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This page lists papers that describe trading strategies (such a momentum, value, pairs trading, etc) and their returns, or evaluation of trading strategies. It also covers technical analysis at the bottom. Papers using machine learning tools to trade are here.

#### **The Interaction of Value and Momentum Strategies

Author Clifford S Asness (Goldman Sachs / AQR)

Published: Financial Analysts Journal March/April 1997

Online: http://momentum.behaviouralfinance.net/Asne97.pdf (PDF)

Keywords: Long-term stock return analysis, stock return factors, Momentum and Value

Folder: Trading Strategies

Looks at interaction between momentum and value factors in long-term stock returns.Finds value and momentum factors negatively correlated, but both effective. Value strategy tends to work best when its forced NOT to short momentum (as it tends to naively), and holding value constant tends to lead to a superior momentum strategy. Value works, in general, but fails on firms with strong momentum. Momentum works, in general, but is strongest for expensive (poor value) firms. Also looks at holding momentum constant and finds dividend yield to be very predictive of high returns for all but recent winner (high momentum). Though a very simple concept, the paper is novel, well presented, easily understood, and finds extremely significant results (maybe that's why the author founded a successful hedge fund?).

#### **Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency, and

#### **Profitability of Momentum Strategies: An Evaluation of Alternative Explanations

Authors: Jegadeesh and Tittman

Published: Journal of Finance March 1993 and April 2001

Online: (Sorry JSTOR only) http://ideas.repec.org/a/bla/jfinan/v48y1993i1p65-91.html, http://ideas.repec.org/p/nbr/nberwo/7159.html

Folder: Trading Strategies

Keywords: Momentum strategies, January effect

This is a paper and a follow-up published 8 years later with newer data. The original paper looks at NYSE and AMEX data from 1965 to 1989 and finds significant profits from buying stocks with recent strong performance and holding them a short period (say 3 to 12 months) while shorting stocks with recent weak performance. The authors consider sorting stocks into deciles by their returns over the last 1,2,3,4 quarters and then buying the highest decile (one with recent strong performance) and selling the weakest, and closing this position after a holding period of 1,2,3,or 4 quarters. They also consider adding a 1-week lag between formation and holding periods to account for bid-ask bounce. They find profits on this zero-capital position averaging about 1% a month, with longer formation periods and shorter holding periods doing better (the best of the many they consider used a 12-month formation period, 3-month holding period, and a 1-week lag between formation and holding periods to earn 1.49% per month, but this should be taken with a grain of salt since the maximum of a set of unbiased estimators can be biased).

Next the authors use an (unspecified) one-factor model to show that the source of profits could be cross-sectional dispersion of mean returns, auto-correlation in factor returns, or idiosyncratic effects. The rest of the authors' analysis uses a 6-month formation period, 6-month holding period strategy (6-6). They show that the winner decile has larger average size and smaller average beta than the loser portfolio, so the long-short portfolio is actually negative beta so systematic risk doesn't explain the returns. They show that (market) factor autocorrelation doesn't explain the momentum profits, nor does a lead-lag model where securities consistently over or under react to the market factor.

The authors sort securities into size and beta sub-samples and look at 6-6 momentum strategies within the subsamples, and find momentum returns increase with beta and aren't as strongly related to size (but perhaps are higher for small firms). Next they find that the 6-6 momentum strategy loses about 7% on average in January (mostly in the small stock sub sample), so it earns 1.66% per month excluding January (1.81% a month in the small-firm subsample). They find returns are positive in about two-thirds of months (60% in big-firm subsample) but positive in 96% of Aprils and 24% of Januaries. The momentum strategies had positive average return in all but one five-year subperiod in the data set.

Interestingly, holding periods longer than 12 months lead to steep declines in return, with every holding-period month after the 12th giving a negative return. Backtesting indicated the strategy did not perform as well before 1960. They conclude that this is a viable strategy with positive risk-adjusted returns, and interpret that investors who buy past winners and sell past losers move market prices from their long-term value TEMPORARILY, with a reversal after about a year.

The momentum strategies are very clearly explained and thoroughly examined, and give significant returns with negligible beta. At least a few sentences mentioning turn-over and transaction costs would have been nice.

**(Summary of follow-up 1998 paper)**

This paper is a follow-up that eximnes the 6-6 momentum strategy's performance in 1990-1998, finding that it earns an even higher average monthly returns (1.39% per month) than it did in the 1965-1989 period (in the small-cap and large-cap subsamples, the average monthly returns were 1.65% and 0.88% in the 1990-1998 period). In this newer study they sometimes exclude the lowest size decile and stocks priced below $5. The negative momentum returns in January continued in the new sample period (-1.2% in Jan.). Over the whole sample period, they find small but negligible loadings on the three Fama French factors, with only the HML loding of -0.22 being close to significant: this means the momentum portfolios have CAPM and Fama-French monthly alphas of 1.24 and 1.36.

Next, they find extreme negative returns to momentum portfolios if the holding period extends longer than 12 months, with cumulative returns peaking after 12 months and then generaly dropping. They use this to reject the idea that different unconditional expected returns cause momentum profits. They also find consistent returns and Fama-French alphas in the subperiods 1965-1981 and 1982-1998.

The continued out-performance of momentum portfolios in the true hold-out strongly rejects the idea that it could have been an artifact of data snooping bias. The only practical caveat is that momentum profits for large-cap stocks (which are cheaper to trade in big amounts and easier to short) are lower, though still positive and significant.

#### **Do Industries Explain Momentum?

Authors: Moskowitz and Grinblatt

Published: The Journal of Finance 1999

Keywords: Momentum, industry momentum

Summary: The authors claim that momentum in industry indexes (over the medium 3 to 12 month term) largely supercedes momentum in individual stocks, and that industry momentum returns are more robust (make more on the buy than the sell side, are more diversified, no one-month reversals, and do well when limited to high-dollar-volume stocks).

The authors use CRSP and Compustat data from July 1963 to July 1995 divided into 20 value-weighted industry portfolios, non of which ever has less than 25 stocks. They decompose the return on a stock at some time as a sum of: (1) the risk free rate (2) linear loadings on non-diversifiable factors which may have non-zero expected return (the Fama-French (FF) factors proxy for these) (3) loadings on zero-mean diversifiable factors (industry factors) (4) idiosyncratic (epsilon) variance. Using the usual notation R_i(t) = return to stock i in month t, R_M(t) = market return, the average over ALL stocks of the quantity E[ ( R_i(t) - R_M(t) ) * ( R_i(t-1) - R_M(t-1) ) ] can be expressed as (1) The variance of unconditional expected returns (from differences in loadings FF factors) (2) autocovariance in the FF factor returns (3) autocovariance in the industry factor returns (4) idiosyncratic autocovariace. They claim momentum returns come from (3): autocovariance in industry returns, since they find negligible autocovariance in the FF Factors ** at the 6 month horizon**.

Anyway, they claim the 6-month formation period, 6-month holding period (henceforth 6-6) strategy applied to individual stocks, buying the top 30% by past 6-month return and shorting the bottom 30% by past 6 month return, earns 0.43% per month [this is smaller than the Jegadeesh Titman result since J-T go long-short the top and bottom decile by past return]. The authors find that a long-short strategy long the top 3 industries (by past 6 month return) and short the bottom 3, held for six month, also earns 0.43% per month: thus they argue that persistence in idiosyncratic components of individual stock return [ item (4) in above paragraph ] doesn't drive momentum strategy profitability, and in fact persistence in industry factors does drive individual stock momentum returns (hence they are the same magnitude). Industry momentum profits remain 0.29% per month after accounting for size, but individual stock momentum profits are only .13% per month after accounting for industry momentum, and even less if accounting for size also.

