Macroeconomic environment, money demand and portfolio choice

Highlights

• Does money demand trigger portfolio rebalancing for a long-term investor?

• Money demand makes risk aversion time-varying.

• Money demand reduces bond positions, having a negligible impact on stock allocation.

• Expected inflation is the stronger macroeconomic determinant of optimal portfolio.

• Risky asset positions and money demand negatively relate to expected inflation.

Abstract

We solve the portfolio choice problem of a long-term investor holding real balances, a stock index, multiple bonds and a remunerated money market account. We relate the factors driving the term structure and the equity premium to macroeconomic variables. When expected inflation decreases, the investor allocates more to the stock market, long-term bonds and unrewarded real balances, reducing short-maturity deposits. The optimal money demand: i) entails time variations in risk aversion; ii) reduces bond market positions when the importance of money in preferences increases, with little impact on the stock market participation; and iii) has quantitative implications in terms of horizon effects.

Introduction

During the Great Recession, modern economies witnessed a significant flight to safety and liquidity. While this phenomenon was mainly associated with a reallocation of portfolios from equities towards bonds, the latter lost some attractiveness because of the low interest rates and concerns of corporate/sovereign defaults. Conversely, physical currency and highly liquid deposits (such as checking accounts), typically held owing to the liquidity services they provide, became even more attractive to economic agents. These instruments entail an opportunity cost for the holders, as they usually do not bear interest. Fig. 1 shows the ratio between the U.S. M1 money stock aggregate, a monetary aggregate including currency, checking accounts and other very liquid means of money supply, and the index of U.S. personal consumption expenditures (PCE), against a proxy for its opportunity cost (3-month T-Bill rate) from 1959 to 2014. The negative correlation between the two is evident,¹ as well as the fact that the ratio M1/PCE skyrocketed during the recent financial crisis.

In this context, it is not surprising to see the recent contributions by Acharya and Sahoo (2010), Lucas and Nicolini (2015), Belongia and Ireland (2015) and Teles, Uhlig, and Valle e Azevedo (2016), supporting a central role of monetary aggregates in the conduct of monetary policy. Disaggregated data provide more details on the holding of money by households. Humphrey (2004) reported that close to 75% of household consumption in 1995 in the U.S. was paid for by cash (currency and checks), and this figure was 46% in 2012 (Bagnall et al., 2016). Ragot (2014) found that large money holders in the U.S. tend to be households where the head of the household is relatively old, more educated, owning a house and participating in the stock market. Aoki, Michaelides, and Nikolov (2016) noted that Japanese households tend to hold more money than in the U.S., while Alvarez and Lippi (2009) identified a significant precautionary demand for currency by Italian households.

Despite sizable M1 and broader monetary aggregates, the quasi-totality of the portfolio choice literature ignores money, exclusively considering investments in interest-bearing money market accounts, stocks or bonds. The objective of this work is to analyze the money demand and portfolio choice of a long-term investor in a multi-asset universe, in relation to the macroeconomic environment. Since Merton (1971), it is well known that an investor with a long-term horizon operating in a stochastic environment, such as a household that needs to sustain a stream of consumption over time, wishes to hedge changes in the investment opportunity set. Financial assets, such as stocks or bonds, on top of their time-varying risk/return characteristics, provide also the investor with this opportunity. This implies that a myopic allocation is suboptimal, while the optimal dynamic portfolio strategy depends on the current state of the economy and on the residual investment horizon. Our investor has a horizon of up to 30 years and solves a dynamic portfolio choice problem under inflation, within a financial market where several bonds, a stock index and a money market account are traded. We implement a no-arbitrage affine term structure model, where the short-term rate and bond risk premia are allowed to be time-varying, along the lines of Dai and Singleton (2002) and Duffee (2002). Sangvinatsos and Wachter (2005) indeed show that investors, who trade bonds with different maturities and take advantage of the predictability of bond risk premia, benefit from significant utility gains. Differing from their empirical implementation, we also allow for a predictable time-varying equity premium.²

In order to include non-interest-bearing money in the investor’s portfolio, we follow the bulk of the monetary economics literature, assuming that preferences are defined over consumption and real balances, thus adopting the money-in-the-utility-function paradigm, introduced by Sidrauski (1967). Several works in monetary economics relied on this insight, such as the contributions by Roubini and Sala-i Martin (1995) and Van den Heuvel (2008). While the implications of this specification for asset prices are well understood, surprisingly much less is known about the portfolio reallocation caused by the presence of real balances.

Using U.S. data from 1952 to 2014 to estimate the model, we show that real balances play a key role in the composition of the optimal portfolio. One component of the portfolio can be associated exclusively with real balances, and we show that it hedges instantaneous changes in relative risk aversion. When the weight of real balances in the utility function increases: i) investors naturally hold a larger fraction of their wealth in real balances, and the more so the shorter their investment horizon; ii) there is a substantial reduction in bond positions; iii) intertemporal hedging demands, driven by the presence of real balances, are substantial; and iv) the stock market position is barely affected, and the impact on consumption is far less impressive than the impact on the real balances-to-wealth ratio.

