Asset Allocation and Factor Investing: An Integrated Solution

1© 2018 Windham Capital Management, LLC. All rights reserved.
Confidential. Not for redistribution.
2018 1
Asset Allocation
and Factor Investing:
An Integrated Solution
Mark Kritzman
Windham Capital Management, LLC
CEO
This presentation is based on an article coauthored by Alain Bergeron, Mark Kritzman, and Gleb Sivitsky entitled “Asset Allocation
and Factor Investing: An Integrated Approach” published in The Journal of Portfolio Management in 2018.

ASSET ALLOCATION VERSUS FACTOR INVESTING
Why allocate to asset classes?
 Asset classes are easy to observe and directly investable.
 Portfolios composed from asset classes are more stable out of sample than
portfolios composed from factors.
Why allocate to factors?
 Factors are the fundamental determinants of portfolio performance, whereas
asset classes are arbitrary constructs.
 Factors carry risk premiums that are not directly available from asset classes.

ESTIMATION ERROR

THE SOLUTION
 Investors should continue to use asset classes as the building blocks
for forming portfolios.
 But they should combine them in a way that balances their expected
return and risk with adherence to a preferred factor profile.
 This approach preserves the benefit of investing in asset classes that
are more stable, while enabling investors to capture preferred factor
exposures.

THE SOLUTION
The traditional approach for constructing portfolios is to maximize expected
utility based only on expected return and variance.
𝐸 𝑈 = 𝜇 𝑝 − 𝜆 𝑅𝐴 𝜎 𝑝
2
𝐸 𝑈 equals expected utility
𝜇 𝑝 equals portfolio expected return
𝜆 𝑅𝐴 equals risk aversion
𝜎 𝑝
2
equals portfolio variance

THE SOLUTION
To integrate asset allocation and factor investing, we simply add a term to
the traditional objective function to reflect aversion to deviating from a factor
profile.
𝐸 𝑈 = 𝜇 𝑝 − 𝜆 𝑅𝐴 𝜎 𝑝
2 − 𝜆 𝐷𝐹𝑃 𝜉 𝐹𝑃
2
𝜆 𝐷𝐹𝑃 equals aversion to deviations from the
factor profile.
𝜉 𝐹𝑃equals deviations from the factor profile

HOW TO BUILD A FACTOR PROFILE
 We define a factor profile as a weighted average of our preferred combination
of factor exposures.
 Because factors are often measured in different units, we record their changes
as logarithms.
𝑅𝑙𝑛 = ln 1 +
𝐹𝑉 𝑇−𝐹𝑉 𝑇−1
𝐹𝑉 𝑇−1
𝑅𝑙𝑛 equals the natural logarithm of the factor
return
ln equals natural logarithm
𝐹𝑉𝑇 equals the factor index value this period
𝐹𝑉𝑇−1 equals the factor index value one period
prior.

HOW TO BUILD A FACTOR PROFILE
 Suppose we are interested in macroeconomic factors such as GDP growth or
inflation.
 The realized values of macroeconomic factors are relatively stable because,
unlike assets, they are not traded and thus not subject to investor uncertainty.
 Moreover, expectations about macroeconomic factors are typically formed from
past realizations, so they too are stable.
 Therefore, the covariances between factor returns and asset returns are too
low to capture meaningful factor sensitivities.
 We overcome this problem by augmenting the factor returns by an
appropriately sized multiplier.

TO SUMMARIZE
1. We estimate the expected returns and covariances of the asset classes in which
we wish to invest.
2. We identify factors to which we seek exposure, either positive or negative.
3. We create factor time series by recording changes in the factor values measured
in log units and rescaling them to render the portfolio reasonably sensitive to
changes in factor values.
4. We define a factor profile by calculating a weighted average of the rescaled
factor returns in accordance with our factor preferences.
5. We estimate the covariances between the asset classes and the factor profile.
6. We solve for a factor-sensitive optimal portfolio by maximizing an expanded
objective function that incorporates both aversion to absolute risk and aversion
to deviations from the factor profile.

CASE STUDY: STAGFLATION
1. Suppose we are concerned about the prospects for stagflation, in
which the economy experiences stagnant growth coupled with high
inflation.
2. We do not feel confident in adjusting the expected returns, standard
deviations, and correlations explicitly.
3. Instead, we want a portfolio whose returns will co-vary positively with
inflation and negatively with economic growth.

Expected Returns, Standard Deviations, and Correlations

Optimal Portfolio Ignoring Factor Exposures

1. If we are equally confident of our views about inflation and economic growth,
we should expect the optimal portfolio to be tilted less toward equities and
U.S. corporate bonds and more toward commodities and cash equivalents.
2. The impact on Treasury bonds should be neutral, because inflation surprises
would be negative for Treasury Bonds, but negative growth surprises would
be positive.
3. If we are twice as confident about our view for inflation compared to
economic growth, we should expect an additional tilt away from Treasury
bonds.

Factor-Insensitive and Factor-Sensitive Portfolios
(Factor Deviation Aversion = 0.2)

CASE STUDY: PORTFOLIO WEIGHTS

CASE STUDY: PERFORMANCE
1. Conditioned portfolios should perform better than the unconditioned portfolio
during periods that correspond to their respective factor profiles.
2. For example, the stagflation portfolios should outperform when inflation is high
and GDP is contracting or expanding at a slower-than-average pace.
3. We compare the performance of four factor-sensitive portfolios by creating
subsamples of returns that correspond to their factor profiles.

In-Sample Performance of Unconditioned and
Conditioned Portfolios
(Factor Deviation Aversion = 0.2)

SUMMARY
 Some investors prefer to allocate to asset classes because they are
observable and because portfolios composed of asset classes are more
stable out of sample.
 Other investors prefer to allocate to factors because they are the fundamental
determinants of performance and because some factors carry risk premiums.
 We introduce a framework for allocating to asset classes but in a way that is
sensitive to a preferred factor profile.
 We offer evidence that factor-sensitive portfolios perform better than
unconditioned portfolios during regimes that correspond to their factor profiles.

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Asset Allocation and Factor Investing: An Integrated Solution

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