Portfolio Optimization Under Uncertainty

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Presentation to the Queen's Master of Finance, Class of 2014

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Portfolio Optimization Under Uncertainty

  1. 1. Portfolio Optimization Under Uncertainty Guest Lecture Adam Butler, CFA CAIA
  2. 2. Risk is the probability of not achieving financial objectives. THE GOLDEN RULE OF INVESTMENT MANAGEMENT ©2014
  3. 3. What is the primary risk for most investors? For most investors, risk is defined as the probability of not meeting financial objectives. Investing should have the exclusive objective of minimizing this risk. ©2014
  4. 4. The smooth geometric growth curve is a myth. ©2014
  5. 5. Investing is a stochastic process; it is all about probabilities. © Gestaltu ©2014
  6. 6. The probability of any investment outcome is a function of expected return, and volatility around that expectation. © Gestaltu ©2014
  7. 7. Given an expected return and volatility we can quantify a range of outcomes at any investment horizon. © Gestaltu Source: Shiller, FRED (2013) ©2014
  8. 8. Portfolios must be robust to many possible market regimes. STRUCTURAL DIVERSIFICATION ©2014
  9. 9. Traditional stock/bond portfolios are very sensitive to market regime. Source: Deutsche Bank ©2014
  10. 10. As a result, investors are vulnerable to an alarming range of outcomes, even over long horizons. © Gestaltu Source: Shiller, FRED (2013) ©2014
  11. 11. How can we make portfolios resilient to a wider range of regimes? ©2014
  12. 12. Financial theory offers clues about how assets will react in different environments. • Stocks react favorably to accelerating economic growth and decelerating inflation. • Treasuries respond favorably to decelerating growth and inflation • Commodities respond favorably to accelerating inflation. • Gold responds well to some kinds of inflation, and to the actions that authorities take to battle deflation. • Etc. ©2014
  13. 13. Portfolios with assets that thrive in each major regime are ‘structurally diversified’. © Gestaltu ©2014
  14. 14. One possible structurally diversified portfolio. © Gestaltu ©2014
  15. 15. Combining structural diversification with dynamic portfolio estimates. RISK BASED OPTIMIZATION ©2014
  16. 16. A simple structurally diversified universe for investigation. U.S. Stocks – VTI Japanese Stocks – EWJ Emerging Market Stocks - EEM U.S. REITs - ICF International REITs - RWX Commodities - DBC Gold - GLD Intermediate Treasuries – IEF ©2014 European Stocks - VGK Long Treasuries - TLT
  17. 17. Equal weight resembles a traditional policy portfolio. 40% Equities 20% Real Estate 20% Alternatives 20% Fixed Income ©2014
  18. 18. Results: Equal Weight, Rebalanced Monthly © Gestaltu Data source: Bloomberg ©2014
  19. 19. Results: Equal Weight, Rebalanced Monthly ©2014
  20. 20. The simple policy portfolio framework has some challenges. • Assets included in the portfolio have wildly different ambient volatilities. • Asset volatilities change profoundly over time. • Asset correlations change dramatically over time. • As a result, asset risk contributions are highly unstable. ©2014
  21. 21. Asset class volatilities are wildly unstable. Ranges of Asset Class Volatility © Gestaltu Data source: Bloomberg ©2014
  22. 22. Dynamic Asset Allocation applies dynamic parameter estimates to re-optimize portfolios at each rebalance period. • Examples of potential dynamic optimizations: – Naïve risk parity – Robust risk parity – Mean-variance optimization • The following examples use short-term historical realized volatility and covariance as inputs for dynamic portfolio optimization. – Volatility estimate = 60 day historical observed volatility – Covariance estimate = 250 day historical observed covariance ©2014