An important contribution to the literature of portfolio choice under stochastic interest rates (Brennan, Xia, 2002, Campbell, Viceira, 2001, Koijen, Nijman, Werker, 2010, Sangvinatsos, Wachter, 2005) is that we relate the optimal allocation to specific macroeconomic variables, rather than referring to latent variables with little economic intuition. We do so by writing a Taylor rule for the short-term rate and relating the risk premia in the economy to expected inflation, output gap and monetary policy shocks. We show that the impact of the macroeconomic environment on the optimal portfolio positions and welfare is substantial. When expected inflation decreases, the investor increases the positions in the stock market and in long-term bonds, reduces short-maturity deposits and augments the demand for money balances. If the initial expected inflation changes from the long-run mean (3.38%) to 0%, ceteris paribus an investor with a 10-year horizon benefits from a 10% increase in certainty equivalent wealth. Conversely, when the initial expected inflation is doubled to 6.76%, the investor suffers a 2.5% loss. While the effects of changes in the output gap are qualitatively similar, they are smaller than for changes in the expected inflation. As pointed out by Clarida, Galí, and Gertler (1999), there has been a significant change in U.S. monetary policy corresponding to the beginning of Paul Volcker’s Fed chairmanship in 1979. Furthermore, in the years after the 2008 financial crisis, the interest rates were close to the zero lower bound, requiring unconventional monetary policy interventions. Because of this, we also verify the robustness of our findings repeating the analysis over a shorter sample (1979–2007), when inflation-targeting has been a key determinant of short-term rates.

While Bakshi and Chen (1996), Gu and Huang (2013) and Lioui and Maio (2014) convincingly showed that real balances matter for asset pricing, we complement their findings by showing that this can likely be rooted to their relevance at the household level. Some authors have already introduced money demand into portfolio choice frameworks, such as Ando and Shell (1975), or, more recently, Aoki, Michaelides, and Nikolov (2014) and Aoki et al. (2016). These last two works investigated money demand within a life-cycle portfolio choice problem with multiple assets, trying to explain the observed patterns in household portfolios. Our analysis differs along three dimensions. Firstly, in their work, asset classes are broadly defined as stocks and bonds, while we distinguish between bonds of multiple maturities. There is in fact no reason why a priori money should be a substitute for either short- or long-term bonds, without any distinction. When implementing a multi-factor dynamic term structure model, we observe that positions in short- and long-term bonds react in different ways when money is introduced in the economy. Secondly, they consider the bond and stock risk premia to be constant, while in our case they are stochastic. Finally, we establish a link relating optimal money demand, consumption and portfolio policy to the macroeconomic environment. An insight of our work is the linkage between money demand, interest rates and risk aversion, which provides a simple theoretical support to the evidence in Bekaert, Hoerova, and Lo Duca (2013) of a strong relationship between risk aversion and the stance of monetary policy.

Our work also contributes to the debate concerning the spanning of the macro variables and risk premia by bond yields. While many existing works assume that macroeconomic variables are spanned by yield factors, Joslin, Priebsch, and Singleton (2014) provided evidence that this assumption is far from being true. Bauer and Rudebusch (2016) revisited their findings, providing support to models based on the spanning assumption when more than three pricing factors are considered. We build an original setting, allowing for an imperfect spanning of macro variables and equity premium by bond yields, which describes the joint dynamics of nominal yields, stock returns and macroeconomic variables. Our specification preserves the nominal market completeness, being thus tractable in a portfolio choice framework, and provides reasonably implementable positions without imposing explicit portfolio constraints. We perform a comparison with a more standard model specification, where macroeconomic variables and risk premia are spanned by nominal yields, showing that our preferred model, while having comparable bond return predictive ability, better performs in describing the co-movements of risky asset returns, risk premia and macroeconomic variables. In this context, our work is related to the literature studying the effects of the macroeconomic environment and the monetary policy onto the term structure of sovereign (Ang, Piazzesi, 2003, Bikbov, Chernov, 2010, Recchioni, Tedeschi, 2017, Renne, 2016) and corporate (Curdia, Woodford, 2010, Takada, Sumita, 2011) bond yields.

The remainder of the paper is organized as follows. In Section 2, we set up the economic framework and derive the optimal strategy. In Section 3, we describe the estimation methodology, present the dataset and discuss the parameter estimates, as well as the impulse response functions. In Section 4, we discuss the results of the optimal portfolio strategy in the base case, then assess the sensitivity to the preference parameters and, finally, the impact of the macroeconomic environment. Section 5 concludes. The technical details, a detailed model comparison and some additional empirical findings are relegated to the Appendix (available online, see the Section Supplementary material at the end of the article).