Investment Horizon, Risk Drivers and Portfolio Construction Institute of Actuaries Australia Insights Seminar 8 th February 2018 A/Prof. Geoff Warren The Australian National University
2 Overview The key drivers of investment risk shift with horizon Short-term: changes in discount rates, cash flow expectations Long-term: expected return level, reinvestment rates, cash flow delivery Optimal portfolios may differ with horizon, depending on: Whether there is mean-reversion Objective function: referencing a target for wealth or returns induces increasing preference for equities with horizon Implications Focus investment process on drivers that matter most for your horizon Consider reference-based utility functions, e.g. prospect theory Mean-variance and factor paradigm is the source of some misdirection
3 Motivation Some influences: CIFR long-term investing research ANU Student Managed Fund MDUF project (see http://membersdefaultutilityfunction.com.au/) Mean-variance optimisation and factor analysis focused on returns over a single (short) period a distraction for long-term investors Need to better connect analysis to objectives especially where they involve longer-term wealth outcomes, e.g. retirement savings Short-term => price drivers Long-term => value drivers Utility defined over wealth places a score on entire distribution
Existing research MPT, horizon and non-iid returns (Campbell & Viceira, etc) Multi-period asset pricing (Merton, etc) Changes in the investment opportunity set Dynamic asset allocation / stochastic control Cash flow vs. discount rate effects (Campbell & Shiller, etc) Cash flow innovations = permanent loss of value Discount rate changes = reordering of return sequence, plus change in investment opportunity set Debate over time diversification and Kelly strategies Kelly strategies: asset with highest geometric return almost stochastically dominates as horizon lengthens Samuelson and Merton beg to differ 4
5 PART A: Analysis of risk drivers and horizon Focus on end-of-horizon wealth More general than first appears Investors typically don t think dynamically, they react to circumstances Estimate expected accumulated wealth over time Includes wealth generated from reinvestment by either: (a) The investor, at prevailing discount rates each period (b) An agent, e.g. companies possibly at a different rate DCF principles, e.g. at any time t, Price = NPV of future cash flows at the discount rate prevailing at that time Equities, 10-year bond, 5-year bond and 1-year bond (cash proxy) Establish baseline expected wealth given cash flows, discount rates and reinvestment rates; then investigate impact of change in inputs
6 Drivers of wealth over time Driver Nature Horizon effect on wealth 1) Expected return Foundation of baseline expected wealth at end of horizon Impact builds with horizon due to compounding 2) Discount rate innovations 3a) Reinvestment rates Distributions 3b) Reinvestment rates Retention 4) Cash flow innovations Causes immediate price change; but level of expected return adjusts thereafter Distributions reinvested by investor at different rate than expected due to change in discount rates Retained cash flows reinvested at different rate than expected due to changing investment opportunities, or agency effects Price and hence wealth impacted by changes in cash flow expectations Relation negative in short term (rise in discount rate => lower price); but impact reduces and may reverse over time Impact increases with horizon Impact increases with horizon Impact felt across all horizons: permanent loss of value
Percentage of Accumulated Wealth 7 Contributions to accumulated wealth 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Equities Price at End Dividends from Existing Operations Dividends from Reinvestment Reinvestment of Dividends 0 5 10 15 20 25 Horizon (Years)
