Volatility‐Managed Portfolios

• Author: TYLER MUIR,ALAN MOREIRA
• Published date: 01 August 2017
• Date: 01 August 2017
• DOI: http://doi.org/10.1111/jofi.12513

THE JOURNAL OF FINANCE •VOL. LXXII, NO. 4 •AUGUST 2017

Volatility-Managed Portfolios

ALAN MOREIRA and TYLER MUIR∗

ABSTRACT

Managed portfolios that take less risk when volatility is high produce large alphas,

increase Sharpe ratios, and produce large utility gains for mean-variance investors.

We document this for the market, value, momentum, profitability, return on equity,

investment, and betting-against-beta factors, as well as the currency carry trade.

Volatility timing increases Sharpe ratios because changes in volatility are not offset

by proportional changes in expected returns. Our strategy is contrary to conventional

wisdom because it takes relatively less risk in recessions. This rules out typical risk-

based explanations and is a challenge to structural models of time-varying expected

returns.

WE CONSTRUCT PORTFOLIOS THAT SCALE monthly returns by the inverse of their

previous month’s realized variance, decreasing risk exposure when variance

was recently high and vice versa. We call these volatility-managed portfolios.

We document that this simple trading strategy earns large alphas across a

wide range of asset pricing factors, suggesting that investors can benefit from

volatility timing. We then interpret these results from both a portfolio choice

and a general equilibrium perspective.

We motivate our analysis from the vantage point of a mean-variance investor,

who adjusts her allocation according to the attractiveness of the mean-variance

trade-off, μt/σ 2

t. Because variance is highly forecastable at short horizons, and

variance forecasts are only weakly related to future returns at these horizons,

our volatility-managed portfolios produce significant risk-adjusted returns for

∗Alan Moreira is with the University of Rochester, Tyler Muir is with UCLA and the NBER.

We thank the Editor (Ken Singleton), two anonymous referees, Matthew Baron, Jonathan Berk,

Olivier Boguth, John Campbell, John Cochrane, Kent Daniel, Peter DeMarzo, Marcelo Fernandes,

Wayne Ferson, Stefano Giglio, William Goetzmann, Mark Grinblatt, Ben Hebert, Steve Heston,

Jon Ingersoll, Ravi Jagannathan, Bryan Kelly, Ralph Koijen, Serhiy Kosak, Hanno Lustig, Toby

Moskowitz, Justin Murfin, Stefan Nagel, David Ng, Lubos Pastor, Lasse Pedersen, Myron Scholes,

Ivan Shaliastovich, Tuomo Vuoltenahoo, Jonathan Wallen, Lu Zhang, and participants at Yale

SOM, UCLA Anderson, Stanford GSB, Michigan Ross, Chicago Booth, Ohio State, Baruch College,

Cornell, the NYU Five Star conference, the Colorado Winter Finance Conference, the Jackson Hole

Winter Finance Conference, the ASU Sonoran Conference, the UBC winter conference, the NBER,

the Paul Woolley Conference, the SFS Calvacade, and Arrowstreet Capital for comments. Weespe-

cially thank Nick Barberis for many useful discussions. Wealso thank Ken French, Lasse Pedersen,

Alexi Savov, Adrien Verdelhan, and Lu Zhang for providing data. Both authors disclose that, af-

ter our work had already circulated, this research was solicited for compensated presentations at

Arrowstreet Capital, Mellon Capital, Panagora Asset Management, and Phase Capital.

DOI: 10.1111/jofi.12513

1611

1612 The Journal of Finance R

the market, value, momentum, profitability, return on equity, investment, and

betting-against-beta factors in equities as well as for the currency carry trade.

Annualized alphas and Sharpe ratios with respect to the original factors are

substantial. For the market portfolio our strategy produces an alpha of 4.9%,

an appraisal ratio of 0.33, and an overall 25% increase in the buy-and-hold

Sharpe ratio.

