OPTIMAL PORTFOLIOS FOR THE LONG RUN

Transcription

1 OPTIMAL PORTFOLIOS FOR THE LONG RUN Michael Finke, PhD, CFP Texas Tech University Co-authors: David Blanchett Morningstar Investment Management Wade Pfau The American College paper available at

2 Is Time Diversification Real? Bodie (1995), Samuelson (1963) not consistent with market efficiency and option pricing Thorley (1995) and others theories exist that explain time diversification Planners historically, have provided inflation protection and solid long-run performance 1 1

3 Stocks for the Long Run = Bull? The standard models that are used to give investment advice to millions of Americans are fundamentally wrong. We're told that over time, stocks get less risky, but that's bull. Stocks are always risky -- whether in the short or long run. From Money Magazine, 2009 Zvi Bodie, Ph.D. Boston University 2 2

4 Time Diversification Debate Zvi Bodie, Ph.D. Boston University Having a long time horizon and being risk averse are two completely different things. The popular literature has basically said if you have a long time horizon you're tolerant towards risk. That's the fundamental fallacy. Source: NAPFA 2004 Conference Stocks are relatively safer in the long run than random walk theory would predict. Doesn't mean they're safe. The whole point is that they are relatively safer... Does the fact that equity returns display long run mean reversion change your equity strategy? The answer is definitely yes. Change your allocation strategy? The answer is definitely yes. Source: NAPFA 2004 Conference Jeremy Siegel, Ph.D. Wharton School 3 3

5 $10,000 Ibbotson SBBI Stocks, Bonds, Bills, and Inflation $26,641 1, Compound annual return Small stocks 12.3 % Large stocks Government bonds Treasury bills Inflation $4,667 $ $21 $13 1 Past performance is no guarantee of future results. Hypothetical value of $1 invested at the beginning of Assumes reinvestment of income and no transaction costs or taxes. This is for illustrative purposes only and not indicative of any investment. An investment cannot be made directly in an index

6 5 5 Holding Period and Standard Deviation Source: Campbell and Viceira, 2002

7 Worst Case Scenarios Over Time ( ) Source: Bennyhoff,

8 40-Year, $5,000 real/year Source: Dolvin, Templeton and Rieber, 2010 Stock/Bond $1 Million $2 Million $3 Million $4 Million $5 Million 0/ % 19.8% 7.0% 2.7% <0.1% 30/ % 59.6% 20.1% 8.9% 6.2% 50/ % 78.8% 49.0% 28.8% 18.1% 70/ % 87.3% 59.9% 40.0% 29.2% 100/0 96.3% 85.8% 68.8% 58.8% 49.1% 100 Age 94.1% 79.3% 49.5% 29.6% 18.9% Age 95.3% 87.6% 68.1% 48.6% 29.7% 7 7

9 8 8 Why Simulations Favor Stocks

10 -10.1% 3.0% 31.0% 34.1% 7.1% Are Returns Random? 8.99% -38.5% 13.7% 23.5% 20.3% -1.5% 4.5% 27.3% -6.6% 12.4% 26.3% 9 9

11 10 10 Robert Shiller s Volatility Puzzle (1981)

12 Standardized Scale Does Risk Tolerance Change Over Time? Changing Appetite for Risk May Affect Stock Prices Jan-07 Apr-07 Jul-07 Oct-07 Jan-08 Apr-08 Jul-08 Oct-08 Jan-09 Date Source: Guillemette and Finke, 2014 Risk tolerance/market correlation (r = 0.90) Risk Tolerance S&P 500

13 Appetite for Risk Changes with Consumer Sentiment Source: Guillemette & Finke,

14 Appetite for Risk Increases As Prices Rise Source: Guillemette & Finke,

15 14 14 Sentiment and Short-Run Returns Source: Baker & Wurgler, 2007

16 Implications of Time Varying Sentiment High short-run stock volatility Prices mean revert over time Standard deviation declines with holding period Long-run investors benefit from higher equity allocation 15 15

17 Portfolio Implications Source: Barberis, 2000 High equity premium + predictability = high optimal stock allocations But, parameter uncertainty makes us more cautious 16 16

18 Criticism: America Got Lucky An International Perspective on Historical Returns 1.28% 1.84% 2.34% 2.72% 4.06% 5.01% Average Compounded Real Return for a 60% stock, 40% bond portfolio: Source: Dimson, Marsh, and Staunton 17 17