Robustness checks: The authors create "random industries" : groupings of stocks with the same individual stock past return profiles as real industries, but stocks are randomly assigned. They find ~zero momentum profits are achievable using these random industries. They find that going long-short (top 30% - bottom 30%) individual stocks within each industry gives only 0.11% per month. However, long losing stocks from winning industries and short winning stocks from losing industries gives 0.3% per month. SImilar to individual stock momentum, industry stock momentum has reversals if portfolios are held for over 12 months. But unlike individual stock momentum, industry indexes don't have one-month reversals: i.e. industries that did well last month do better this month (~1% per month) even if only the largest 20% of stocks are traded. Interesting, this one-month return persistence is even stronger (1.56% a month) if the universe of stocks is limited to only the 20% with the largest dollar trading volume (i.e. the most liquid). These results are surprising because, with individual stocks, those that did well last month do poorly this month (strong reversals on a one-month time scale). Also, in industry momentum strategies the long position contributes most profit (long - mid = 0.36% per month, mid - short = 0.07%). Finally, they perform Fama-French-like cross-sectional regressions, and find that coefficients on industry momentum factors are more significant (statistically) that those on individual stock momentum for explaining cross-sectional returns (there are many more details in the paper).

#### **Paralells Between Cross-Sectional Predictability of Stock and Country Returns

Authros: Clifford S. Asness, John M. Liew, and Ross L. Stevens

Published: Journal of Portfolio Management 1997

Keywords: Zero-cost strategies, momentum, value , size, country returns, country momentum, January effect

References within this paper: to January effect, Short-term reversal effects (in endnotes)

Summary: This paper shows that, just as zero-cost strategies that makes bets on size (market cap.), book-to-market, and recent performance have predictive performance and earn high returns in US stocks, these same strategies earn high returns across country indexes.

Uses data from 07/1963 to 12/1994 for stocks and (02/1975-12/1994 and 01/1970 to 12/1994) for countries, and uses all stocks traded on the NYSE, NASDAQ, or AMEX meeting data requirements, and local country returns for almost all countries in the MSCI world index. The strategies sort stocks or countries into equal-weight tritiles based on size (SMB), book-to-market (HML), or momentum (MOM), and go long one tritle (small size, high book-to-market, strong momentum over the past 12 months, excluding last month) and short the other.

The returns (in BP per month) and annual Sharpe ratios to stocks and countries are:

Stocks: HML: 85, 1.00. SMB 44, 0.39. MOM 71, 0.79

Countries: HML: 78, 0.85 SMB: 55, 0.63 MOM: 103, 0.85

The paper finds that ALL of the SMB return to stocks occurs in January (the non-January returns are statistically insignificant), and almost all of the SMB returns to countries also occurs in January. Finds correlations between zero-cost stock and country returns is small (~0.2) but stat. significant.

Looking at risk adjustment, the authors mention that small size and high BE/ME proxy for distress risk (the latter because it implies low earnings). Find small and high book-to-market firms have lower CF/equity than their counterparts before and after portfolio formation, but CF/equity improves for 3 years after portfolio formation. Firms with strong momentum had lower CF/EQ 3 to 1 year before portfolio formation, but it strongly improves in the two years surrounding portfolio formation and has higher-than-average CF/equity from 1 to 3 years after portfolio formation. So high returns to the MOM portfolio preceed a period of high profitability.

I really enjoyed this paper: as is usual with Asness's papers, it's quite dense and hard to summarize because most of the results are so relevant

** **

#### **Style-Timing: Value versus Growth

Authors: Clifford S. Asness,Jacques A. Friedman, Robert J. Krail, and John M. Liew

Published: Journal of Portfolio Management 2000

Keywords: value strategies, forecasting value returns, return-persistence in value strategies

References within this paper: Cites 5 papers forecasting value returns using things like S&P earnings yield, the yield curve, corporate credit spreads, and macro variables.

Summary: This paper examines whether or not returns to zero-cost value strategie are predictable, and finds some evidence of their predictability based on the size of a composite value rating spread between a value portfolio and a growth portfolio.

Uses the Gordon growth model, that E( return) = E / P + g, where g is future earnings growth and E / P is the current earnings yield: earnings over stock price. Uses this to show that the return spread between a value and a growth portfolio should be: E( Val. Ret. - Growth Ret.) = (E/P_val - E/P_growth) - (g_growth - g_value). That is, the expected return difference between value and growth stocks should be an E/P spread minus a growth spread, both expected to be positive.

Uses data from Dec.1981 - Sept 1999 and three value measures: E/P, B/M (Book / Mkt), and S/C (Sales / Capital = eq. + bonds). The investment universe is the 1,100 most liquid US stocks at any given time. An industry-relative value version of each value measure is created for E/P, B/M, and S/C by subtracting its industry average. All stocks are ranked on the industry adjusted version of each value measure, and the average of the 3 ranks for each stocks its used as its composite value measure for portfolio formation. A long-short equal-weight portfolio is created that is long the top decile and short the bottom decile, with deciles short on the above composite value measure. This zero-cost portfolio performs well (6.79% annually), better than sorting on E/P of B/M alone (but sorting on S/C does best). The authors also create EPS growth forecasts for each stock using median analyst forcasts (this gives the "g" in the gordon growth model).

To forecast value versus growth performance, the authors

1) Create a value and growth portfolio as described above (long top decile, short bottom on composite industry-adjusted value measure)

2) Compute median E/P, B/M, and S/C for the growth and value portfolios. This defines a "spread" as the difference in each value measure between the portfolios, and a composite measure is the average of these three spreads. These are the value-spreads

A growth spread is defined as the expected growth for the growth portfolio minus that for the value portfolio: note the order is different. So a historically high value spread forecasts a high return on value - growth, while a high growth spread forecasts a low return on value - growth. The authors find that the value spread and the growth spreads are highly positively correlated, so a good forecast should use both.

Lastly they perform predictive regressions, with the returns of the (value - growth) zero-cost portfolio (Ret) as dependant variable and the various spreads as the independant variables. They find the best regression forecasts the returns using the composite value spread and the growth spread as the predictive variables, with:

Ret = 8.29 + 15.52 * Composite Value Spread - 9.48*Earnings Growth Spead

This has an R^2 of .387, and very significant slopes and intercept that are of the correct sign according to the Gordon Growth Model.

Some important points are that the authors find making zero-cost value bets on industry-adjusted value measures is higher Sharpe ratio than the non-industry-adjusted value bets. Also, they report that value strategies have long periods of sub-par performance (return persistence)

This paper was written before the tech bubble burst and the author was forecasting strong future value returns relative to growth!

#### **Evidence of Predictable Behavior in Security Returns

Author: Narasimhan Jegadeesh

Published: The Journal of Finance 1990

Keywords: Short-term reversal, autoregression, serial correlation, autocorrelation

References: Serial correlation (Fama and French 1988, Lo and MacKinley 1988)

Summary: Jegadeesh finds strong evidence of monthly revesals in security returns, and develops a strategy to profit from them, giving 2.49% risk-adjusted return per month before transaction costs

I begin with some definitions, **r(i,t)** is stock i's return in month r, and **R(i,t-k)**is stock i's average return from month **t-k **to month **t-1, r(i)** is stock i's (unknown) expected return, and **r(t)** is the market's return in month **t**. Jegadeesh considers an autoregressive-like model

**r(i,t) - r(t) = a_0 + sum_k( a_k*R(i,t-k))**

where stock i's return above its average depends on its passed cumulative returns. He finds that this model has an R^2 of 0.1 on individual stocks in 1934-1987, which is outstanding considering the "noise" in stock returns. He finds the **a_1, ** coefficients tend to be negative (short-term reversals), especially in January. The coefficients on cumulative past returns going back further tend to be positive, but negative in January. When we go as far back as **a_12, **the coefficients are positive in and outside January.