Accumulated Wealth per $1 Invested Accummulated vs. Target Wealth 6 5 4 3 2 1 Expected wealth, target wealth and shortfall Horizon and Expected Wealth Equities (7% Expected Return) 10-Year Bond (3.0% Yield) 1-Year Bond (2% Yield) Target 4.5% Return (Real 2.5%) 0 5 10 15 20 25 Horizon (Years) 80% 70% 60% 50% 40% 30% 20% 10% 0% -10% -20% -30% -40% -50% Horizon and Expected Shortfall Equities 10-Year Bond 1-Year Bond 0 5 10 15 20 25 Horizon (Years) Expected return may be considered return on offer in the market Easier to observe for bonds than equities Effect of mis-estimating expected return compounds with horizon 8
Change in Wealth 9 Impact of +1% increase in discount rates 30% 25% 20% 15% 10% 5% 0% -5% -10% -15% 1-Year Bond 5-Year Bond 10-Year Bond Equities 0 5 10 15 20 25 Horizon (Years) (Duration determines initial price decline, and breakeven point)
% Change in Wealth 10 Wealth effects of various innovations for equities 14% 12% 10% 8% 6% 4% 2% 0% -2% -4% -6% -8% -10% -12% -14% Discount Rate +1% in Year 1 Cash Flows Dislocate -12% in Year 1 Company Reinvestment Rate -1% 0 5 10 15 20 25 Horizon (Years)
11 Inflation Real effects are the issue Discount rates: Inflation changes affect nominal rates. But do they affect real rates? Or do rates fully adjust, and neutralise the impact? Cash flows: How do real cash flows respond to inflation changes? Nominal bonds real value of promised cash flow decreases. This is a cash flow effect under the framework. Equities depends on how cash flows respond Inflation-linked bonds cash flow is guaranteed in real terms (but they are still exposed to discount rate and reinvestment rate effects)
Change in Real Wealth 12 Effect of +1% inflation innovation 8% 4% 0% -4% -8% -12% -16% 1-Year Bond 5-Year Bond 10-Year Bond Equities 0 5 10 15 20 25 Horizon (Years) Chart assumes: Inflation +1% Nominal rates +1%; real rates unchanged Equity reinvestment rates increase by 1% (+0.5% growth at 50% retention rate); but existing cash flows do not adjust
Change in Real Wealth 13 Possible equity cash flow impacts of inflation +1% 10% 5% +1% Reinvestment Rate, +1% Organic Growth 0% -5% +0% Reinvestment Rate, +1% Organic Growth -10% -15% +1% Reinvestment Rate, +0% Organic Growth -20% -25% +0% Reinvestment Rate, +0% Organic Growth 0 5 10 15 20 25 Horizon (Years)
Risk drivers: Implications for investment processes Investors of all horizons need to worry about cash flow effects Cash flow innovations amount to a permanent change in wealth. Short-horizon investors might focus on when cash flow innovations will change market expectations, and hence impact on prices. Timing is unimportant to long-horizon investors. For them, it is about what cash flows will be delivered eventually. Discount rate effects vary with investor horizon Short-horizon investors need to worry about repricing effects Long-horizon investors should care about impact on reinvestment rates Asset duration vs. investor horizon matters Long-term investors should also be more concerned with: Reinvestment rates under agency arrangements Initial expected returns 14
15 PART B: Creating distributions of wealth Various methods available (should embed covariance structure) Simulations from historical data Statistical models, e.g. VAR, regime switching Structural models imposing relations between variables (e.g. Wilkie) Value-based models, e.g. plowback models for equities Scenario analysis Framework of Part A implemented using basic model: Structural model with two state variables: a) Inflation drives discount rate and reinvestment rate syndrome b) Equity cash flows from existing operations random walk Statistical models based on US equity, bond and inflation data Calibrated to generate plausible expected returns and volatility