19 Answer: Use International Data Equity Risk Premium Geometric Average Real Annual Return Vs. Cash Vs. Bonds Cash Bonds Stocks Australia 6.55% 5.60% 0.70% 1.60% 7.30% Belgium 2.73% 2.25% -0.26% 0.20% 2.46% Canada 4.09% 3.38% 1.54% 2.23% 5.70% Denmark 2.79% 1.78% 2.16% 3.18% 5.01% Finland 5.75% 5.32% -0.51% -0.10% 5.21% France 5.95% 2.96% -2.81% 0.01% 2.98% Germany 5.56% 4.85% -2.38% -1.71% 3.05% Ireland 3.16% 2.61% 0.67% 1.20% 3.85% 18 18

20 Criticism: Equity returns are higher than bonds, but must consider downside risk Answer: Use a utility function to estimate optimal portfolios Invest wealth now and consume all in future period Ignore volatility between investment and consumption Estimate utility maximizing portfolio based on risk aversion 19 19

21 Accounting for Decreasing Marginal Utility 20 20

22 Data and Methods Rolling return data from 20 countries between 1900 and 2012 (DMS data) Create rolling periods from 1 to 20 years Estimate growth in portfolios over each rolling period Estimate how much utility we d get from consuming portfolio at end of period Optimize asset allocation that maximizes utility for each set of rolling periods Calculate optimal allocations for varying levels of risk aversion 21 21

23 Optimal Equity Allocation Model Optimal Equity Allocation Based on Holding Period Example: The United States Intercept = optimal short-run equity allocation.. Slope = time diversification benefit (optimal increase per year) 100% 80% y = x R² = % 40% 20% 0% Investment Period 22 22

24 Select Individual Country Results Low Risk Aversion Risk Aversion = 4 Risk Aversion = 8 High Risk Aversion Intercept Slope Intercept Slope Intercept Slope Intercept Slope Australia 81.69% 0.38% 90.06% 0.07% 93.96% -0.11% 94.37% -0.07% Belgium 61.37% 2.45% 45.76% 2.78% 40.63% 2.26% 51.46% 2.07% Canada 97.26% 0.19% 60.12% 2.66% 25.89% 4.31% 7.13% 5.33% Denmark 74.40% 1.74% 46.52% 3.48% 26.72% 4.59% 22.50% 4.45% Finland 82.44% 1.20% 81.43% 1.27% 89.50% 0.60% 84.78% 0.83% France 81.38% 1.28% 77.29% 1.59% 72.96% 1.84% 69.14% 2.07% Germany 94.37% 0.40% 98.04% -0.35% 79.38% 0.51% 73.94% 0.64% Ireland 58.40% 2.50% 19.47% 4.00% 9.39% 2.18% -3.39% 1.93% 23 23

25 Equity Allocation Asset Allocation & Holding Period y = level of risk aversion (higher more averse) 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Year γ = 1 γ = 2 γ = 4 γ = 8 γ =

26 Optimizing Portfolios by Holding Period What stock allocation would have produced the greatest expected utility if you waited 1, 4, 7, years to spend it? What stock allocation would have been optimal if you were risk tolerant? What if you were risk averse? 25 25

27 Level of Risk Aversion Level of Risk Aversion Optimal Equity Allocation by Risk Aversion Coefficient and Investment Period United States 1 (Very Low) 20 Country Average 1 (Very Low) Equity Allocation 4 4 # 0%-10% # ## # ## 11%-20% 21%-30% 31%-40% # ## # ## 41%-50% 51%-60% 61%-70% (Very High) (Very High) # ## 71%-80% # 81%-90% ## 91%-100% Investment Period (Years) Investment Period (Years) 26 26

28 Anomalies Australia Switzerland 27 27

29 Simulating with an Autoregressive Model Fama & French (1988) estimate 5-year mean reverting process Identify 5-year autoregressive model from DMS data Simulate returns based on past return distributions from DMS with autoregressive process 28 28

30 Autoregressive Simulation Captures Time Diversification AR(5) Simulation No AR Simulation 29 29

31 What if the Equity Premium Is Going Away? (Short Baa Corp, Long S&P for 10 Years) Source: Blanchett, Finke and Pfau,

32 What Happens in a Low Equity Premium Environment? Source: Asness,

33 How Low Would Equity Premium Need to Be to Abandon Time Diversification? Average Equity Premium Risk tolerant (y=4), 5 year -0.3% Risk tolerant, 10 year -0.7% Risk tolerant, 20 year -1.6% Risk averse (y=8), 5 year -0.4% Risk averse, 10 year -1.6% Risk averse, 20 year -2.2% 32 32

34 Is Time Diversification Going Away? Time Diversification Benefit (% increase per year) Optimal Initial Equity Allocation

35 Conclusions Strong evidence that stocks are more attractive for longrun investors Mean reversion drives long-run equity advantage Reward for ignoring short-run performance Written investment policy statement and target date funds can help maintain long-run focus 34 34