Figure 1provides intuition for our results for the market portfolio. In line

with our trading strategy, we group months by the previous month’s realized

volatility and plot average returns, volatility, and the mean-variance trade-off

over the subsequent month. There is little relation between lagged volatility

and average returns but there is a strong relationship between lagged volatility

and current volatility. This means that the mean-variance trade-off weakens

in periods of high volatility. From a portfolio choice perspective, this pattern

implies that a standard mean-variance investor should time volatility, that is,

take more risk when the mean-variance trade-off is attractive (volatility is low),

and take less risk when the mean-variance trade-off is unattractive (volatility

is high). From a general equilibrium perspective, this pattern presents a chal-

lenge to representative agent models focused on the dynamics of risk premia.

From the vantage point of these theories, the empirical pattern in Figure 1

implies that an investor’s willingness to take stock market risk must be higher

in periods of high stock market volatility, which runs counter to most theories.

Sharpening the puzzle is the fact that volatility is typically high during re-

cessions, financial crises, and in the aftermath of market crashes when theory

generally suggests investors should, if anything, be more risk averse relative

to normal times.

Our volatility-managed portfolios reduce risk-taking during these bad

times—times when the conventional wisdom is to increase risk-taking or hold

risk-taking constant.1For example, in the aftermath of the sharp price declines

in the fall of 2008, a widely held view was that those that reduced positions

in equities were missing a once-in-a-generation buying opportunity.2Yet, o ur

strategy cashed out almost completely and returned to the market only as the

spike in volatility receded. Indeed, we show that our simple strategy worked

well throughout several crisis episodes, including the Great Depression, the

Great Recession, and 1987 stock market crash. More broadly, we show that our

volatility-managed portfolios take substantially less risk during recessions.

These facts may be surprising in light of evidence showing that expected

returns are high in recessions (Fama and French (1989)) and in the after-

math of market crashes (Muir (2016)). To better understand the business cycle

1For example, in August 2015, a period of high volatility, Vanguard—a leading mutual fund

company—gave advice consistent with this view :“What to do during market volatility? Perhaps

nothing.” See https://personal.vanguard.com/us/insights/article/market-volatility-082015.

2See, for example, John Cochrane (“Is now time to buy stocks?” 2008, Wall Street Journal)

and Warren Buffet (“Buy America. I am,” 2008, The New York Times) make the case for this view.

However,consistent with our main findings, Nagel et al. (2016) show that many households respond

to volatility by selling stocks in 2008 and that this effect is larger for higher income households,

which may be more sophisticated traders.

Volatility-Managed Portfolios 1613

Figure 1. Sorts on the previous month’s volatility. Weuse the monthly time series of realized

volatility to sort the following month’s returns into five buckets. The lowest, “low vol,” looks at

the properties of returns over the month following the lowest 20% of realized volatility months.

We show the average return over the next month, the standard deviation over the next month,

and the average return divided by variance. Average return per unit of variance represents the

optimal risk exposure of a mean-variance investor in partial equilibrium, and also represents

“effective risk-aversion” from a general equilibrium perspective (i.e., the implied risk aversion, γt,of

a representative agent needed to satisfy Et[Rt+1]=γtσ2

t). The last panel shows the probability of

a recession across volatility buckets by computing the average of an NBER recession dummy. Our

sorts should be viewed as analogous to standard cross-sectional sorts (i.e., book-to-market sorts)

but are instead done in the time series using lagged realized volatility.(Color figure can be viewed

at wileyonlinelibrary.com)

behavior of the risk-return trade-off, we combine information about time-

variation in both expected returns and variance. Using a vector autoregres-

sion (VAR), we show that, in response to a variance shock, the conditional

variance initially increases by far more than the expected return. A mean-

variance investor would decrease his or her risk exposure by around 50% after

a one-standard-deviation shock to the market variance. However, since volatil-

ity movements are less persistent than movements in expected returns, our