In this article we analyze the advantages of combining together value and momentum long/short portfolios in many asset classes and in different geographical areas. In fact, they have historically shown negative correlation between them. You can exploit it by including value and momentum in a portfolio, which will have a reduced risk in terms of lower standard deviation with respect to both the two. The ideas expressed in this article come from several papers written by Cliff Asness and other researches at AQR Capital Management (we put the references at the bottom of the article). In particular, the article is structured in four parts. In the first part we introduce value and momentum giving a brief description of them. In the second part we analyze the advantages of combining value and momentum showing how you can get higher Sharpe Ratios and attenuate big losses. In the third part we analyze the recent performance of value and momentum verifying whether their returns have deteriorated over time. Finally, we take a look at how these academically findings were implemented in practice and show the importance of the short book to obtain the desired diversification effects. By investigating two Indices of Solactive, a global Index provider, we further show how refined value characteristics improve the identification of value stocks.

**Introduction**

Value and momentum are probably the most famous anomalies of CAPM. Indeed, these two investment strategies have been proved over time to generate positive risk adjusted returns. Value strategies consist in buying assets considered “cheap” and sell those considered “expensive”. The typical definition of “cheap” and “expensive” in value is based on the ratio between book value of equity and its market value (BE/ME). So a value strategy is basically a long/short portfolio which goes long on a portfolio of stocks with relatively high BE/ME and short on a portfolio of stocks with relatively low BE/ME.

Momentum strategies instead consist in buying “winners” and selling “losers”, where “winners” and “losers” are those stocks which have performed relatively better and worse than the average. You must not confuse momentum with trend following, in which you buy stocks with past positive returns and sell those with negative ones. In fact, in case of a bear market, the “winners” of momentum strategies can have negative past returns, as far as they are above the average. The measure commonly used to identify “winners” and “losers” is the return of the past year where you don’t consider the return of the most recent month (PAST(2,12)), in order to avoid the so called “reversal effect”. So, a momentum strategy is basically a long/short portfolio which goes long on a portfolio of stocks with relatively high PAST(2,12) and short on a portfolio of stocks with relatively low PAST(2,12).

We described value and momentum as referred exclusively to the stock market. However, interestingly, Asness et al.(2013) showed that they work also in different asset classes such as currencies and commodities. In order to prove these results, the authors built a very ample dataset of value and momentum portfolios in every asset class that they keep updated and you can freely download it from AQR’s website. We will use this dataset throughout all the article (we will refer to it as the AQR dataset), so now we briefly describe the procedure followed to build its value and momentum portfolios.

They considered eight different asset classes: US stocks (US), UK stocks (UK), European stocks (EU), Japanese stocks (JP), government bonds (FI), equity index futures (EQ), currencies (FX) and commodities (COM). At first, before building the value and momentum portfolios they selected within each asset class the most liquid asset such that value and momentum strategies can be replicated in practice without too high transaction costs. Then they formed the value and momentum portfolios.

Before starting to analyze the advantages of combining value and momentum it is worth highlighting that they don’t represent arbitrage opportunities, they are simply investment strategies which have historically shown significant and positive abnormal return when regressed against the market. However, this doesn’t imply that there are not periods in which they aren’t significant or don’t generate positive excess returns.

**Benefit of combining Value and Momentum**

In the world of factor investing value and momentum represent the most famous and used factors. However, they are typically exploited by different investors. Usually you see that people using one factor are skeptical about the other. In particular, who uses value investing strategies often criticize momentum and express his doubts about its effectiveness. Therefore, there is a sort of contrast among academics and also practitioners regarding which is the strongest and the most useful factor.

The main aim of this article is to show that, regardless of which one is the most effective factor, the best thing you can do is actually to combine them, using a portfolio which invest in both.

*1 – Negative correlation means higher Sharpe Ratio *

The rationale in combining value and momentum comes from the fact that historically, they have both shown positive excess returns (which are almost completely abnormal returns since their beta is very close to zero as they are both long/short portfolio) and more importantly they have also shown a negative correlation between themselves. Typically, in the market is very rare to find a negative correlation but this is one of the few lucky cases. We can exploit this negative correlation by combining value and momentum and obtaining a portfolio with lower positive return but lower risk in terms of standard deviation. We built the simplest portfolio you can think of: a portfolio which invest 50% of its capital in the value portfolio and the remaining 50% in the momentum one. Using the AQR dataset we computed for each asset class and every geographical area the mean excess returns, the standard deviations and the Sharpe Ratios of the value portfolio, the momentum one and our equally-weighted portfolio of value and momentum (as an example we report the statistics for the US stock market then we summarize all the other asset classes in the second table where we report only the Sharpe Ratios).

