Momentum

Momentum is the tendency of investments to persist in their performance. Assets that perform well over a 3 to 12 month period tend to continue to perform well into the future. The momentum effect of Jegadeesh and Titman (1993) is one of the strongest and most pervasive financial phenomena. Momentum investment strategies have been mostly applied to equities (see momentum in equities), however there is large evidence documenting momentum across different asset classes. Typical strategy consists of a universe of major indices on equity, bonds, real estate and commodities. The aim is to keep long only portfolio where an index with positive past 12 month returns is bought and negative returns sold. A well-known example of trend following momentum strategy is from Faber (2007). He creates 10 month moving average for which assets are sold and bought every month based on price being above or below the moving average. Using a 100 years of data, Faber claims to outperform the market with the mean return of 10.18% , 11.97 % volatility and max draw-down of 50.29%, compared to S&P 500 return of 9.32%, volatility of 17.87% and max draw-down of 83.46%.

In general, we distinguish between absolute and relative momentum. Absolute momentum is captured by trend following strategies that adjusts weights of assets based on past returns such as relative level of current prices compared to moving averages. Relative or cross sectional momentum, on the other hand, use long and short positions applied to both the long and short side of a market simultaneously. It makes little difference whether the studied markets go up or down, since short momentum positions hedge long ones, and vice versa. When looking only at long side momentum, however, it is desirable to be long only when both absolute and relative momentum are positive, since long-only momentum results are highly regime dependent. In order to increase performance, the simple momentum strategy is expanded to capture both relative and absolute momentum creating a long short portfolio.

Various extensions to the simple strategies shown above have been suggested. For example we can deploy mean-variance optimisation to re-weight our assets to minimise the risk given return. Moreover, we can diversify the strategy by restricting the weights to different asset classes and risk factors as well as adding various risk management practices to decrease leverage during heightened volatility periods. Furthermore, taking into account the cyclicality and idiosyncratic momentum of various sub-indices to Faber’s original asset classes produces even stronger improvements to risk-adjusted returns. Unfortunately, cross-sectional strategies use high number of stocks resulting in high trading costs. Luckily, it has been found that using sectors and indices instead of individual stocks still earns similar momentum returns while having lower trading costs.

Numerous empirical studies report on benefits of extending momentum strategy across asset classes (see Rouwenhorst 1998, Blake 1999, Griffin, Ji, and Martin 2003, Gorton, Hayashi, and Rouwenhorst 2008, Asness, Moskowitz, and Pedersen 2009). For example, including commodities in a momentum strategy can achieve better diversification and protection from inflation while having equity like returns (Erb and Harvey, 2006). Foreign exchange is another asset class with published momentum effects. Okunev and White (2003) find the well-documented profitability of momentum strategies with equities to hold for currencies throughout the 1980s and the 1990s. Contrary to already mentioned asset classes, bond returns have generally not displayed momentum. However, some later evidence suggests that assorting bonds with volatility adjusted returns leads to observation of momentum. Using 68,914 individual investment-grade and high-yield bonds, Jostova et al. (2013) find strong evidence of momentum profitability in US corporate bonds over the period from 1973 to 2008. Past six-month winners outperform past six-month losers by 61 basis points per month over a six-month holding period. Last but not least, momentum has been documented in real estate with a cross-sectional momentum buy/sell strategy significantly reducing volatility and drawdown of a long only REIT fund.

An often cited benefit of momentum strategies is their sustainable performance attributed to a true anomaly rather than skewedness in the return probability distribution that is cited to be responsible for value and carry strategy. Reasons explaining the momentum anomaly include analyst coverage, analyst forecast dispersion, illiquidity, price level, age, size, credit rating, return chasing and confirmation bias, market-to-book, turnover and others.

The Size Effect Has a Lottery-Style Payoff

11.January 2019

A new research paper related mainly to:

#25 – SIze Premium

Authors: McGee, Olmo

Title: The Size Premium As a Lottery

Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3279645

Abstract:

We investigate empirically the dependence of the size effect on the top performing stocks in a cross-section of risky assets separated by industry. We propose a test for a lottery-style factor payoff based on a stochastic utility model for an under-diversified investor. The associated conditional logit model is used to rank different investment portfolios based on size and we assess the robustness of the ranking to the inclusion/exclusion of the best performing stocks in the cross-section. Our results show that the size effect has a lottery-style payoff and is spurious for most industries once we remove the single best returning stock in an industry from the sample each month. Analysis in an asset pricing framework shows that standard asset pricing models fail to correctly specify the size premium on risky assets when industry winners are excluded from the construction of the size factor. Our findings have implications for stock picking, investment management and risk factor analysis.

