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The Equity Risk Premium and other things

The Equity Risk Premium and other things. Craig Ansley. November 2009. Outline. What is the ERP? Historical values Estimation The ERP puzzle Failure of financial theory A new model for investment returns A solution to the ERP puzzle Solutions to other puzzles in finance

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The Equity Risk Premium and other things

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  1. The Equity Risk Premiumand other things Craig Ansley November 2009

  2. Outline • What is the ERP? • Historical values • Estimation • The ERP puzzle • Failure of financial theory • A new model for investment returns • A solution to the ERP puzzle • Solutions to other puzzles in finance • Implications for investment strategy

  3. What is the Equity Risk Premium? • Based on index returns • Commonly long-term government bonds B. Cornell “The Equity Risk Premium” 1999

  4. Historical ERP Typical forecasts around 4%

  5. Outline • What is the ERP? • Historical values • Estimation • The ERP puzzle • Failure of financial theory • A new model for investment returns • A solution to the ERP puzzle • Solutions to other puzzles in finance • Implications for investment strategy

  6. Utility and Risk Aversion More risk-averse Less risk-averse

  7. Consumption Asset-Pricing ModelLucas 1978 Maximise utility:

  8. The Equity Premium PuzzleMehra & Prescott 1985 Asset risk premium Sharpe ratio = σ(Asset return) = γx σ(Δc) x ρ(Δc) = 4 x 0.01 x 0.2 = 0.008 If equity volatility is 15%, then ERP should be 0.008 x .15 = 0.12% Observed ERP not explained by economic theory

  9. Outline • What is the ERP? • Historical values • Estimation • The ERP puzzle • Failure of financial theory • A new model for investment returns • A solution to the ERP puzzle • Solutions to other puzzles in finance • Implications for investment strategy

  10. Output At evolves as random walk + drift iid N(0,σ2) Drift Disaster model for economic outputBarro 2005 Disaster model vt = 0 large probability = large loss small probability

  11. What’s a disaster? • Natural disaster • Credit crisis • Wars • Bubbles • Agricultural disaster

  12. Calibrating the model--GDP Probability of disaster = 1.7% Source: Barro, NBER 2005 Based on 60 economic disasters in 35 countries 1900-2000

  13. A new model for asset returnsRiesz (1988), Barro 2005 Return over a given period = Expected return + Normal deviation + Disaster return Disaster return = 0 large probability = large loss small probability Predicted ERP close to historical values

  14. Time varying probability of disasterGabaix 2008 If the probability of disaster varies over time, several puzzles in finance are explained: • Equity premium puzzle • Excess volatility puzzle • Value-growth puzzle • Corporate bond spread puzzle • Correlations between asset classes close to 1 in bad times • High price of out-of-the money puts • Uncovered interest parity puzzle

  15. Equity premium puzzle • Economic theory predicts ERP of 0.1%(Mehra & Prescott, 1985) • Average ERP since 1880 has been 7% • ERP predicted by Barro’s model 7.1%

  16. Uncovered interest parity puzzle • Country A has interest rate 3%Country B has interest rate 1%Country A’s currency should depreciate by 2% • But FX rates of high interest rate countries do not trend down! • Carry traders subject to crash risk (Brunnermeier, Nagel & Pedersen, 2008) • Disaster model predictions:For countries with high disaster probabilities • High interest rates • Appreciating currencies • Currency crash risk (Farhi & Gabaix, 2009)

  17. High ERP is here to stay Disaster model • Explicit allowance for unusually bad events • Explains many problems with conventional theory • Can be calibrated from historical data

  18. Outline • What is the ERP? • Historical values • Estimation • The ERP puzzle • Failure of financial theory • A new model for investment returns • A solution to the ERP puzzle • Solutions to other puzzles in finance • Implications for investment strategy

  19. A simple example • Target fund $100 in T years • Contributions Ct at t = 0,1,…,20 • Ct set each year by valuing at rate i

  20. Penalty function

  21. Power penalty

  22. Assumptionsfrom Barro (2005) with Barro’s disaster model

  23. Equity Return Density

  24. Comparison of model allocationsi = 4.0%, d = 4.5%

  25. Dynamic Asset Allocation • Conventional: constant asset allocation • Alternative: change in response to performance • Dynamic programming problem e.g. Dempster et. al., British Actuarial Journal, 2002

  26. Dynamic Asset AllocationQuartiles of simulated strategies γ = 3, i = 4.0%, d = 4.5% Optimal constant strategy 29% equities

  27. DAA is worth an increase of 1.2% in returns Advantage of Dynamic Asset Allocation • Optimal penalty with constant strategy 641.7 • Optimal penalty with DAA 494.7 • If all returns raised by 1.2%, optimal constant strategy penalty drops to 494.7

  28. Conclusions • Standard model can’t explain ERP (or other things) • Disaster model solves many puzzles in finance • Historical disaster experience consistent with ERP • Disaster model requires lower equity allocations • DAA outperforms conventional approach

  29. Effect of Valuation Rateγ = 2.5, d = 4.5%

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