As you can see in the second table, in all asset classes our simple strategy was able to maintain a quite high mean excess return while reducing its standard deviation and so getting a Sharpe Ratio which is higher than both those of value and momentum.

However, it is worth mentioning that in order to exploit this negative correlation, it is essential to use both the long and the short leg of the value and momentum portfolios. In fact, in the market there are lots of long only indices and funds which try to replicate value and momentum but if you compute their correlation you find that it is actually positive and very high. This comes from the fact that since you are not using the short leg, the long value and momentum portfolios share a common exposure towards the market which makes them highly correlated. Therefore, you need to pay attention to “long only” value and momentum funds because in these cases the benefit of negative correlation is lost.

** 2 – Why Value and Momentum are negatively correlated
** The negative correlation between value and momentum, besides being quite high (-0.54 in the US stock market), appears to be widespread across different asset classes. Interestingly, Asness et al.(2013) showed that not only value and momentum are negatively correlated inside the same asset class, but they are negatively correlated also across different asset classes. It means, for instance, that value returns in the US stock market are negative correlated with momentum ones in the commodity market. This is a very strong and surprising result if you think that different markets are typically characterized by different kind of investors following different investing objectives.

Regarding the reasons of this negative correlation, we have to say that many possible explanations have been proposed but it does not exist a universally recognized one yet. Asness et al. (2013) showed that value and momentum are linked in opposite ways to liquidity risk. In particular, momentum seems to perform better when liquidity is largely available in the market while on the contrary value tends to do better when there are liquidity shocks. Therefore, value and momentum appear to have respectively negative and positive correlation with liquidity risk and this could partially explain their negative correlation. This is not a complete explanation because it fails to explain the positive expected return of a portfolio which invests in both value and momentum and that, according to this logic, would not be exposed to any liquidity risk.

An intuitive idea regarding the opposite behavior of value and momentum with respect to liquidity risk is that momentum represent the most popular trades, done by most of investors, while value could be viewed as a sort of contrarian investment strategy. Then, when you have a liquidity shock, as it happened in 2008, the sell-offs in the market put lot of pressure on the most popular assets (momentum) because everyone wants to liquidate their positions while they affect less strongly the fewer contrarian trades (value).

** 3 – Avoid crashes
** Beside getting higher Sharpe Ratios in all the asset classes our equally-weighted value and momentum portfolio allows us to have fewer large left tail events (it reduces the number of times in which you experience very big losses), as pointed out by Asness et al.(2014).

In the recent past the two biggest losses in value and momentum portfolios were respectively in 1999 and 2009.

The 1999 crash of the value portfolio is quite simple to understand: we were reaching the peak of the dotcom bubble that would explode the following year and the overvalued companies which seemed very expensive in terms of “value” (so they were in the short leg of the value portfolio) were instead continuing grow very quickly, causing heavy losses to the value portfolio. If we consider the US stock market (where we had the biggest losses related to the value portfolio), value in 1999 performed -30.85% while our equally-weighted value/momentum portfolio made +4.28%, exploiting the positive return of momentum in that year.

The biggest recent loss of the momentum portfolio was instead in 2009. Typically, momentum tends to suffer a lot when you have rapid market growth following a significant bear market. This was exactly the case in 2009 after the crisis. According to Daniel and Moskowitz (2013) this kind of behavior is due to high market exposure of the short leg of the momentum portfolio. In fact, after a bear market if you buy the “winners” and sell the “losers” you are basically long on low beta stocks and short on high beta ones, then if the market starts to go up rapidly then you. This was what happened in 2009 and considering again the US stock market, momentum in 2009 performed -33.93% while our equally-weighted value/momentum portfolio made -15.61%. Therefore, as you can see in the graph below our strategy, exploiting the negative correlation between value and momentum, was able to avoid or at least attenuate the biggest losses of the two.

** 4 – The case of Japan
** Japan is a very interesting case because it is the only stock market in which momentum strategies have not worked historically. In fact, as you can see from the table below, momentum shows non significant excess return in the full sample from 1981 to 2018.

