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3年弱前 (2014/01/14)にアップロードin政治・経済

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

- Portfolio Optimization Under Uncertainty

Guest Lecture

Adam Butler, CFA CAIA - Risk is the probability of not achieving financial objectives.

THE GOLDEN RULE OF INVESTMENT

MANAGEMENT

©2014 - 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 - The smooth geometric growth curve is a myth.

©2014 - Investing is a stochastic process; it is al about probabilities.

© Gestaltu

©2014 - The probability of any investment outcome is a function of

expected return, and volatility around that expectation.

© Gestaltu

©2014 - Given an expected return and volatility we can quantify a range

of outcomes at any investment horizon.

© Gestaltu

Source: Shiller, FRED (2013)

©2014 - Portfolios must be robust to many possible market regimes.

STRUCTURAL DIVERSIFICATION

©2014 - Traditional stock/bond portfolios are very sensitive to market

regime.

Source: Deutsche Bank

©2014 - As a result, investors are vulnerable to an alarming range of

outcomes, even over long horizons.

© Gestaltu

Source: Shiller, FRED (2013)

©2014 - How can we make portfolios resilient to a wider range of

regimes?

©2014 - Financial theory offers clues about how assets wil 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 - Portfolios with assets that thrive in each major regime are

‘structural y diversified’.

© Gestaltu

©2014 - One possible structural y diversified portfolio.

© Gestaltu

©2014 - Combining structural diversification with dynamic portfolio estimates.

RISK BASED OPTIMIZATION

©2014 - A simple structural y diversified universe for investigation.

U.S. Stocks – VTI

European Stocks - VGK

Japanese Stocks – EWJ

Emerging Market Stocks - EEM

U.S. REITs - ICF

International REITs - RWX

Commodities - DBC

Gold - GLD

Intermediate Treasuries – IEF

Long Treasuries - TLT

©2014 - Equal weight resembles a traditional policy portfolio.

40% Equities

20% Real Estate

20% Alternatives

20% Fixed Income

©2014 - Results: Equal Weight, Rebalanced Monthly

© Gestaltu

Data source: Bloomberg

©2014 - Results: Equal Weight, Rebalanced Monthly

©2014 - The simple policy portfolio framework has some chal enges.

• 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 - Asset class volatilities are wildly unstable.

Ranges of Asset Class Volatility

© Gestaltu

Data source: Bloomberg

©2014 - Dynamic Asset Al ocation 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 - In an equal weight portfolio, the lunatics run the asylum.

Proportion of rolling 60-day historical volatility

© Gestaltu

Data source: Bloomberg

©2014 - 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 - Results: Naïve Risk Parity, Rebalanced Monthly

© Gestaltu

Data source: Bloomberg

©2014 - Results: Naïve Risk Parity, Rebalanced Monthly

Data source: Bloomberg

©2014 - Naïve risk parity assumes al assets have similar returns, and are

similarly correlated. Is this a reasonable assumption?

© Gestaltu

Data source: Bloomberg

©2014 - 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 - Robust risk parity seeks portfolio weights which equalize

marginal risk contributions.

© Gestaltu

Data source: Bloomberg

©2014 - Results: Robust Risk Parity (Equal Risk Contribution),

Rebalanced Monthly

© Gestaltu

Data source: Bloomberg

©2014 - Results: Robust Risk Parity (Equal Risk Contribution),

Rebalanced Monthly

Data source: Bloomberg

©2014 - Maximizing portfolio Sharpe ratio.

MEAN VARIANCE OPTIMIZATION

©2014 - Asset returns are even more unstable than volatility and

covariance.

© Gestaltu

Data source: Bloomberg

©2014 - 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

Value (long-term mean-reversion)

sweet spot

Data source: Bloomberg

©2014 - 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 - Results: Long-term average returns with dynamic covariance

estimates.

© Gestaltu

Data source: Bloomberg

©2014 - Results: Mean variance using long-term average returns with

dynamic covariance estimates.

Data source: Bloomberg

©2014 - This intuition is sound because returns are empirical y and

theoretical y proportional to risk.

Source: Bridgewater

Data source: Bloomberg

©2014 - 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(r ) = E(σ ).

i

i

Data source: Bloomberg

©2014 - Volatility is not the only measure of risk. And it’s worthwhile

considering other simple methods like rank.

Downside

Volatility

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 - Results: Heuristic mean-variance optimization with alternative

return estimates.

max.drawdown

rank

downside.semi

volatility

© Gestaltu

Data source: Bloomberg

©2014 - Results: Heuristic mean-variance optimization with alternative

return estimates.

Data source: Bloomberg

©2014 - Did we achieve our goal of minimizing the risk of not achieving financial

objectives?

REVISITING THE GOLDEN RULE

©2014 - Thoughtful optimization can material y reduce the probability

of not achieving financial objectives.

© Gestaltu

Data source: Bloomberg

©2014 - Thank you very much.

Questions?

©2014 - Contact info

Adam Butler

416.572.5477

adam@gestaltu.com

©2014