His empiriacal tests create return forecasts using the time-series autoregression

**r_hat(i,t) = a_hat(0) + sum_{k = 1 to 12}( a_hat(k)*R(i,t-k))+a_hat(13)*R(i,t-24)+a_hat(14)*R(i,t-36)**

The coefficients **a** are estimated cross-sectionally for all stocks, using the past 60 months of data, for all stocks with that data. Thus at each data **t**, roughly 15 **a_hat** coefficients are estimated using past returns for all stocks, giving small errors compared to trying to estimate an **a_hat** for EACH stock. That is, in Jegadeesh's model the same **a_hat**s are used to make forecasts for all stocks at some time **t**. Three strategies are considered

1) S0: A position is taken in each stock proportional to **r_hat(i,t)**, its expected return, normalized so the position is zero-cost (i.e. long and short equal dollar amounts)

2) S1: 10 portfolios are formed each month based on each stock's return last month: go long the portfolio with the stocks which had the lowest return last month, and short the portfolio with the stocks which had the highest return last month

3) S12: Same as S1, but form portfolios based on each stock's return last year, and we go long the portfolio with high returns over the past 12 months, short the one with low returns.

Each portfolios excess return is its CAPM alpha: its return minus the risk-free rate minus a CAPM beta adjustment. Note that, in long-short portfolios, the risk-free rate will cancel out. ALL RETURNS REPORTED ARE RISK-ADJUSTED IN THIS MANNER. Anyway, S0 earns 2.49% per month (4.37% in January), S1 earns 1.99% per month (3.89% in January), and S12 earns 0.93% per month (1.73% in January). He finds adding a size adjustment to the portfolios' risk -adjusted returns doesn't reduce the "spread" profits much, but does bring the January returns down to the same level as the returns in othe rmonths, and allowing a time-varying beta makes no difference. An adjustment to reduce bid-ask-bounce bias, which forms portfolios excluding the return on the final day of the final month of the portfolio formation period, seems to reduce long-short return spreads by about 20% (though this uses a different sample period, beginning in the 1960s).

#### **Value and Growth Investing: Review and Update

Authors: Louis K.C. Chan and Josef Lakonishok

Published: Financial Analysts Journal 2004

Reference: Fama-French (1998) "Value vs. Growth: International Evidence"

The authors cite evidence of continued outperformance by value strategies, and show that the results of the 1995-2001 period do not contradict the general trend that value strategies have outperformed growth strategies. They first look at three studies, finding that the decile of stocks with the highest book-to-market value outperforms the decile with the lowest book-to-market value by 0.5% to 1% a month, depending on the period, and this outperformance isn't explained by firm size. They mention that CF/P (Cashflow to price) is an equally effective value metric, but price to earnings seems to be less effective. They find this to be roughly consistent across developed markets (1975-1995). They argue convincingly that the value portfolio isn't riskier in any reasonable sense, and that inventing an ad-hoc "value-exposure" risk factor isn't right. Rather, they find that the glamour portfolio, though priced to have high future income growth, doesn't realize higher 5-year income growth, and often has poor returns around earnings announcement dates (by contrast, the value portfolio has strong performance around earnigns announcements, indicating positive surprices). Thus they argue that a behavioral cause probably causes value's outperformance.

Next they look at data in the 1995-2001 period: growth significantly beat value in 1998-1999, but value more than gained back its ground in 2000-2001. Also, the higher performance in the growth portfolio was due to rising P/E or P/CF, not rising fundamentals. Looking at the whole period, they use Russel indexes, which break half the market cap into value and half into growth (so these are not "extreme" decile bets). Then value (large-only value) returns 14.7% (13.9%) annualized while growth (large-only growth) returned 8.9% (11.8%). The Russel indexes us Book/Mkt and long-term growth forecasts to determine value or growth properties. The authors create a composite value indicator using B/Mkt, CF/P,E/P, Sales/P, and some unspecified robust regression methods to make value bets on high and low deciles, and find (1969-2001) the value portfolio 16.4% versus 4.5% for growth when restricted to large-cap stocks, or 18.3% versus -2.8% for small-cap. Value strategies seem to be holding up well.

#### **Practical Active Currency Management for Global Equity Portfolios

Author: Tod F Reinert

Published: Journal of Portfolio Management 2000

Keywords: Currency hedging, currency trading, movng average rules

The author looks at the currency hedging question in international equity portfolios, and finds that an active currency strategy improves portfolio performance (return and Sharpe ratio) versus a passive hedging or no hedging. He chooses from a class of moving average rules to decide whether or not to hedge. Specifically, he hedges the portfolio if the dollar is relatively high compared to its moving average, measured in local currencies. There may be data mining bias issues in the study, since I'm not sure how many rules (i.e. moving average durations) the author considered, but he still presents a very interesting study.

#### **Enhanced Active Equity Strategies

Authors: Bruce Jacobs and Kenneth Levy

Published: Journal of Portfolio Management 2006

Keywords: Long-short investing, stock loan account, enhanced prime brokerage

They contrast equity strategies in order of increasing "active" return: index, enhanced index, active, enhanced active, and market neutral long-short. Enhanced active allows shorting: for example, 120% long, 20% short, while active doesn't short. They justify the value of enhanced active strategies by noting that "active" weights are a stock's weight in the portfolio minus its index weight, and since over half the stocks in the Russell 3000 have index weight below 0.01%, the no-short-sale constraint in an active strategy prevents negative active weights below -0.01%: a serious constraint if the manager has a negative view. Enhanced active allows shorting, and by using the proceeds of the short sale in the long position this increases the amoung of negative position the manager can take, especially in small caps. They stress the importance of optimizing an enhanced active (say 120-20) portfolio in an integrated manner: not as a seperate long-short 20-20 and long-only 100% portfolio. They also describe a stock loan account, an enhanced prime brokerage feature, and its mechanics. This allows qualified asset managers to get around short-sale constraints and margin requirements and use the proceeds of their short sales.

#### **Fads, Martingales, and Market Efficiency

Author: Bruce Lehmann

Published: The Quarterly Journal of Economics 1990

Keywords: Weekly reversals, short-term reversals

References: Long-term reversals (Debondt and Thaler 1985, Fama and French 1987, Poterba and Summer 1987).

Buying stocks cheaper after a decline (Baesel, Shows, Thorp 1983, Beebower and Priese 1979, Sweeny 1986)

Summary: Lehman shows very strong return reversals at the weekly level, and argues that this represents inefficiency because the time scale is so short that time-varying expected return can't account for it.

Lehman argues that simple autocorrelation tests to see if stock returns are martingales or IID can't test market efficiency: they can only find that stock's aren't IID or that expected returns are time varying. Thus he suggests that looking at returns of arbitrage portfolios as a stronger test of market efficiency, because its unlikely that expected / required return for a stock changes significantly on a weekly basis. He creates a strategy that builds a portfolio with weights

**w(i,t) = - [ r(i,t-k) - R(t-k) ]**

where **w(i,t)** is the weight of stock **i** in the portfolio at time **t** (negative indicates a short), **r(i,t)** is the return of stock **i** at time **t**, and **R(t)** is the market return at time **t**. The profit from this strategy over one period is

**profit = sum_i [ w(i,t)*r(i,t) ] = - sum_i [ ( r(i,t-k) - R(t-k) ) *( r(i,t)-R(t) )**

or roughly the autocovariance at lag **k **(I say roughly because the weights **w** are scaled by a constant of proportionality). He shows the the average profit of this strategy, over **T** periods, depends

1) Positively on market autocovariance (N/T)*cov( R(t), R(t-k) ) [N = # stocks]

2) Negatively on individual stock autocovariance ( -(1/T)*sum_i [ cov( r(i,t), r(i,t-k) ]

3) Negatively on cross-sectional variance in individual stock returns

Thus if the market and individual stocks have zero autocovariance, the strategy loses money. Next he argues that the transaction costs and constraints aren't that bad: transaction costs are cheap for big stocks, short-sale constraints aren't an issue if this strategy is used a a delta from a normal portfolio, etc. He also argues that bets on reversals are cheap because buying a stock that just dropped / selling one that just rose helps provide liquidty and meets some demand of market makers.

