James., 1968, Monthly Moving AveragesAn Effective Investment Tool, Journal of Financial and Quantitative Analysis,. Consequently, we devote Section 3 entirely to empirically evaluate the extent to which measurement errors may affect our results and inferences. Finally, it is important to note that all the small-sample biases noted above are derived under the null hypothesis that returns are independently and identically distributed. Specifically, consistent with the prediction of the random walk model, the profits increase geometrically with the holding period, k see Equation (8) and the discussion in Section.2. French., 1988, Permanent and Temporary Components of Stock Prices, Journal of Political Economy,. The bias in the cross-sectional variance of the mean returns of the individual securities in this sample should also be relatively small. 9 All medium-term (3- to 12-month) strategies are implemented on the bootstrap sample, and this exercise is replicated on 500 bootstrapped samples.

We therefore will largely rely on the sign and statistical significance of the averages of the time series of the pi_t (k s; that is, we examine whether expected profits are statistically significantly positive (or negative). Citing articles via Web of Science Standing on the Shoulders of Giants: The Effect of Passive Investors on Activism. All estimates of the cross-sectional variation in weekly mean returns are multiplied by 100. To minimize small-sample biases in estimators of the components of the profits of trading strategies (see Appendix and to increase the power of our tests, we implement trading strategies for overlapping holding periods on a monthly frequency (for all k except k 1 week). We find that an important determinant of the profitability of trading strategies is the estimated cross-sectional dispersion in the mean returns of individual securities comprising the portfolios used to implement these strategies. Purchase Subscription prices and ordering Short-term. The mean profits of the bootstrap strategies are always greater than the corresponding estimates in panel A and the p-values are large, ranging between.69 and.00. We use overlapping data to minimize small-sample biases in estimates of the components of profits to trading strategies, but we recognize that measurement errors in in-sample mean returns could nevertheless affect our inferences (see Appendix ). Specifically, consider buying or selling stocks at time t - 1 based on their performance from time t - 2 to t - 1, where the period t -1, t spans any finite time interval.

Although the cross-sectional variance of the mean returns of firms in this sample is likely to be measured with reasonable accuracy, it is also likely to provide a lower bound on the cross-sectional variance of the mean returns. Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency. Table 3, panel A, contains the results from the bootstrap simulations. We first implement the strategies for the period because it corresponds with the time period used in several past studies see,.g., Lehmann (1990), Lo and MacKinlay (1990), and Jegadeesh and Titman (1993). We show that less than 50 of the 120 strategies implemented in the article yield statistically significant profits and, unconditionally, momentum and contrarian strategies are equally likely to be successful. Related articles in Web of Science Google Scholar. Specifically, a security's past performance relative to some benchmark (e.g., the average return of the portfolio of all securities) is supposed to be informative about future innovations in the security's prices. Strategies : An Evaluation of Alternative Explanations. The implied cross-sectional variance can explain between 16 and 119 of medium horizon strategies implemented over the various time periods. Quarterly Journal of Economics, 109(2 309-340.

This bias could be nontrivial in small samples which, in turn, could materially affect inferences about the relative importance of the sources of profits to trading strategies. Close mobile search navigation Article navigation. Don't already have. To determine the robustness of the profitability of the simulated strategies to extreme mean returns observed in the data, we conduct two additional Monte Carlo experiments. Obviously, different specifications of the model for unconditional required returns could affect the conclusions of our analysis. Jegadeesh., 1990, Evidence of Predictable Behavior of Security Returns, Journal of Finance,. Titman., 1989, Mutual Fund Performance: An Analysis of Quarterly Portfolio Holdings, Journal of Business,. First, the positive or negative sign preceding the expression on the right-hand side reflects an investor's (institution's) beliefs; that is, whether the investor believes in price continuations or reversals (and therefore recommends and/or follows a momentum or a contrarian strategy). Finally, note that the minor differences between the population parameters C_1 (k) and O_1 (k) in Equation (4) and their sample counterparts are reflected above in the last element of C_1t(k) and the fracN - 1N2 factor in O_1t(k). The profits are invariably positive due to noise, but the magnitudes of the average profits are small:.0015,.0069,.0127, and.0144 for the 3- to 12-month strategies, *an anatomy of trading strategies* respectively. This created a substantial mismatch between the number of securities used in the actual trading strategy and the simulated strategy, since the resampling of vectors scrambled the missing values as well. You do not valutahandel wiki have access to this article. Note that if one were to assume that cross-sectional differences in mean returns are due entirely to differences in risk characteristicsa viewpoint not uncommon even among proponents of the return-based trading strategies see,.g., Jegadeesh and Titman (1993, 1995a ) and.

An alternative way to **an anatomy of trading strategies** evaluate the relative importance of the cross-sectional versus time-series components of the profits of momentum strategies is to note that there are only two instances in which these strategies gain from continuations. 6 The usefulness of the random walk model in Equation (5) as a benchmark, particularly for this study, becomes obvious since trading strategies that rely on time-series predictability in returns cannot be profitable by construction because textCovR_it (k R_jt - 1 (k) 0,forall,i,j,k. Cootner., 1964, The Random Character of Stock Market Prices, MIT Press, Cambridge, Mass. And again, the difference between the average profits of the simulated and real strategies increases significantly with an increase in the holding period, implying that there are reversals in the real data at least at the 9- and 12-month horizons. It is important to determine the sources of the apparent profitability of trading strategies because of (i) the explicit assumption in the literature that time-series patterns in stock prices form the sole basis of return-based trading strategies, and. Since the number of weekly observations are large (up to 1,434 for the period the effects of measurement errors in mean returns on estimates of the cross-sectional variance in mean returns should be small (see Appendix ). All of this evidence appears to be an outcome of severe and unusual price movements during the subperiod. Mayers., 1982, The Value Line Enigma (19651978 A Case Study of Performance Evaluation Issues, Journal of Financial Economics,. Prospect Theory: An Analysis of Decision Under Risk. The results of this experiment are shown in Table 3, panel. Titman., 1993, Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency, Journal of Finance, 48,.

