This document summarizes a guest lecture on portfolio optimization under uncertainty. The lecture discusses that risk is the probability of not achieving financial objectives. It is explained that investing should minimize this risk. Different portfolio optimization techniques are explored, including equal weighting, naive risk parity, robust risk parity, and mean-variance optimization using different return estimates. Dynamic parameter estimates based on historical volatility and covariance are used to re-optimize portfolios periodically. The results show that thoughtful optimization can materially reduce the probability of not achieving financial objectives compared to traditional static portfolios.

1. Portfolio Optimization Under Uncertainty
Guest Lecture
Adam Butler, CFA CAIA

2. Risk is the probability of not achieving financial objectives.
THE GOLDEN RULE OF INVESTMENT
MANAGEMENT
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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.
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4. The smooth geometric growth curve is a myth.
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5. Investing is a stochastic process; it is all about probabilities.
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6. The probability of any investment outcome is a function of
expected return, and volatility around that expectation.
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7. Given an expected return and volatility we can quantify a range
of outcomes at any investment horizon.
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Source: Shiller, FRED (2013)
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8. Portfolios must be robust to many possible market regimes.
STRUCTURAL DIVERSIFICATION
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9. Traditional stock/bond portfolios are very sensitive to market
regime.
Source: Deutsche Bank
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10. As a result, investors are vulnerable to an alarming range of
outcomes, even over long horizons.
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Source: Shiller, FRED (2013)
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11. How can we make portfolios resilient to a wider range of
regimes?
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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.
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13. Portfolios with assets that thrive in each major regime are
‘structurally diversified’.
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14. One possible structurally diversified portfolio.
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15. Combining structural diversification with dynamic portfolio estimates.
RISK BASED OPTIMIZATION
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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
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European Stocks - VGK
Long Treasuries - TLT

17. Equal weight resembles a traditional policy portfolio.
40% Equities
20% Real Estate
20% Alternatives
20% Fixed Income
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18. Results: Equal Weight, Rebalanced Monthly
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Data source: Bloomberg
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19. Results: Equal Weight, Rebalanced Monthly
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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.
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21. Asset class volatilities are wildly unstable.
Ranges of Asset Class Volatility
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Data source: Bloomberg
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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
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23. In an equal weight portfolio, the lunatics run the asylum.
Proportion of rolling 60-day historical volatility
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Data source: Bloomberg
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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
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Data source: Bloomberg
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25. Results: Naïve Risk Parity, Rebalanced Monthly
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Data source: Bloomberg
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26. Results: Naïve Risk Parity, Rebalanced Monthly
Data source: Bloomberg
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27. Naïve risk parity assumes all assets have similar returns, and are
similarly correlated. Is this a reasonable assumption?
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Data source: Bloomberg
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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
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Data source: Bloomberg
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29. Robust risk parity seeks portfolio weights which equalize
marginal risk contributions.
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Data source: Bloomberg
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30. Results: Robust Risk Parity (Equal Risk Contribution),
Rebalanced Monthly
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Data source: Bloomberg
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31. Results: Robust Risk Parity (Equal Risk Contribution),
Rebalanced Monthly
Data source: Bloomberg
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32. Maximizing portfolio Sharpe ratio.
MEAN VARIANCE OPTIMIZATION
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33. Asset returns are even more unstable than volatility and
covariance.
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Data source: Bloomberg
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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
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Value (long-term mean-reversion)

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
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36. Results: Long-term average returns with dynamic covariance
estimates.
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Data source: Bloomberg
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37. Results: Mean variance using long-term average returns with
dynamic covariance estimates.
Data source: Bloomberg
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38. This intuition is sound because returns are empirically and
theoretically proportional to risk.
Source: Bridgewater
Data source: Bloomberg
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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
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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
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41. Results: Heuristic mean-variance optimization with alternative
return estimates.
max.drawdown
rank
downside.semi
volatility
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Data source: Bloomberg
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42. Results: Heuristic mean-variance optimization with alternative
return estimates.
Data source: Bloomberg
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43. Did we achieve our goal of minimizing the risk of not achieving financial
objectives?
REVISITING THE GOLDEN RULE
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44. Thoughtful optimization can materially reduce the probability of
not achieving financial objectives.
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Data source: Bloomberg
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45. Thank you very much.
Questions?
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46. Contact info
Adam Butler
416.572.5477
adam@gestaltu.com
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