Carry Trade And Trend In Lots Of Places by Vineer Bhansali, Josh Davis, Matt Dorsten, Graham A. Rennison, PIMCO
Investors intuitively know two fundamental principles of investing: (1) Don’t fight the trend, (2) Don’t pay too much to hold an investment. But do these simple principles actually lead to superior returns? In this paper we report the results of an empirical study covering twenty major markets across four asset classes, and an extended sample period from 1960 to 2014. The results confirm overwhelmingly that having the trend and carry in your favor leads to significantly better returns, on both an absolute and a risk-adjusted basis. Furthermore, this finding appears remarkably robust across samples, including the period of rising interest rates from 1960 to 1982. In particular, we find that while carry predicts returns almost unconditionally, trend-following works far better when carry is in agreement. We believe that this simple two-style approach will continue to be an important insight for building superior investment portfolios.
If we decompose the total return of any investment as the sum of returns from change in the underlying pricing factors and from the passage of time, then carry can be best thought of as the return attributable to the second component, i.e., the expected return from the passage of time. Carry is defined by Koijen  as the “expected return on an asset assuming that market conditions, including its price, stay the same.” Thus, carry may be thought of as a naïve, yet robust, modelfree measure of the risk premium in a given asset class. In this regard, it is plausible that being on the side of positive carry should earn a higher return, on average, but accepting potentially greater risk as well since the assumption of static prices is rarely true in practice.
Historically, the literature has focused on the concept of carry mainly in the currency markets. Following the collapse of Bretton Woods, market practitioners started broadly pursuing currency carry trade strategies in the 1980s and 1990s. Academia has followed this closely, and a host of plausible explanations have been put forth for the effectiveness and persistence of currency carry as a predictor of future returns. In a no-arbitrage finance setting, for currency carry to predict returns, it must be compensation for “market” risk that cannot be diversified away. Academic finance posits that the currency risk premium is a direct consequence of the co-variation of returns with the stochastic discount factor. Lustig  observes that currency carry tends to work empirically due to the co-variation of the payoff on carry trades with consumption growth. Viewing currency carry through the lens of locally hedged option prices, Bhansali  and Menkhoff  offer an intuitive connection between this carry risk premium as compensation for exposure to volatility risk.
In his seminal work “Treatise on Money” , Keynes proposed that backwardation in commodities, or the tendency of futures contracts to trade below spot contracts, is normal and related to producers of commodities seeking to hedge by locking in future prices, thus constructing a premium that can be earned by speculators who provide the insurance. Gorton  provides a comprehensive analysis of the drivers of these risk premia (including current and future levels of inventories) and shows that price measures, such as the futures basis (a measure of carry), contain relevant information for predicting future returns.
In fixed income markets, the nominal U.S. Treasury bond risk premium is often directly measured by the steepness of the yield curve, which is related to the term premium. Fama and Bliss  show that expected returns on bonds vary through time and the variation of the term premium is closely related to the business cycle. Cochrane and Piazzesi  and Campbell, Sunderam and Viciera  relate the bond risk premium directly to the concavity in the yield curve, defined loosely as the level of intermediate interest rates relative to the average of short- and longer-term bond yields. Using an empirical data set spanning 150 years, Giesecke, Longstaff, Schaefer and Strebulaev  show that, on average, at least half of the carry on corporate bonds, given by credit spread corresponding to the yield difference between corporate bonds and duration-matched Treasury bonds, is a risk premium. Furthermore, these authors show that actual defaults are closely related to equity returns and volatility.
While the computation of carry in equities is less analogous, in equity futures, the implied dividend yield less the local risk-free rate is one determinant of carry. Fama and French  document that dividend yields help to forecast equity returns, with better predictive ability at longer horizons. Because carry as a concept is less popular in equity markets, our approximation used below should be taken as one attempt at making it similar to the one used for other assets, with further room for improvement.
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