Empirically, he uses data July 1962 to Dec 1986, and chooses one week (strating wednesday, ending Tuesday), and uses all NYSE and AMEX stocks. Then the strategy described above earns 1.79% per week, with only 1.56% standard deviation, and is net positive in 93% of periods (I think a period is like 26 weeks, couldn't find it exactly sorry!). Excluding the return on the Tuesday of the formation period reduces returns to 1.2% per week. Lagging one-week between formation period and holding period eanrs only 0.5% per week (still ~26% annualized). The profits on the winner and loser portfolios are negatively correlated, leading to the low standard deviatio. The losers (long) portfolio contributes about 2/3 of profits. He argues that, despite the **massive** turnover, the profits survive a 0.2% transaction cost.

However, one issue I have with this paper is that the table on page 20-21 (table IV) shows that the returns are MASSIVELY driven by the smallest-market capitalization stocks: if I interpret the table right, half of the portfolio's investment is in the smallest 20% of stocks, and these contribute over 3/4 of the profit. For some reason the text doesn't dwell on this. It's hard to interpret how well the strategy would do if limited to the largest quintile of stocks by market capitalization: Table IV seems to suggest that the return spread among these large stocks is only 0.04% per week.

#### **Does the Stock Market Overreact

Authors: Werner De Bondt and Richard Thaler

Published: The Journal of Finance 1985

Keywords: Long-term reversals, extrapolation bias

Summary: The authors, both behavioral economists, predict that past stock market performance is reversed, and the more extreme the past performance the stronger the reversal. They find evidence of stock return reversal over long (~3+ year) time horizons.

The authors use CRSP data from 1926 to 1982, and create equally-weighted portfolios based on stocks' excess return over the market (i.e. assume all betas are equal to one). They (1) Compute the residual return (stock return - market return) for every stock with 85 months of prior data (2) Every three years starting in December from Dec. 1932, compute the **average excess return** of each stock as the average of the residual returns over the past 36 months (3) Define a winner portfolio as the (top 35,top 50,top 10%) of stocks by **average excess return**, and define a loser portfolio similarly (4) Compute CAR (cumulative average return over market) for winner and loser portfolios over the 16 test periods (1932-1935,1935-1938,.). The results are that the 35-stock loser portfolio outperforms the market by ~19.6% cumulative over the 36-month test period, while the winner portfolio returns 5% under the market, for a ~24.6% spread over the 3 years. Most of the return difference is in January, and most is in the second two years of the holding period. They find a formation period of at least two years is required for the reversal, and the reversals continue even if the holding period is 5 years. They also note that holding a more stocks in the winner and loser portfolio (e.g. winner and loser portfolios long/short the top and bottom deciles, instead of long/short only the most extreme 35 stocks) give a smaller return spread. Lastly they consider risk adjustment, and find that the loser portfolio has lower CAPM beta (1.03) than the winner (1.37), so the CAPM-adjusted returns are ** higher **since the winner portfolio (which they short) has higher beta.

Conclusion: This paper is less detailed than the later momentum papers, probably because of limited computing power, but it uncovers a clear anamoly. An interesting note is that the last line of table 1 reveals momentum profits of ~7.6% a year using a 12-12 strategy, a precursor to Jagedeesh and Titman's famous momentum paper, but the authors of this paper don't comment on the one-year momentum.

#### **Contrarian Investment, Extrapolation, and Risk

Authors: Lakonishok, Shleifer, and Vishny

Published: The Journal of Finance 1994

Cites: Value strategies in Japan (top of page 1542)

Keywords: Value strategies (conditioning on two variables), extrapolation bias, contrarian, Compustat NASDAQ expansion and look ahead bias

Summary: The authors argue that "value" strategies have higher expected return due to sub-optimal investor behavior, and are not riskier. They also show that value strategies which condition on two variables (e.g. past sales growth and book/market) earn higher return.

The authors define glamour stocks as those which have performed well in the past and are priced to perform well in the future (e.g. perform well = sales growth, EPS growth, etc). They argue that differences in expected growth between value and glamour stocks partly results from investors incorrectly extrapolating forward past growth, ignoring mean reversion. They generally use past sales growth (occasionally weighted) as a proxy for past growth, and ratios X / price (X = book value, CF, earnings) as a proxy for expected future growth. They use data from April 1963 to April 1990, though the first five years are needed for portfolio formation so their strategy returns are April 1968 to April 1990. They discuss the look-ahead bias in Compustat, which they mitigate by ignoring firms with under 5 years of Compustat returns and by using only NYSE and AMEX firms. They look at long (5 year) return spreads between value and growth portfolios after portfolio formation. First they look at forming decile portfolios based on one variable, and look at the five-year return spread between the value and growth deciles, in absolute and size adjusted returns. Sorting on book to market of CF/price gives an ~11% five-year average return spread (~8 or 9% size adjusted), E/P gives 7.6% (5.4% size adjusted), and past sales growth gives 6.8% (4.6% size adjusted) [portfolios with low past sales growth do better]. Next, splitting stocks roughly into thirds by CF/P or Book/Mkt and into thirds by past sales growth (giving 9 portfolios) can give spreads around 12% annually for value-value minus glamour-glamour, with size adjusted spreads slightly lower again. Limiting the universe to the top 50% or 20% of stocks by market cap reduces the dual-sorted portfolio spreads to about 8% annually but the size-adjusted spreads are also about 8%. Cross-sectional regressions find CF/P, E/P, and past sales growth explain most variance in univariate model, but CF/P and past sales growth and the strongest in the full multivariate model.

They find value portfolios have lower past growth in (CF, earnings, sales) than glamour, and after portfolio formation value portfolios still have lower growth in these variables than the glamour portfolio (though the difference shrinks), but the difference in port-formation growth of CF, sales, earnings, etc. isn't nearly enough to justify the differences in multiples (CF/P, E/P) for the value and growth portfolios. Thus they conclude investors wrongly guessed that the glamour portfolio would have much higher future growth than it ends up having. They find no evidence that value strategies are riskier. Value portfolios outperform glamour in 17 to 19 or the 21 years, and value beat glamour over every five year period. Value portfolios have marginally higher beta and volatility, but nowhere near enough to explain the difference in returns. Also, value portfolios don't perform worse in extreme down markets or recessions.

This is a great paper, and very convincing. I would like the see the authors consider the possibility that value stocks individually have higher idiosyncratic risk, but that sub-optimal investors aren't realizing that this is irrelevant and will be diversified away in a portfolio.

#### **The 52-Week High and Momentum Investing

Authors: Thomas J. George and Chuan-Yang Hwang

Published: The Journal of Finance 2004

Keywords: Momentum, 52-week high, anchoring bias, behavioral finance

References: Anchoring BIas (Kahneman et. al, Ginsberg et. al.). Behavioral model leading to LT reversal (Grinblatt 2002, Klein 2001), Dynamic Risk Adjustment (Grundy and Martin 2001)

Summary: The authors find that a stock's nearness to its 52-week high is more predictive of its future performance than its past return, and stocks sorted by 52-week high don't experience future reversals. The authors explain this by saying that traders are reluctant to push a stock past its 52-week high, but once sufficient information arrives to cause them to do so, the stocks moves up strongly. They point out that this is strange since 52-week high is published in almost all financial magazines and so is readily available.

