HIDDEN SLIDE. How do low interest rates affect asset allocation? What pension funds do and should do. Own research

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1 Pension fund asset allocation in a low interest rate environment How do low interest rates affect asset allocation? Dennis Bams, Peter Schotman and Mukul Tyagi Peter Dennis Rogier Mukul Schotman Bams Quaedvlieg Tyagi (Maastricht University) 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, ManagementScience 2015 (with Bart Diris and Franz Palm) Strategic asset allocation for long-term investors: parameter uncertainty and prior information, Journal of Applied Econometrics 2014 (with Roy Hoevenaars, Roderick Molenaar and Tom Steenkamp) Strategic asset allocation with liabilities: beyond stocks and bonds, Journal of Economic Dynamics and Control 2008 (with Roy Hoevenaars, Roderick Molenaar and Tom Steenkamp) Long memory and the term structure of risk, Journal of Financial Econometrics 2008 (with Rolf Tschernig and Jan Budek) HIDDEN SLIDE

2 Pension fund portfolio holdings Descriptive statistics 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 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 funds in 2011 Portfolios before/after 2008 Difference in average allocation between and Equity Bonds Alternatives Aggregate -7.0*** 2.4 *** 4.4 *** US Non-US -4.0 *** 0.7 *** 3.4 ** Public Non-public -8.0 *** 4.7 *** 3.3 *** DB Non-DB -4.3 ** -0.8 *** 4.8 Large Small *** 3.0 *** Old Young -6.6 ** 1.2 *** 5.2 * Portfolios before/after 2008 Difference in average equity allocation between and

3 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 Strategic allocation and state variables Asset only EQUITY Asset- Liability Asset only BONDS Asset- Liability Interest rate Dividend yield Credit spread +? -? Yield spread fixed effects: focus on explaining time series variation strategic weights reported by funds Residual asset class is Cash Dividend yield explains equity allocation, but with the wrong sign?!

4 Actual allocations Active allocation Active investment decisions: asset class return Explain active allocations using variables that signal investment opportunities portfolio return 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

5 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 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 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 , reflecting a move towards a more conservative asset allocation. Cross-sectional stdev in actual minus strategic Basic regression model CEM data, all funds

6 Hypotheses Extensions 1. Parameters dependent on past returns Returns implicit in passive change Asymmetry with dummy for MSCI<0 β 1 = 0 Portfolio change cannot be attributed to passive change (past returns) β 2 = 1 Actual change fully reflects strategic change β 3 = 1 Full adjustment to target 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 Coefficients do not depend on fund characteristics and past returns Basic model Dependent variable: actual change Passive change (t-stat) Strategic change Adjustment Fund FE N Y N Y Year FE N N Y Y R Asymmetry (1) Dependent variable: actual change Passive change (t-stat) Strategic change Adjustment (MSCI<0)*Passive Fund FE Y Y Y Y Year FE Y Y Y Y R

7 Asymmetry (2) Fund characteristics (1) Dependent variable: actual change Passive change (t-stat) Strategic change Adjustment (MSCI<0)*Passive Fund FE Y Y Y Y Year FE N N N N R β 1 β 2 β 3 Passive Strategic Adjustment Constant log(size) % Retired PUBLIC DB US Fund FE Y Year FE N R Fund characteristics (2) β 1 β 2 β 3 Passive Strategic Adjustment Constant log(size) % Retired PUBLIC DB US Fund FE N Year FE Y R Alternative assets Risky Equity Alternatives Passive t-stat Strategic Adjustment Fund FE Y Y Y Year FE Y Y Y R

8 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? Euro swap data (discount rate yield curves) Score-Driven Nelson-Siegel: Hedging Long-Term Liabilities Rogier Quaedvlieg, Peter Schotman (Maastricht University)

9 Hedging long-term liabilities Related own research Nelson-Siegel is a popular 3-factor term structure model that parsimoniously explains the shape and time variation in interest rate levels 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) A liability hedge is a portfolio with the same factor exposure as the liability and minimal residual risk. HIDDEN SLIDE How stable are factor loadings? How did they change after 2008? Duration plus A recent yield curve (March 31, 2014) Discount yields extracted from euro swap rates 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.

10 Parallel shifts Time-variation in λ t Rolling window estimates Much variation since 2008 sensitive to auxiliary econometric assumptions heteroskedasticty: both cross-sectional as well as time series Econometric model Estimation results SLIDES TO INCLUDE FROM OTHER PRESENTATION Estimates of lt sensitive to model for residuals

11 Hedging problem Hedge portfolio Fixed liability with very long duration: w 0 = -1 Find portfolio with same factor exposure and minimal residual risk 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 λ t 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.