancing is in alternatives

Caveat

• Our analysis is conditional on strategic weights

– controls for much of the heterogeneity among funds

– alleviates the need for a firm fixed effect

• What determines the strategic weight?

– How is it related to fund characteristics and past returns?

Score-Driven Nelson-Siegel: Hedging Long-Term Liabilities

Rogier Quaedvlieg, Peter Schotman

(Maastricht University)

Euro swap data (discount rate yield curves)

Hedging long-term liabilities

• Nelson-Siegel is a popular 3-factor term structure model that parsimoniously explains the shape and time variation in interest rate levels

• A liability hedge is a portfolio with the same factor exposure as the liability and minimal residual risk.

• How stable are factor loadings?

– How did they change after 2008?

Related own research

What does a term structure model imply about very long-term discount rates? (with Anne Balter and Antoon Pelsser), October 2015

Robust Long-Term Interest Rate Risk Hedging in Incomplete Bond Markets (with Antoon Pelsser and Sally Shen), March 2015

The Volatility of Long-term Bond Returns: Persistent Interest Shocks and Time-varying Risk Premiums (with Daniela Osterrieder), February 2015 (under revision)

HIDDEN SLIDE

Duration plus …

• First factor in Nelson-Siegel model is a parallel shift in the yield curve

– level factor

– corresponds to duration hedging

• Other two factors are slope and curvature

– both governed by a single parameter λ.

A recent yield curve (March 31, 2014)Discount yields extracted from euro swap rates

Parallel shifts Time-variation in λt

• Rolling window estimates

• Much variation since 2008

• sensitive to auxiliary econometric assumptions

– heteroskedasticty: both cross-sectional as well as time series

Econometric model

• SLIDES TO INCLUDE FROM OTHER PRESENTATION

Estimation results

Estimates of lt sensitive to model for residuals

Hedging problem

• Fixed liability with very long duration: w0 = -1

• Find portfolio with same factor exposure and minimal residual risk

Hedge portfolio

The top graphs show the portfolio allocation for hedging a liability with 10-year maturity, the bottom graphs for hedging a 50-year liability. The graphs on the left show Duration hedging; graphs on the right show NS factor hedge portfolios using λt from the NCS-DS model. The shaded area is the empirical distribution of the portfolio weights over time.

Hedging results• Hedging 50 years liability• Model estimated using

maturities up to 20 years• Rolling window T = 1000 • Mean Absolute Error

Conclusion

• Substantial variation in Nelson-Siegel shape parameter

– Especially relevant since 2008

– Interaction with residual GARCH

• Model with time-varying shape outperforms in out-of-sample hedging.