The authors use monthly data from 1963-2001 compare a Jegadeesh-Titman (JT) like momenutm strategy (long top 30%, short bottom 30%, based on past return, 6-6 [meaning 6 mo. holding period, 6 mo formation]), a Moskowitz Grinblatt (MG) like strategy (long and short industries based on past return, also 6-6), and a 52-week high (GH) strategy that goes long top 30%, short bottom 30%, based on nearness to 52-week high. Finds monthly returns, including and excluding January, of:

JT: 0.48% (1.07%) MG: 0.45% (0.50%) GH: 0.48% (1.23%)

Fama-French risk-adjusted returns were even higher. Next does double 3x3 sort on stocks, first sorting on (JT) past returns, then on (GH) nearness to 52wk high, and finds that using the 52wk high strategy constrained to a JT winner or loser portfolio still returns ~0.5% a month (over 1% w/out Jan.), but sorting on 52wk high and then using a momentum strategy based on relative strength within the 52wk-high sorted portfolios returns only ~0.1% to 0.2% a month. Next the authors do the same 3x3 sort on MG industry momentum and GH 52wk high, and find these returns are more independent. Using either long-short strategy constrained to the portfolio defined as losers (weak past returns or farthest from 52wk high) sill returns ~0.6% a month, and the 52wk high strategy within the MG loser portfolio returns 1.38%/month excluding January. Thus they argue that most of the returns to (JT) past-return based momentum are explained by nearness to 52wk high, while the reverse is not true.

Next the authors do cross-sectional regression of a stock's future returns on 6 dummy variables, saying if each stock was in the JT, MG, or GH winner or loser portfolio (plus some size and auto-corr correction terms), and find that all coefficients have the right sign, but the coefficients on 52-week high are about twice as large (though only slightly more statistically significant). They also find no evidence of reversal (and some evidence of persistence) in 52wk high sorted portfolios even after 3 years, while past-return sorted portfolios have reversals in the future (after 12 months).

Next they add a fourth dummy based on a Grinblatt and Han 2002 behavioral model saying investors don't want to realize losses: this isn't well explained and they compute this using the previous 60 months of return and volume data, and find that this coefficient reduces the size off all the other 6 coefficients and dominates the JT and MG effects outside of January. Using proximity to 52wk low has essentially no -predictive power. More tests find similar results if the formation period on the JT strategy is 12 months and the holding period 6-12 months, and they found that dynamic risk adjustment didn't change the results.

Conclusion: This is another interesting and easy to read momentum paper. It suggests that proximity to the 52-week high ahs predictive power even conditioning on the stock's past returns. It suggests that the previous integrated thesis, explaning momentum in stock returns for ~12 months followed by reversals as an effect of under and then over reaction to information, is flawed, since price * level* is important. Thus perhaps some anchoring bias (traders are slow to adjust their price priors) explains momentum better (but may not explain long-term reversals which occur in returns, but not in 52-wk high momentum). It should be pointed out that all the strategies in

**this**paper differ from the ones in the original Jegadeesh and Titmann paper since in this paper the long and short portfolio each have to top and bottom 30% of stocks, while JT only have the top and bottom 10%. This could effect results since JT found that much of the performance came from the extreme deciles.

#### **International Momentum Strategies

File: International Momentum Strategies.pdf

Folder: Trading Strategies

Author: K. Geert Rouwenhorst

Published: The Journal of Finance (1998)

Keywords: Momentum, international

Summary: Using momentum strategies exactly like those of Jegadeesh and Titman (long top decile of recent performers, short bottom decile, formation period 3 to 12 months, holding period 3 to 12 months), the authors find strong momentum-related returns of 0.7% to 1.35% per month on stocks traded in Europe in 1978-1995, and that country-neutral momentum portfolios do have returns very nearly as high with only about 60% the standard deviation.

The authors use a sample of returns on 2190 European firms (which is biased to big firms) from 12 European countries and find one-year return persistence, using a strategy just like Jegadeesh and Titman (from now JT) in 1993. Like JT, they find the return persistence of winners over losers lasts almost exactly one year, and both winners and losers have about unit market beta vs. MSCI index, and the momentum portfolio works out to about zero-beta but somewhat high variance.

Country-neutral portfolios (forming deciles on performance relative to country peers) with 6-6 strategy has 0.93% average monthly return, giving the country neutral 6-6 strategy a lower return (0.93% vs. 1.16%) but MUCH lower std. deviation (2.39 for country-neutral vs. 3.97 for the general strategy), indicating country diversification reduces risk and momentum.

Size-neutral portfolios (forming deciles on performance relative to size decile peers) with 6-6 strategy has 1.17% average monthly return, and winners beat losers in all size categories, but the small decile (ret 1.45% per month, sigma 5.88%) beats the large decile (0.73% return, 4.739% sigma). Size-and-country neutral portfolios (with size being small, med, or big) where stocks are compared to their size-country peers gets ret=0.85% per month and sigma=2.21%.

Fama-French size and market risk adjusted alphas are even higher than raw returns, since losers load more on the size factor than winners, even in size-neutral portfolios. The author makes the strange observation that recent loser stocks have higher beta in up markets and lower in down markets, and winnes are the opposite, and the winner-minus-loser momentum portfolio has beta=0.24 in down markets and beta=-0.25 in up markets, which would suggest negative performance, though of course the momentum portfolio does very well.

In event time, the author finds returns go negative in month 12 of the holding period and stay (insignificantly) negative through month 24. Finds in 1980-1995 the correlation US momentum returns and country-neutral European momentum returns is 0.43. Regressing European momentum returns on US momentum returns, or vice versa, gives an intercept of about 0.65% per month, indicating that much of the (US,EU) momentum returns aren't explained by the other region.

References:

Weak momentum in country indexes - Richards (1996) Bekaert (1996), Ferson and Harvey (1996)

Griffin and Karolyi (1996) - large country-specific factors in returns

Asness, Liew, Stevens (1996) - persistence of country returns

Chan (1998), DeBondt and Thaler (1987) - assymetric betas (p278)

#### **Momentum Strategies

Authors: Chan, Jegadeesh, and Lakonishok

Published: The Journal of Finance Dec. 1996

Keywords: Momentum, Earnings Momentum

Summary: The authors see if earnings momentum and return momentum are seperate factors, or if one subsumes the other. Generally they find that, while controlling for either factor reduces the effect of the other, they both independently explain some amount of return variation, though for large stocks price momentum is more important

The authors use NYSE, AMEX, and NASDAQ stocks from Jan 1977 to Jan 1993, and use a 5-day gap between formation and holding periods. They define three measures of earnings momentum (meaning a recent increase in earnings) and one of price momentum: standardized unexpected earnings (SUE), abnormal return over the market around earnings date (ARM), and a measure of analyst revision (ARV), and the past-6-months' return to measure price momentum (RET6). All four of these measures have low pairwise correlation (~0.2). They find going long the highest RET6 decile and short the lowest yields ~15% per year (long decile 9 and short decile 2 gives only 6.4%). The highest RET6 decile scores highly on all measures of earnings momentum.

To measure earnings momentum, they find going long decile 1 and short decile 10 on SUE-sorted deciles earn 7.5% per year (with 6.8% coming in the first 6 months of the holding period). Doing the same on ARM-sorted deciles earns 8.3% a year (5.9% in first 6 months), and the same strategy on AR sorted deciels yield 9.7% per year. Next they jointly sort into 9 portfolios, sorted into three levels of RET6 and three levels of earnnigs momentum (ARM,SUE, or AR). Going long the hi-hi and short the low-low portfolios (in each of the three experiments) gives about 7.9% to 8.8% over 6-months.