  23. 23. In an equal weight portfolio, the lunatics run the asylum. Proportion of rolling 60-day historical volatility © Gestaltu Data source: Bloomberg ©2014
  24. 24. If we can estimate volatility, we can use these estimates to scale weights by inverse volatility: naïve risk parity. Portfolio weights scaled by 1/rolling 60-day historical volatility © Gestaltu Data source: Bloomberg ©2014
  25. 25. Results: Naïve Risk Parity, Rebalanced Monthly © Gestaltu Data source: Bloomberg ©2014
  26. 26. Results: Naïve Risk Parity, Rebalanced Monthly Data source: Bloomberg ©2014
  27. 27. Naïve risk parity assumes all assets have similar returns, and are similarly correlated. Is this a reasonable assumption? © Gestaltu Data source: Bloomberg ©2014
  28. 28. An asset contributes risk to a portfolio in proportion to its volatility AND its correlation to the portfolio itself. 37% Volatility Reduction Negative MRC © Gestaltu Data source: Bloomberg ©2014
  29. 29. Robust risk parity seeks portfolio weights which equalize marginal risk contributions. © Gestaltu Data source: Bloomberg ©2014
  30. 30. Results: Robust Risk Parity (Equal Risk Contribution), Rebalanced Monthly © Gestaltu Data source: Bloomberg ©2014
  31. 31. Results: Robust Risk Parity (Equal Risk Contribution), Rebalanced Monthly Data source: Bloomberg ©2014
  32. 32. Maximizing portfolio Sharpe ratio. MEAN VARIANCE OPTIMIZATION ©2014
  33. 33. Asset returns are even more unstable than volatility and covariance. © Gestaltu Data source: Bloomberg ©2014
  34. 34. Returns are more forecastable in the very short term, and the very long term. Not so much in the middle. High frequency arms race Momentum sweet spot Data source: Bloomberg ©2014 Value (long-term mean-reversion)
  35. 35. Is it helpful to use long-term average return estimates with dynamic covariance estimates? Long-Term Returns* DBC 3.8% EEM 9.0% EWJ 7.8% GLD 4.3% ICF 6.8% IEF 4.3% RWX 6.0% TLT 3.3% VGK 7.8% VTI 7.5% *Source: JPM Long Term Capital Market Return Assumptions, December 2013 ©2014
  36. 36. Results: Long-term average returns with dynamic covariance estimates. © Gestaltu Data source: Bloomberg ©2014
  37. 37. Results: Mean variance using long-term average returns with dynamic covariance estimates. Data source: Bloomberg ©2014
  38. 38. This intuition is sound because returns are empirically and theoretically proportional to risk. Source: Bridgewater Data source: Bloomberg ©2014
  39. 39. Are historical averages the only source of return estimates? • Mean variance optimization is implemented by maximizing the Sharpe Ratio. • Maximum Diversification (Choueifaty, 2008) is mean-variance optimization where E(ri) = E(σi). Data source: Bloomberg ©2014
  40. 40. Volatility is not the only measure of risk. And it’s worthwhile considering other simple methods like rank. Volatility Downside Semivariance Drawdown Rank DBC 12.5% 16.0% 60.3% 1 EEM 13.1% 19.4% 69.9% 5 EWJ 14.4% 19.5% 58.9% 5 GLD 9.0% 11.9% 38.8% 1 ICF 10.2% 16.6% 77.6% 4 IEF 4.2% 5.5% 11.4% 2 RWX 8.3% 13.0% 73.8% 4 TLT 6.9% 9.8% 26.6% 3 VGK 11.4% 16.7% 63.3% 5 VTI 10.1% 14.1% 55.5% 5 Data source: Bloomberg ©2014
  41. 41. Results: Heuristic mean-variance optimization with alternative return estimates. max.drawdown rank downside.semi volatility © Gestaltu Data source: Bloomberg ©2014
  42. 42. Results: Heuristic mean-variance optimization with alternative return estimates. Data source: Bloomberg ©2014
  43. 43. Did we achieve our goal of minimizing the risk of not achieving financial objectives? REVISITING THE GOLDEN RULE ©2014
  44. 44. Thoughtful optimization can materially reduce the probability of not achieving financial objectives. © Gestaltu Data source: Bloomberg ©2014
  45. 45. Thank you very much. Questions? ©2014
  46. 46. Contact info Adam Butler 416.572.5477 adam@gestaltu.com ©2014

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