Machine learning and asset allocation

• DOI: http://doi.org/10.1111/fima.12303
• Published date: 01 December 2019
• Date: 01 December 2019

DOI: 10.1111/fima.12303

ORIGINAL ARTICLE

Machine learning and asset allocation

Bryan R. Routledge

TepperSchool of Business, Carnegie Mellon

University, Pittsburgh, Pennsylvania

Correspondence

BryanR. Routledge, Tepper School of Business,

CarnegieMellon University, 4765 Forbes Ave,

Pittsburgh,PA 15213.

Email:routledge@cmu.edu

Abstract

Investorshave access to a large array of structured and unstructured

data. We consider how these data can be incorporated into finan-

cial decisions through the lens of the canonical asset allocation deci-

sion. We characterize investorpreference for simplicity in models of

the data used in the asset allocation decision. The simplicity param-

eters then guide asset allocation along with the usual risk aversion

parameter. We use three distinct and diverse macroeconomic data

sets to implement the model to forecast equity returns (the equity

risk premium). The data sets we use are (a) price-dividend ratios, (b)

an array of macroeconomic series, and (c) textdata from the Federal

Reserve’s FederalOpen Market Committee (FOMC) meetings.

1INTRODUCTION

There is no shortage of data. At your fingertips are 237,000 data series at the St. Louis Federal Reserve Bank’s Eco-

nomic Data (FRED). The Securities and ExchangeCommission (SEC) received 304,000 corporate filings (e.g., 10K, 10Q,

8K, Form 4) during the first quarter of 2018. The SEC has over 18 million electronic filings from 1994. Mix in social

media sites likeTwitter and data sets of size in the billions are common.1Is any of these data helpful in decision making?

In the finance context we look at here,despite all data sets and sources available, we still have only about 840 monthly

observations of, say,postwar equity returns. Does that limit the value of the larger data sets? The goal of this paper

is to explain how machine learning—specifically regularized regressions—capture how individuals might use large and

varied data for decision making. Here, we look at the canonical asset allocation problem and characterize individuals

preferences over “models” for data. Viewed through the lens of a portfolio optimization, we look at how these data

become information.

The economic context for the model is a simple stock-bond asset allocation problem. At the core of this problem is

the level and dynamic properties of the equity premium (the rate of return on a broad portfolio of equities in excess

of the risk-free return). From data, and much finance research, we know the equity premium has substantial variation

in its conditional mean. The unconditional expectation of the equity premium is around 6%. However,the conditional

expectation commonly swings substantially from 0% to 12% (see Cochrane, 2011) or as evidenced in the term struc-

ture, see van Binsbergen, Hueskes, Koijen, and Vrugt(2013). Similar time variation in risk premiums show up in bonds

c

2019 Financial Management Association International

1Forexample, O’Connor, Balasubramanyan,Routledge, and Smith (2010), and, Coppersmith, Dredze, Harman, and Hollingshead (2015).

Financial Management. 2019;48:1069–1094. wileyonlinelibrary.com/journal/fima 1069

1070 ROUTLEDGE

(Ludvigson & Ng, 2009), oil futures (Baker & Routledge, 2013), and foreign exchange(Koijen, Moskowitz, Pedersen, &

Vrugt, 2013). The implication of the time variation in the mean return is that expost returns are, to some degree, pre-

dictable. Indeed, the main empirical support for the time variation in expected returns is the regression predicting the

excessreturn at horizon h,rt+hwith information at date t,Xt.

rt+h=𝜃′Xt+𝜖t+h.(1)

Across markets, the set of predictors varies. The aggregate price-dividend ratio is used as a forecaster in equity mar-

kets, the slope of the futures curve works in oil markets.In the bond market, Ludvigson and Ng (2009) use predictors

extracted as the principle components of 130 economic series. In addition, as you would expect, realized returns are

veryvolatile and so the precision (R2) of the predictive regression is low. More relevant here, not everyone is convinced

that the predictability is particularly useful. Welch and Goyal (2008) point out that out-of-sample forecasts are not

reliable.2

Toinvestigate this question, we use the framework of Gilboa and Schmeidler (2010), Gilboa and Samuelson (2012),

and, Gilboa and Schmeidler (2003) to represent a decision maker’s preference over “models” of the data. In particu-

lar, we propose a representation and assume a functional form that captures the dual objectives: people likemodels

that explain the data (e.g., likelihood) and people likemodels that are simple (e.g., a small number of parameters). Of

course, these two desires are often at odds. A model with more parameters fits the data better (at least in-sample).

Machine learning tackles this trade-off by “regularizing” overparameterized models (see Tibshirani, 1996, 2011; Zou

& Hastie, 2005). These techniques look to exploit patterns in data that perform well out of sample. Here, we interpret

this approach through the axiomatic foundations of Gilboa and Schmeidler (2010). This lets us interpret and control

the transition from data to information used in decision making as preference parameters akin to a coefficient of risk

aversion. When we embed all this in the familiar portfolio problem we can see if we have preference parametersthat

generate sensible behavior.3

First, we use the Gilboa and Schmeidler (2010) setting to characterize simplicity or parsimonyin data models. Next,

we sketch an example with a two-state equity premium to clarify the model’s preference structure. Then, to see how

this might work in practice, we use multiple sources of economic data. For now, we simplify to the “static” (or single

period) portfolio problem. This is helpful since the simplicity of the decision step let us focus on the new feature of

“model” preference. We implement this using three different, and different in character, data sets. First, we use the

familiar price-dividend data as in Cochrane (2011). Second, we use an array of several hundred monthly macroeco-

nomic series from the St. Louis Fed’s data (FRED).This is along the lines of the data used in Ludvigson and Ng (2009).

Finally, we use text as data. Specifically, we use the Beige Book reports of the Federal Reserve staff economists that

characterize the economy using informal surveys.

2DECISION MAKING AND SIMPLICITY

Gilboa and Schmeidler (2010), and related papers Gilboa and Samuelson (2012) and Gilboa and Schmeidler (2003),

present an axiomatic foundations for using data and incorporating a preference for simplify or parsimony.To summa-

rize and adapt this setting to asset allocation, we start by characterizing “data.”Data are of the form (xn,y

n).xn∈𝕏is

a (perhaps large) vector of “signals.” yn∈𝕐is a scalar “state.” The signal xn, is known by the decision makerand may be

useful in predicting the unobserved state yn.(𝕏,𝕐)is the set of joint probability distributions over 𝕏×𝕐.

2Kimand Routledge (2019) look at the corporate finance implications of ignoring or not time variation in the risk premium.

3Our model here is in different from the related paper of Gabaix (2014). That paper characterizes a nonmaximizing or “bounded’ rationality” (Simon, 1959)

approach to capture the idea that some data are “ignored.” Here, we will define preferences and an optimization so any data that are “ignored” are an opti-

malchoice.