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The predictability of relative asset returns

Empirical research suggests that it is easier to predict relative returns within an asset class than to predict absolute returns. Also, out-of-sample value generation with standard factors has been more robust for relative positions than for outright directional positions. This has been shown for bond, equity and currency markets. Importantly, directional and relative predictability have been complementary sources of investment returns, suggesting that using both will produce best performance.

Haddad, Valentin, Serhiy Kozak, and Shrihari Santosh (2017), “Predicting Relative Returns”, NBER Working Paper No. 23886, September 2017

The post ties in with SRSV’s lecture on fundamental value estimates.
The below are excerpts from the paper. Emphasis and cursive text have been added.

Basic points

“We have proposed…a systematic approach to study the time-series predictability for cross-sections of assets. Our method relies on estimating the predictability of important [principal] components of each family of assets…We then study the predictability of these portfolios…Across Treasury bonds, stocks, and currencies, a common set of facts emerges….

  • First, relative returns—the components of returns beyond the index—are highly predictable, typically more so than the index.
  • Second, this variation in expected relative returns is more robust out of sample than that of expected index returns, making it exploitable by investors in real time.
  • Third, the risk premia of relative returns appear to be only weakly related to aggregate risk premia, suggesting the presence of multiple sources of variation in expected returns.”

“For Treasuries, slope is more predictable than level. For equities, dominant principal components of anomaly long-short strategies are more predictable than the market. For foreign exchange, a carry portfolio is more predictable than a basket of all currencies against the dollar.”

“These results highlight the importance of going beyond aggregate predictability to understand common movements in risk premia over time…We show the commonly used practice to predict each individual asset is often equivalent to predicting only their first principal component, the index, which obscures the predictability of relative returns.”


“The problem we are interested in is the time-series predictability of a family of returns [such as an asset class].”

“The starting point of our analysis is to reduce the dimensionality of the cross-section [i.e. characterize the asset class by a few factors rather than by a large number of individual assets]…We operationalize the notion of importance by choosing specific linear combinations of returns, implemented as portfolios… A natural choice for these portfolios are long-short strategies formed by sorting returns based on characteristics, such as maturity for bonds, where characteristic selection is driven by economic motivation…Alternatively one can use guidance from statistical analysis, focusing on the largest principal components of the family of returns.”

“For each asset class, we reduce the cross-section of assets to a few portfolios along dimensions suggested by economic analysis, statistics, or both. We then study the predictability of these portfolios…We apply this approach to Treasury bonds, stocks and exchange rates…Naive methods which ignore the factor structure typically suffer from overwhelming spurious in-sample predictability.”

“To focus directly on common variation in risk premia, we use a more top-down methodology. We directly measure the predictability of aggregate components and then project it back onto individual assets.”


“Common predictors put forward in previous literature forecast the average level of returns with coefficients of determination around 20%. We show that a portfolio trading long against short maturities exhibits a similar degree of predictability… in addition to the existing evidence on aggregate predictability…[This relative return] predictability…would be missed by looking at the standard individual asset-level regressions.”

“We obtain yields on zero-coupon Treasury bonds with maturities from 1 to 15 years…The sample is 1985-2015… We calculate log excess returns from yields. We then rescale the excess returns of bonds of maturity n by dividing them by n – 1… Rescaling largely eliminates scale effects across bond returns. Scaled returns have approximately equal standard deviation… returns. We obtain ‘level’, ‘slope’, and ‘curve’ factors for returnsThe first two factors, level and slope, capture more than 99% of the variation in realized bond returns…The slope factor has 95% correlation with changes in the slope of yields and nearly zero correlation with changes in the level.”

“To explore predictability of relative returns, we consider a maturity sorted portfolio, which is approximately the mimicking portfolio for changes in the slope of the yield curve …We find that yields forecast returns on this slope portfolio with similar explanatory power to level, but this predictability is only evident upon direct examination of slope… A researcher who forecasts bond returns equation-by-equation would conclude that the slope factor is not an important predictor of excess returns though it obviously significantly predicts the return on a… maturity-sorted portfolio.”

“We further illustrate how individual tests can fail to capture patterns of predictability by considering the Chicago Fed National Activity Index (CFNAI). Whereas CFNAI doesn’t significantly predict any individual bond return, it predicts the second principal component of returns [i.e. yield curve slope] with a similar magnitude as bond yields.”

“We conclude that relative returns are as predictable as aggregate returns, and there are at least two independent drivers of time-varying risk premia.”

“The figure below shows realized returns for the managed portfolios…The full-sample Sharpe ratio for [a portfolio based on the level factor] is 0.35 compared to 0.60 [for a portfolio based on the slope factor]… Out-of-sample [for a shorter period]…the Sharpe ratio falls from 0.20 to 0.12 for the level factor. For the slope factor, in contrast, it barely declines from 0.67 to 0.59.”


“For stocks we also find strong predictability beyond the market return. Long-short portfolios of so-called anomalies exhibit common variation that we extract using principal components. These components are also predictable, more so than the market.”

“Portfolios include all NYSE, AMEX, and NASDAQ firms…The sample is monthly from November 1973 to December 2015.”

“Rather than forecasting individual stock returns, we consider 50 well-known anomaly long-short portfolios, which we orthogonalize with respect to the aggregate market return. The residuals exhibit a moderate factor structure, with two [principal] components explaining close to 40% of the remaining variation. We find evidence that these additional dimensions —relative returns— are also highly and robustly predictable. Using the cross-section of book-to-market ratios as predictors, we find an out-of-sample coefficient of determination of 42% for relative returns when predicting the first component of long-short anomalies.”

“Strong predictability of large common components of stock returns also imply substantial levels of predictability of individual equity anomalies, stemming from their loading on these highly predictable principal components…”


“Currency returns, sorted by interest rate differentials, are more predictable than a strategy of trading all currencies against the dollar.”

“We sort the individual currencies into five portfolios based on their forward spread with the US…Portfolios are rebalanced daily based on the average of the forward spread in the recent month. We add and drop countries to portfolios as new data becomes available. The sample is from January 1985 until January 2017…For ease of comparison, we normalize each portfolio return to have 5% standard deviation in the full sample.”

“We use interest rate differentials as predictors. We find that an index of all currencies against the dollar is less predictable than a portfolio of currencies sorted by interest rate differential. Specifically, whereas the out-of-sample coefficient of determination is negative when predicting the aggregate dollar carry portfolio, it is reliably around 5% for the relative carry returns of high against low interest rate differential currencies.”

“The Sharpe ratio of the Relative-Carry strategy is more than 50% larger than that of the Dollar-Carry strategy.”


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