However, we see that even in this weird case, our equally-weighted value/momentum strategy would have done better with a Sharpe Ratio of 0.602 which is still slightly better than that of value only (0.569). Momentum is not significant in Japan but it is still negatively correlated with value. If fact, according to Asness (2012), the absence of momentum in Japan can be explained by the fact that value has performed extraordinarily well (mean excess return of value is 8.4%)

Furthermore, following Asness et al.(2014), we computed the optimal weight of momentum in a portfolio of value and momentum as a function of its expected return in order to maximize the Sharpe Ratio of the whole portfolio. As you can see in the graph below, thanks to the negative correlation, even when the expected return of momentum is zero, its optimal weight is positive (8.13%). It is necessary an expected return lower or equal to -1% in order to make its optimal weight equal to zero.

Therefore, combining value and momentum is convenient even when one of the two factors has not significant positive returns.

*Analysis of the performance of Value and Momentum *

** 1 – Building global portfolios of different asset classes
** In order to better analyze the performance of value and momentum taking into consideration at the same time their performance in different asset classes we built three new portfolios. The first one invest in the four stock markets considered in the AQR dataset (US, UK, continental Europe and Japan), the second one invest in the four asset classes different from stock in the AQR dataset (equity index futures, government bonds, currencies and commodities) and the third comprises all the eight different asset classes.

STOCK_t=w_{US}US_t + w_{UK}UK_t + w_{EU}EU_t + w_{JP}JP_t

NONSTOCK_t=w_{EQ}EQ_t+w_{FI}FI_t+w_{FX}FX_t+w_{COM}COM_t

ALL_t=w_{STOCK}STOCK_t+w_{NONSTOCK}NONSTOCK_t

Following the procedure used in Asness et al.(2013) in each portfolio we weighted every asset class by the inverse of its ex post sample volatility (actually we used the standardized version of the inverse of volatility such that the weights sum up to one).

At this point we split the full sample of years in subsamples of length equal to 4 years (so to have at least 48 data points in each subsample) and for each one of the three portfolios we computed the mean excess return, the standard deviation and the Sharpe Ratio of value and momentum strategies for every subsample. The results are summarized in the tables below:

As you can see in the last 4 year-subsample (2014-2018) value and momentum show different patterns in the stock portfolio and in the non-stock one. In particular, value seems to be suffering in the global stock markets while momentum is suffering in the non-stock asset classes. In the portfolio which comprises both these two effects balances and neither value or momentum showed significant returns in the last four years. Moreover, considering the last subsample in the stock portfolio, besides having a negative return for value also momentum was not so brilliant in terms of Sharpe Ratio (0.35). Therefore, in the last four years at least in the global stock markets value a momentum strategies have not performed so well.

** 2 – Evidence of degradation
** Given the not too large returns of value and momentum in the recent period, you may think that the reduction of transaction costs in financial markets and more importantly the fact that more and more investors use value and momentum strategies could have reduced the expected returns of value and momentum. Following Israel and Moskowitz(2013), in order to verify whether value and momentum returns have experienced a deterioration through time, we used two different methods.

The first consist in regressing for each of our three portfolios the time series of monthly returns for value and momentum against dummy variables for the 4-year subsamples we built before and looking to whether the betas of these regressions are significant and large in order to detect any time trend in value and momentum returns.

The second method is slightly different from the first but the idea is basically equivalent. In this case we for each of our three portfolios we regressed the time series of monthly returns for value and momentum against a linear time trend instead of the 4-year subsamples dummy variables and we looked again to whether the betas of these regressions are significant and large in order to detect any time trend in value and momentum returns. As you can see in the table below, both for the regressions on the 4-year subsample dummy variables and those on the linear time trend, almost all the betas are not significant at a confidence level of 95%. However, there are five exceptions in which betas are significant (they are highlighted in yellow in the table). For example, looking at the negative beta of the time trend regression for the “ALL” portfolio, it seems that there is a tendency for value excess returns to decrease over time. These five cases certainly deserve further investigation, anyway we need to be cautious in interpreting these results. In particular, we used a quite large sample (36 years of monthly data), so the small standard error of betas could be responsible for the high t-stat even when the beta itself is considerably small. Indeed, looking at these five significant betas, they are all very small in absolute value. Therefore, even if a time trend does exist, its size and consequently its practical relevance is really limited.