Notable quotations from the academic research paper:

" Firms with small market capitalization tend to outperform larger companies. Investors are attracted to lottery-like assets with positively skewed returns because they o ffer a very large payoff with a small probability, which the investors overweight. This demand makes positively skewed securities overpriced and likely to earn low returns. In this article we test whether the size/market capitalization attribute, and associated factor-mimicking portfolios, receive a lottery-like payoff . The implications of this are that most small stocks do not payoff and the returns to a size strategy are driven by a small number of winners. This type of payo ff can be captured through diversi fication but leaves an under-diversifi ed investor exposed. The risk being that they will not include winning stocks and their resulting return expectation is negative.

To investigate the e ffect of winning stocks on the performance of investment portfolios based on the size we propose a conditional logit model for ranking di fferent investment portfolios based on size and assess the robustness of the ranking to the inclusion/exclusion of the best performing stocks in the cross-section. This parametric choice is embedded within a stochastic utility model for explaining the investment decisions of under-diversi fied size investors aiming to exploit the so-called size premium. under-diversifi ed individuals maximize their expected utility in each period by choosing the stock that is predicted to yield the highest return (highest positive skew). This choice is driven by market capitalization of the portfolio and modeled parametrically using the conditional logit model.

In order to obtain cross-sectional variation on the relationship between the size e ffect and portfolio performance we split the whole cross-section of stocks into di fferent industries and fi t the conditional logit model to each industry separately. We apply the conditional logit model at an industry-speci fic level across three ranked sorted portfolios based on market capitalization: a small, mid-size and big portfolio created from the stocks in each tercile of the cross-section of assets in a speci fic industry ranked by asset size. This exercise is repeated for 20 industries over the period January 1970 to November 2015. Our results reveal that the size e ffect vanishes once the top performing stocks in an industry are removed from the sample.

size lottery

Our empirical findings also highlight the role of industry momentum in determining the relationship between market capitalization and portfolio performance. Speci fically, market capitalization has signi ficantly better predictive ability for portfolio return performance in the months following a positive return in an industry than in the months following a negative industry return.

Given these findings, we investigate further the influence of the winning stocks in industry-speci fic size portfolios. In particular, we propose an alternative size portfolio that we denominate as the winner-weighted index, based on the forecast rank probabilities of stocks provided by the conditional logit model. Intuitively, those stocks that are predicted to be winners in the next period receive a larger allocation of wealth than those stocks that have a low probability of becoming winners. More formally, the allocation of wealth to each asset in the portfolio is determined by the forecast winning probabilities obtained from the conditional logit model and driven by asset size. The performance of this portfolio is compared against a cap-weighted index benchmark portfolio. The weights in the latter portfolio are also driven by market capitalization, however, in contrast to our winner-weighted index portfolio, smaller stocks within an industry receive a smaller allocation of wealth. We consider statistical and economic measures such as the Sharpe ratio, Sortino ratio, the certainty equivalent return of a mean-variance investor and portfolio turnover. We observe the existence of two regimes in portfolio performance. During positive industry momentum periods, the winner-weighted index outperforms the cap-weighted portfolio for 19 out of 20 industries, the exception being the utilities industry. This result is, however, reversed in periods of negative industry momentum for which the cap-weighted index outperforms the winner-weighted index in 18 out of 20 industries.

Our second objective is to explore the influence of winning stocks on the size portfolio pricing factor widely used in the empirical asset pricing literature. Our empirical results for both a top-minus-bottom trading portfolio and a long-only portfolio show that standard asset pricing models are not able to adequately capture the contribution of the size premium to the overall risk premium when the winning stocks are removed from the size factor portfolio. In contrast, we note that the factor loadings ( Beta's) associated to the size portfolio pricing factor in standard models are robust to the inclusion/exclusion of the winning stocks. The removal of winning stocks is a ffecting the risk premium rather than the covariance of portfolios with the risk factor."

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