They also find that neither price nor earnings momentum completely subsumes the other: fixed the level of earnings momentum and trading price momentum (or fixing price momentum and trading earnings momentum) still earns a 3% to 4.5% return per year. However, the return from trading earnings momentum is shorter-lived, and marginally price-momentum-sorted deciles have a higher spread (they hypothesize that this is because changes in price capture more information than just earnings). They find that a multi-variate regression of six-month returns on a stock's size and percentile RET6, SUE, ARV, and AR have all four momentum coefficients significant and positive, with ABR's coef. slightly smaller than the others, which are all about equal. However, when one-year return is regressed on the same variable, the coefficient on RET6 almost triples while the others stay roughly the same, indicating that price-momentum is relatively more significant in explaining one-year than six-month returns.

They show that returns after one year aren't explained by the momentum measures, except that the bi-sorted loser portfolio continues to perform poorly for up to three years. So they generally don't find evidence of return reversal. In a sample confined to large stock, they find an almost-as-significant return spread (on the winner minus loser decile) on RET6 (14% per year), but the return spread on the earnings momentum deciles is lower (2.9% to 7.6%) and in bi-sorted portfolios (sorted by RET6 and an earnings momentum measure) RET6 is relatively more important in large stocks.

Looking at Fama-French risk-adjusted returns, they find winner and loser portfolios one bi-sorted portfolios have similar market betas (around 1.05), similar loadings on SMB (0.78), but the loser portfolio has a small positive loading on HML (0.25) while the winners have a small negative loading (-0.18), making the Fama-French alpha from the spread portfolio even higher than the raw return spread.

The authors conclude that ~"earnings momentum strategies draw upon the market's underreaction to different pieces of information". This paper is well done and provides an interesting look at the interaction of different momentum strategies.

#### **Cross-Sectional and Time-Series Determinants of Momentum Returns

Authors: Jegadeesh and Titman

Published: The Review of Financial Studie 2002

Keywords: Momentum, cross-sectional returns

References: Grundy and Martin (2001): existence of momentum profits as early as 1920s

Summary: This paper largely refutes a Conrad and Kaul (1998) who say that momentum profits are laregly as a result of cross-sectional dispersion in expected stock returns.

An earlier Conrad and Kaul paper had claimed that momentum profits make money because, in buying past winners, one tends to buy stocks with high expected return, and thus even if there is no time-series predictability momentum strategies are profitable by, roughly, buying high-expected-return stocks and selling low-expected-return stocks. Like Conrad and Kaul, this paper considers a weighted momentum strategy where each stock is purchased with weight proportional to its past return (over some ranking period) minus the market return over that period. The expected profit from this strategy is as follows, where R(t) is the market return and R_j(t) is a stock return:

P = -Cov( R(t),R(t-1)) + (1/N)sum_j( Cov(R_j(t), R_j(t-1)) + var( E(R_j))

Conrad and Kaul empirically compute returns to this weighted momentum strategy and find they are roughly the same as Var( E(R_j)), the cross-sectional variance of expected return. This paper says that Conrad and Kaul's methodology was flawed because Conrad and Kaul used past return (over a few years) to estimate expected return E(ret_j) for each stock j, but past return measures expected return with error! Thus by computing the variance of the estimate of expected return(which is actual past returns), the variace of this estimate is

VAR( E_hat(R_j) ) = VAR( E(R_j)) + VAR( epsilon )

where epsilon is the error in measurement of E_hat. Since Conrad and Kaul use past return to proxy for expected future return, this suggests that roughly 20% of stocks have negative expected return, and other have expected returns over 80%.

Anyway, this paper finds that the weighted momentum strategy earns about 4% every six months, and they compute 3 different "better" estimates of expected return (for example, by using more data, from betas, fama french loadings, and longer history of past returns) and find that variance in cross-sectional expected return explains only a tiny (few percent at most) part of momentum returns.

The authors also find that the bootstrap experiments in Conrad and Kaul (1998) suffer from the exact same bias as the empirical experiments (including variance in error in estimated expected return in cross-sectional variance of E(ret), thus over-estimating cross-sectional variance of E(ret)). With the bootstrap experiments, the problem was the Conrad and Kaul re-sorted time-series of stock returns by sampling WITH replacement: the authors show that this leads to bias in estimation of momentum profits. The authors perform unbiased bootstrap experiments, sampling without replacement to re-sort time series, and find essentially zero momentum profits on these bootstrapped return series.

#### **Pairs Trading: Performance of a Relative-Value Arbitrage Rule

File: Pairs Trading - Performance of a Relative Value Arbitrage Rule.pdf

The Review of Financial Studies 2006 (though I heard the original draft was as early as 1998)

Authors: Evan Gatev, Willian M Goetzmann, and K. Geert Rouwenhorst

Folder: Trading Strategies

Online: http://rfs.oxfordjournals.org/cgi/content/abstract/19/3/797 (probably have to pay)

Keywords: Pairs Trading, Arbitrage, relative value

The authors examine the profitability and risk characteristics of a simple type of pairs trade where (1) Pairs of stocks that move together based differences in normalized price are identified during a formation period based on Euclidean distance (or correlation which is equivelent) (2) If those pairs diverge during a trading period, the lower one is purchased and the higher one shorted, requiring no capital, in the hopes that the prices will converge again.

This strategy has annualized returns of 11% in 1962-1999 on a conservative estimate of commited capital and a very conservative estimate of transactions costs. The authors were careful not to optimize their strategy based on the data at all to avoid data snooping bias: entry points were defined as a 2 standard deviation difference in relative normalized price. The test periods consisted of a formation period lasting a year and a trading period lasting 6 months, and the data set was divided into hundreds of overlapping test periods staggered by 1 month. The returns to this strategy are largely not explained by market, Fama French, or momentum or reversal risk ractors, but there does seem to be a common latent factor behind pairs trading returns since there is correlation returns when pairs-trading non-overlapping pairs of stocks. Pairs trading returns bean excess market returns with significantly lower variance, even using the authors' high estimate of 162bp round-trip transaction costs. Most pairs identified were in the utility sector, but other sectors provided almost-as-good results. Also, most pairs identified and traded were large-cap (liquid) stocks. The authors also found that most profit comes from the long positions. Lastly, though they don't present results in detail, pairs trading returns for the recent 1999-2002 period were as high as the in sample returns, suggesting they haven't yet been arbitraged away.

This paper is quite novel, easy to understand, and quite thourough, and the authors are careful to avoid data snooping bias and treat transaction costs conservatively.

** **

#### **An Anatomy of Trading Strategies

Author: Jennifer Conrad and Guutam Kaum

Published: The Review of Financial Studies 1998

Keywords: Trading Strategies, momentum, reversal, mean return dispersion

References: Kaul (1997) reviews some papers on predictability. Hansen (1982) on Robust standard errors

Summary: The authors find that momentum strategies are profitable over a medium (3-12 month) holding / formation period, while long-term reversal strategies are profitable over a longer multi-year holding/formation period, but only in the 1926-1947 time frame. They argue that most of the returns to momentum strategies are from variation in mean return, not time series predictability.

The authors consider data from 1926-1989 (making several sub-periods) and consider momentum and contrarian strategies based purely on past return over a formation period. Their holding period and formation period are always the same, and they create trading portfolios that hold stocks long or short with a weight proportional to thier holding-period return relative to the market. They say that this strategy correlates strongly with Jegadeesh's strategy of long the top decile, short the bottom decile.