% of Draws < -30% -20- -10-0% 0-10% 10-20% 20-30% 30-40% 40-50% 51-60% 60-70% >60% % of Draws < -2% -2-0% 0-2% 2-4% 4-6% 6-8% 8-10% 10-12% 12-14% 16 >16% Distributions over 1-year and 10-year horizons 60% Growth in Wealth over 1-Year 90% Growth in Wealth over 10-Years 50% 40% 30% 1-Year Bond 10-Year Bond Equities Equities - Stochastic Mean 80% 70% 60% 50% 40% 1-Year Bond 10-Year Bond Equities Equities - Stochastic Mean 20% 30% 10% 20% 10% 0% 0%
17 PART C: Portfolio construction A distribution of wealth outcomes for candidate portfolios can be generated uisng wealth projections for each asset Covariance should be embedded within the joint distribution Modelling may assume rebalancing or other pre-specified conditional strategies, if desired. A score is given to each point on the resulting wealth distribution using an objective (i.e. utility) function Optimal portfolio is the one that maximises expected utility
18 Objective functions Reference-dependent - general form (drawing on Tarlie, 2017): U PT = I W W 1 γ W W 1 I W W <1 λ W W U PT = prospect theory utility W / W* = wealth / target wealth I = indicator function (1, 0) α = curvature parameter on gains, i.e. wealth > target (α = 0.62) β = curvature parameter on losses, i.e. wealth < target (β = 0.88) γ = weighting parameter on gains, i.e. wealth > target (γ = 1) λ = weighting parameter on losses, i.e. wealth < target (λ = 2.25) β 1 Power utility U PU = W 1 CRRA 1 CRRA U PU = power utility CRRA = coefficient of relative risk aversion (= 5.1)
% of Draws < 0.7 0.7-0.8 0.8-0.9 0.9-1.0 1.0-1.1 1.1-1.2 1.2-1.3 1.3-1.4 1.4-1.5 > 1.5 % of Draws < 0.6 0.6-0.8 0.8-1.0 1.0-1.2 1.2-1.4 1.4-1.6 1.6-1.8 1.8-2.0 2.0-2.2 2.2-2.4 2.4-2.6 19 > 2.6 Asset distributions through to portfolios 55% 50% 45% 40% 35% 30% 25% 20% 15% 10% 5% 0% 1-Year Horizon Fixed Income (0/60/40) Balanced (60/30/10) Equities Only Optimal (40/60/0) 80% 70% 60% 50% 40% 30% 20% 10% 0% 10-Year Horizon Fixed Income (0/60/40) Balanced (60/30/10) Equities Only (Optimal Prospect) Optimal Power Utility (87/13/0) Wealth / Target Wealth / Target
20 Portfolio statistics Portfolio Fixed Income Balanced (60/30/10) 1-Year Horizon Equity Only 40/60 Portfolio, Calibrated Utility Parameters Fixed Income Balanced (60/30/10) 10-Year Horizon Optimal: Prospect Theory Equity Only Optimal: Power Utility Wealth vs Target Mean -0.7% 2.9% 5.0% 2.3% -16.0% 14.0% 33.6% 27.3% Standard Deviation 4.9% 11.8% 18.2% 9.5% 5.0% 27.6% 45.0% 39.3% Percentiles 100% 13% 64% 106% 51% 3% 189% 320% 277% 95% 7% 24% 38% 19% -8% 66% 118% 101% 90% 6% 18% 29% 15% -10% 51% 93% 79% 75% 3% 10% 16% 8% -13% 29% 57% 48% 50% -1% 2% 3% 2% -16% 10% 27% 21% 25% -4% -5% -8% -4% -19% -6% 1% -1% 10% -7% -11% -17% -10% -22% -17% -17% -17% 5% -9% -15% -21% -12% -24% -23% -26% -25% 0% -18% -31% -42% -28% -35% -47% -60% -55% Shortfall Measures Probability Shortfall 56% 43% 43% 42% 100% 34% 24% 26% Expected Shortfall -4% -8% -11% -6% -16% -13% -16% -15%
21 What if mean-reversion is removed? 100% Optimal Equity Weighting 80% Probability of Underperformance 90% 80% 70% 60% 50% Prospect Theory Utility Power Utility 70% 60% 50% 40% Bonds vs. Target Wealth Equities vs. Target Wealth Equities vs. Bonds 40% 30% 30% 1 2 3 4 5 6 7 8 9 10 Horizon (Years) 20% 1 2 3 4 5 6 7 8 9 10 Horizon (Years)
22 Takeaway messages Horizon matters for the risks of most concern to an investor, and hence investment process design Objective functions are influential Samuelson was right within a narrow frame. However Adding a wealth target makes quite an impact Prospect theory functions are well worth considering when a target is involved (like retirement) plus the units are more intuitive Mean reversion matters as the horizon extends beyond one period Mean-variance optimisation should be replaced by utility function analysis for many applications. MDUF.v1 is a start!
23 Questions? Discussion?