*Solactive European Tradable Factor Indices*

In this section we want to switch sides and see how practitioners implemented the apparent pricing abnormalities arising from Value and Momentum trades. For this means, two indices from Solactive, a Germany-based index provider that operates globally, caught our attention: the Solactive Tradable European Value Factor Index and Price Momentum Factor Index. Investors can invest in both strategies via two ETFs that Invesco provides on them. The table below shows the annualized mean return and standard deviation of the returns of the two Solactive factor indices as well as of the returns of the value and momentum portfolios in Asness et al. (2013). Specifically, the shown portfolios in the table from Asness et al. (2013) are constructed on Continental Europe equities. VAL3EU and MOM3EU are the statistics for the portfolios of stocks with the highest value and momentum characteristics, respectively. The last two columns of the table report the same statistics for the spread portfolios, e.g. long the portfolio with the highest value/momentum characteristics and short the portfolio with the lowest highest value/momentum characteristics. All results are obtained for the period January 2011-January 2019. We confirm the negative correlation between the value and momentum returns, as can be inferred from the third value in the third row of the table, showing a correlation of -64.24% for the period under consideration. Thus, combining a value and momentum strategy improves the efficient frontier for investors, as pointed out in Asness et al. (2013). One need to be aware of the fact though, that this negative correlation stems from relationships between the long and the short book. Indeed, the portfolio returns between the stocks with the highest value and momentum characteristics show a remarkably strong correlation of 87.19%, the second value in the third row of the table. This may be rather surprising since generally stocks that appreciated strongly in price over the recent past (momentum stocks) are not high value stocks. That this relationship generally holds true can be verified from the strong correlations between the two return pairs (MOM1EU, VAL3EU) and (MOM3EU, VAL1EU). Low momentum stocks show a correlation of 94.45% with high value stocks. Similar, high momentum stocks show a correlation of 96.19% with low value stocks. By combining value and momentum strategies, it’s the strong negative correlation between the short and the long book that allows investors to earn better risk-adjusted returns. This effect is by no means attained by a combination of pure long value and momentum strategies.

Further, the table reports that the Solactive Value and Momentum Factor Indices experience a remarkable smaller correlation between their returns. Both Indices compromise the 50 European-stocks that have the highest exposure to value and momentum, respectively. Asness et al. (2013) and Solactive are consistent in considering only stocks with sufficient liquidity for the construction of their factor portfolios and in the definition of price momentum (past 12 months returns, skipping the most recent month). However, while Asness et al. (2013) simply defines value as the ratio of the book-value of equity to the market-value of equity, Solactive uses a more sophisticated approach by considering earnings-to-price ratio, book-to-price ratio, and dividend yield. At this point it needs to be clarified that the authors didn’t intend to test the best value predictors but to guarantee a uniform and consistent approach among the different asset classes and markets considered in their study, the approach applied by Solactive seems to be an enhancement in selecting value stocks.

**References**

Asness, C. (1997). The Interaction of Value and Momentum Strategies. Financial Analysts Journal, 53(2), pp.29-36.

Asness, C. (2011). Momentum in Japan: The Exception that Proves the Rule. The Journal of Portfolio Management, 37(4), pp.67-75.

Asness, C. and Frazzini, A. (2011). The Devil in HML’s Details. SSRN Electronic Journal.

Asness, C., Frazzini, A., Israel, R. and Moskowitz, T. (2014). Fact, Fiction and Momentum Investing. SSRN Electronic Journal.

Asness, C., Frazzini, A., Israel, R. and Moskowitz, T. (2015). Fact, Fiction, and Value Investing. SSRN Electronic Journal.

Asness, C., Moskowitz, T. and Pedersen, L. (2013). Value and Momentum Everywhere. The Journal of Finance, 68(3), pp.929-985.

Daniel, K. and Moskowitz, T. (2013). Momentum Crashes. SSRN Electronic Journal.

Israel, R. and Moskowitz, T. (2013). The role of shorting, firm size, and time on market anomalies. Journal of Financial Economics, 108(2), pp.275-301.

You can download the AQR dataset from the following link: https://images.aqr.com/-/media/AQR/Documents/Insights/Data-Sets/Value-and-Momentum-Everywhere-Portfolios-Monthly.xlsx

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