Using these portfolios, the authors statistically decompose momentum profits into a component from auto-correlation in individual stock returns and (negative) autocorreation in the market (together these are the time-series component) and a component from cross-sectional variation in expected return across stocks. The authors assume expected return is constant, so momentum strategies will buy high E(ret) stocks and sell low E(ret) stocks, but suffer from an errors-in-variables problem since return, not E(ret), is observed. They find that about half of the (very simple) momentum and contrarian strategies they consider have statistically significant profits, and half of these are momentum, half contrarian. They also find very-short-term (like monthly or less) contrarian profits that would not be capturable due to transaction costs. They find that dispersion in mean returns explains almost all profits from momentum strategies, NOT time series predictability. Of the 18 trading strategy / time period combinations where momentum strategies are profitable, in 16 cases dispersion in expected return contributes over 100% of the profit. They also find that contrarian strategies would have much larger profits, but these are reduced by the cross-sectional dispersion in mean return.

Next they perform bootstratp tests focusing on the 1964-1989 subperiod., which preserve the cross-sectional dispersion of returns but remove any time-series properties, and find that the boot-strap samples have on average HIGHER momentum returns than the on the real data momentum. Monte-carlo samples produce largely the same result

This paper is interesting and makes a great contribution. However, as Jegadeesh and Titman (1993) showed, portfolios formed on past return experience reversals, indicating that, for example, (12,12) momentum portfolios capture something more than a cross-sectional dispersion of expected returns. Also, the idea of expected return being constant over a long period, or of estimating it well from empirical returns, is difficult to accept.

#### **The Illusory Nature of Momentum Profits

Authors: Lesmond, Schill, and Zhou

Published: Journal of Financial Economics 2004

Online: PDF

Keywords: Transaction Costs, momentum strategies

The authors argue that momentum strategies like Jagadeesh and Tittman incur very high transaction costs since they frequently trade high-cost securities. The authors look at two JT strategies: the original from their 1993 paper and their one from the 2001 paper that excludes stocks below 5 and excludes the smallest size decile, and use data from 1980 to 1999. They find that in both cases the loser portfolioes (which are shorted) are small-capitalization, off-market (NASDAQ as opposed to NYSE), high beta. The authors ignore some transaction costs like price impact, immediacy cost, taxes, commisions. They use four transaction cost estimates (1) Quoeted spreads from NYSE TAQ database (2) some direct effective spread like ( Price - 0.5*(bid+ask)) (3) Some measure of negative-autocorrelation to capture bid-ask bounce (4) some out-dated commision quotes and average transaction sizes is TAQ database. They estimate 1%-2% round-trip cost for big stocks, 5% to 9% for small stocks, and quote Jones and Sequin (1997) saying NASDAQ bid-ask spread is 12%-18% for small stocks. Generally they find transaction costs eliminate basically all momentum profits, and limiting the momentum trading to low-transaction cost stocks, gives much lower profits in the low-transaction-cost stocks and higher profits only in stocks that are expensive to trade.

The paper is interesting but I have absolutely no way to verify their cost estimates. They estimates to sound quite high, since a grad student with a scott-trade account can trade large stocks for well under 0.4% round trip and small stocks not much more, and I always imagines I-banks could trade big stocks for well under 0.1% since that's where bid-ask spread are, but what do I know.

**Score: 7/10**

#### **The Cost of Trend Chasing and The Illusion of Momentum Profits

Author: Donald B Keim

Published: Knowledge@Wharton 2003

Online: http://knowledge.wharton.upenn.edu/paper.cfm?paperID=1232&CFID=1079456&CFTOKEN=89415614

Folder: Trading Strategies

Keywords: Momentum Profits, Transaction Costs, Price Impace

Summary: The author uses trade data from 33 institutions trading in over 30 countries for two one-year periods in 1996-1997 and 2000 and estimates that price impact costs alone basiclly eliminates momentum profits.

The author finds a higher cost of buying rising stock and of selling falling stock, even correcting for market cap effects, and correctly argues that this is what momentum strategies do. He uses institutional data to compute price impact costs per order, where an order may be executed in multiple trades. The data set divides institutions into momentum, index, and value investors. He finds that momentum investor institutions pay ~1.21% in price impact cost, for 1.82% total, and that they pay far more than the other kinds of investors in both years studied and across markets, and buys and sells. He finds momentum trades have about 3x the price impact of other trades. Lastly he estimates a linear model of price impact on market cap, trade side, and price, and finds in this model momentum trades have a higher intercept and generally a steeper slope as a function of trade size.

This paper is convincing since the author uses actual institutional trade data

#### **Risk Adjustment and Trading Strategies

File: Risk Adjustment and Trading Strategies.pdf

Authors: Dong-Hyun Ahn, Jennifer Conrad, and Robert F Dittmar

Published: The Review of Financial Studies Summer 2003

Folder: Trading Strategies

Keywords: Stochastic discount factor, risk adjustment

The authors argue that CAPM-like measures are mis-specified since they rely on a model and propose a market-wide stochastic discount factor on which to define alpha. They use as basis assets industry portfolios and try to explain Jagadeesh and Tittman momentum strategies through a static or dynamic linear combo of industry portfolios (the authors point out that this relies on industry portfolios being priced correctly). Their unconditional tests indicate that, unlike CAPM and Fama-French factors which increase the alpha of JT momentum strategies, they can find a static linear combination of industry portfolios that explains about half of the excess returns to momentum strategies and reduces many of the momentum strategies to statistically insignificant alphas. Their conditional tests reveal that conditioning on term spread (10-yr minus 1-yr T-Bill), S&P Dividend yield, and short-term T-Bill rates can, together with the industry portfolios, explain 63% of mometum profits. They find that "winner" (top decile returns in formation period) portfolios load more heavily on the stochastic discount factor beta than losers, while winners and losers have similar CAPM betas.

They also define a "Law of one price" defining an efficient mean-variance frontier using lin. combos of industry portfolios suggesting that no strategy should dominate this frontier: they find both the market and momentum strategies are well within it. Interestingly, the authors find that the industry momentum strategies defined in Moskowitz and Grinblatt "Do Industries Explain Momentum" have almost none of their excess returns explained by Ahn, Conrad, and Dittmar's Stochastic discount factor.

I find this paper unconvincing. First, the econometrics of the stochastic discount factor method is poorly explains. But far more importantly, saying that momentum profits are insignificant because we can explain historical momentum profits with a combination fo 20 industry portfolios is engaging in massive data snooping, since we have no way to know what linear combo. of industry portfolios to use a-priori and their is no economic reasoning behind it. One would expect that even a fantastic trading strategy could be beaten HISTORICALLY by going very long in an industry portfolio that did well, very short in one that did poorly, and using positions in the other 18 to cancel variance. But this lin. combo. is not a viable future strategy since it's just a result of heavy optimization on the sample period and probably won't perform well at all out of sample. Though the paper is interesting, I find it hard to believe that a smart person, having read it, would say "Oh, why should I do this momentum trading when I can just hold an unspecified combination of 20 industry portfolios with no economic reasoning behind it".

#### **Volatility Forecasting and Delta-Neutral Volatility Trading for DTB Options on the DAX

File: Vol Forecasting and Delta-Neutral Vol Trading on the DAX.pdf

Authors: Bartels and Lu

Online: (PDF)

Published: 2000 Proceedings of the 10 th International AFIR Colloquium. S. 51-66.

Folder: Trading Strategies

Keywords: GARCH, EGARCH, volatility forecasting and trading

This paper compares four methods of volatility forecasting on german DAX index options using data from July 1995 to July 1997: implied volatility AR(1), 15-day-MA historical volatility, GARCH, and EGARCH. Methods are judged by profitability of a trading strategy going long or short at-the-money straddles, and finds GARCH and EGARCH to be clearly superior. Two trading strategies are tested: in both, the forecast uses today's closing price, but TS1 (trading strategy 1) assumes the position is opened at today's closing price and closed tomorrow, and TS2 assumes the position is opened tomorrow and closed the next day. GARCH and EGARCH total (over two year) profits for TS1 are 423% and 249%, and using TS2 are 126% and 207%. Historical and implied volatility total profit is around 40%-70% using TS1 and nothing using TS2. All profit numbers are net of a transaction cost that is 1% or 0.1% for each transaction (the paper is unclear). The superioriority of GARCH for TS1 (essentially next-day forecasts) and EGARCH for TS2 (two-day-ahead forecasts) is pointed out and the authors interpret it as meaning that the time-validity of GARCH forecasts is shorter. The authors also find that "filters", which don't trade unless the model forecast differs from the market price by more than some number, significantly decrease returns without decreasing standard deviation much.

Despite the fantastic sounding results, the paper does have some problems. The data set is tiny (two years), and the return distribution isn't examined in detail to look at riskyness or factor exposures, and even standard deviation of returns isn't discussed in detail. Also, the paper is plagued by mis-spellings and grammar mistakes. (e.g. "Where mu_t is very good fitted"), though since it's not published in a journal perhaps this isn't too serious, and the version I have could, perhaps, be dated. With respect to transaction costs, the authors say "As proposed by CFP, a 1% mark should be appropriate. In other words, tthe transaction cost of a straddle is DEM 0.80 with the average straddle value about DEM 800": I don't understand if this is 1% or 0.1%. Lastly, there is no mention of data snooping bias. One positive aspect of this paper is that it's a non-US market.

## Technical Analysis

#### **Data Snooping, Technical Trading Rule Performance, and the Bootstrap

Authors: Sullivan, Timmerman, and White

Published: The Journal of Finance 1999

Keywords: Technical Trading Rules, Bootstrap, Data Snooping

Summary: Uses a data-snooping-adjusted P-value metric to see if any of a large number of technical trading rules are profitable, and find that certain rules worked very well through 1986 but not in the 1986-1996 period.

The authors spend a considerable amount of space discussing how data snooping can be a problem, even when journal authors are careful, because the financial community as a whole may remember only trading rules that worked well in the past. They also show how their large universe of rules subsumes the rules of a previous Brock, Lakonishok, and LeBaron (BLB) by making comparisons to BLB's best rul ein most tables.

The authors do technical trading on the Dow Jones Index from 1897-1996 and consider 7,000+ rules, which are moving average, filter rules, break out rules, based on various parameters. The benchmark to which trading rules are performed is T-bills. They find the best trading rules over various sub-periods use only short windows of past data and generate high returns (16%-25% annually) with very low data-snooping-adjusted p-values (~0.002). They also find that if, at every time t, the best rule up to time t is used, one can earn a return 14.9% over the benchmark with balanced short-long trades but more money coming from the longs. Delaying trades by a day from the trade signal drops returns to ~8%, but still significant by adj. p-value. They found a break-even transaction cost of 0.27% on the best rule over the whole period.

In the hold-out sample (1986-1996) they found that the best rule considered does not earn statistically significant profits by the adj. p-value, though it does earn 14.4% annually. In the 1986-1996 period, a trader selecting and implementing the bets rules from previous periods (via some moving average) would earn only 2% annually. The trading rule profits are also completely insignificant when trading S&P futures.

The results for the performance of the best trading rules on the past (in-sample) data are impressive, but more surprising is that their method of works well (they claim 14.9% in sample) when a rule at time T is chosen based on its performance before time t. Still, the lack of performance out of sample is disappointing.

#### **Technical Trading Rule Profitability and Foreign Exchange Intervention

Author: Blake LeBaron

Published: Journal of International Economics 1999 (also an NBER working paper I think)

Online: http://ideas.repec.org/p/nbr/nberwo/5505.html

Keywords: FX, technical trading

Summary: The author finds evidence of trading rule profiability in the FX market from 1979 to 1992 using a simple moving average rule, but this profitability largely disappears when days of Fed. Reserve intervention are removed

The author defines a simple trading rule that buys when the exchange rate is above its (150-day, 30 week) moving average, and otherwise sells. He uses Yen and German Mark FX data, daily and weekly. The rules trade infrequently and the author claims 7% to 10% annual returns with ~10% annual standard deviation, giving a Sharpe ration of ~2X buy-and-hold in the US market. Calculating returns with or without the interest rate differential makes no difference. He finds that, if days of federal reserve intervention are removed, the profits drop by a factor of ~10 for the German Mark and ~3 for the Yen. He notes that the returns aren't driven by volatility, and that the correlation of trading rule profit and days of fed. intervention doesn't imply causality.

**Score: 6/10**

#### Foundations of Technical Analysis: Computational Algorithms, Statistical Inference, and Empirical Implementation

#### Includes Discussion by Jegadeesh

File: Foundations of Technical Analysis.pdf, Foundations of Technical Analysis Discussion.pdf,

Authors: Andrew Lo, Harry Mamaysky, Jiang Wang

Published: Journal of Finance 2000

Keywords: Technical Analysis, Kernel Regression, Head and Shoulders

Summary: Lo et. al. use Gaussian Kernel Regression to smooth daily CRSP stock price data (1962-1996) and search these smoothed data for ten technical indicators (like head and shoulders) and find some difference in the conditional distribution of future returns having seen the indicator versus the marginal distribution.

The authors' description of kernel regression for smoothing and cross validation, along with selection of a bandwidth (kernel width) is superb. They search for technical patterns by examining the extrema in smoothed 38-day over-lapping windows, searching for patterns and using a kernel with based on anecdotal discussions with technical analysts. They find the occurance of indicators is larger than would be expected in log-normal data. They also find that the conditional distributions having observed an indicator is different from the marginal for 7 or 10 indicators in NYSE/AMEX data and 10/10 in NASDAQ data, and find that additionally conditioning on volume gives little extra info. They use a Kolmogorov-Smirnov test and look at what deciles returns fall into to assess significance of the difference of conditional distributions.

The argument that technical indicators affect conditional distribution is somewhat convincing, but not practically significant: perhaps simply observing an extrema (in the smoothed data) affects the conditional distribution in the same way. Also, no direct examination of profitability is made, and the conditional mean return (having observed an indicator) is almost never more than 0.05 standard deviations above the marginal mean return, which probably amounts to no more than a few basis points.

In the discussion, Jegadeesh decries a lack of a theoretical justification for the use of charting techniques, and disagrees with Lo et. al.'s statement that a large reason for academics' skepticism of technical analysis is a linguistic barrier. Jegadeesh also focuses on the lack of indication of profitability in the paper.

**Score: 6/10**

** **

#### **Naive Trading Rules in Financial Markets and Wiener-Kolmogorov Prediction Theory: A study of Technical Analysis

Author: Salih N Neftci

Published: The Journal of Business 1991

Keywords: Technical Analysis, Markov Times, non-linearity

The author's goal is to see if technical analysis rules are well defined and if they improve on Vector Autoregressive predictions, which are best linear predictiors. The author notes evidence of non-linearity in market returns, and goes on to define Markov times as time that depend only on past information, because any usable technical trading must generate a signal only at Markov times. For example, the first time an asset reaches a price of 50 is a Markov time, since past data can tell us that, but the time an asset reaches a 52-week low isn't a Markov time, since at that time we can't know that the asset won't go lower in the future. Also, inflection points aren't Markov times. Much of the paper is devoted to such definitions, and only at the end does the author look at a simple moving average rule, which has some predictive power but isn't better than a vector autoregressive forecast. Profitability isn't even discussed.