Contrary to the commonly held belief that forms the basis of return-based strategies, the evidence suggests that time-series patterns in security returns are unlikely to result in statistically significant net profits to trading strategies. The implied estimates of the cross-sectional variation in mean returns are obtained as sigma 2 hat mu (k) n2 sigma 2 hat mu (textit week where n is the number of weeks in the holding period, k, of the trading strategy. 9 To maintain the cross-sectional correlation in the returns, in one of our bootstrap experiments we attempted to scramble entire vectors of returns. The Profitability of Trading Strategies We consider a set of trading strategies that either explicitly mimic or capture the essence of previously implemented strategies. Inflation Forecast Errors and Time-Variation in Term Premia. The model in Equation (5) also has economic appeal as a benchmark because changes in stock prices will (generally) be unpredictable in a risk-neutral world with an informationally efficient stock market see,.g., Samuelson (1965). This is in sharp contrast for the average profits for the real strategies reported in the second column, which increase with the holding period, but less than geometrically, and eventually exhibit no change between the 9- and 12-month strategies. We believe our analysis and results should be of interest to both technical traders and producers of asset-pricing models. Specifically, the cross-sectional dispersion in mean returns witnessed during different time periods can potentially generate the observed profits of the most consistently profitable strategy, the momentum strategy implemented at medium horizons. Of the 18 cases in which positive profits are observed for momentum strategies (see estimates in bold in Table 2 the percentage contributions of sigma 2 hat mu (k) are typically greater than 100. Governance Under Common Ownership.

View Large Table 4 contains the implied cross-sectional variances in mean returns for all three samples of firms for the medium horizons (3 to 12 months). We are especially thankful to an anonymous referee and Bob Korajczyk and Ravi Jagannathan for helping us focus on the main issues addressed in this article, to Michael Cooper for his invaluable research assistance, and to Sonja Dodenbier for helping prepare this manuscript. The most important property of the model in Equation (5), when combined with the decomposition of total expected profits in Equation (4), however, lies in the fact that it helps demonstrate that momentum (contrarian) strategies will be profitable (unprofitable) even. Consequently, we chose to preserve the placement of missing values in scrambling the individual security returns and thus maintain the same set of securities in the simulations that are used in the actual strategy. This is quite contrary, for example, to the random walk model of stock prices which implies that changes in stock prices are completely unpredictable (see Section 2 for further details). Our simulation analysis is similar in spirit to the work of Knez and Ready (1997), who show that the size effect can be explained by 1 of the outliers in the data. We follow the weighting scheme implied in Equation (1) instead, especially since a decomposition of the profits is central to this article. In this section, we provide some additional evidence and interpretation that may shed more light on this issue. Fuller., 1976, Introduction to Statistical Time Series, John Wiley Sons, New York. Table 2 The decomposition of average profits to trading strategies Strategy interval hat Epi_t (k) hat P(k) - hat c_1 (k) hat o_1 (k) sigma 2 hat mu (k) hat P(k) sigma 2 hat mu (k) Panel A: week.035. Conditioning Variables and the Cross Section of Stock Returns. Table 1 Average profits to trading strategies for different horizons and periods Subperiods (19261989) Strategy interval (I) (II) (III) week.035 (23.30) 3 months.027.67).165 (2.42).557 (2.99).070 (2.91).020 (0.43) 6 months.360 (4.55).147. We, on the other hand, define P(k) to emphasize that total expected profits to return-based trading strategies do not result entirely from time-series predictability in returns.

It is important to note that our decomposition of trading profits is based on the assumption of mean stationarity of the returns of individual securities during the period in which the strategies are implemented. First, the momentum strategy usually nets positive and statistically significant profits at medium horizons, except during the subperiod. 1998 The Society for Financial Studies Download all figures). Fama., 1970, Efficient Capital Markets: A Review of Theory and Empirical Work, Journal of Finance,. For example, in the most recent study on trading strategies, Jegadeesh and Titman (1993) implement 32 different 3- to 12-month momentum strategies over the period and find each one to be profitable. Panel E provides the average profits, average t-values, and p-values of trading strategies implemented on randomly sampled firms from normal distributions with identical means but variances mat match the sample counterparts. MacKinlay., 1988, Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test, Review of Financial Studies, 1,. 10 These results suggest that the cross-sectional properties of the returns observed between 19lone have the potential to explain the profits of momentum strategies. The bootstrap results confirm the findings of our decomposition analysis. Investor Psychology and Security Market Under- and Overreaction. This finding suggests that the profitability of momentum strategies at medium horizons may not be due to price continuations potentially induced by market inefficiencies. The most important general finding for the beta-sorted strategies is that, although there is a substantial reduction in the point estimates of the cross-sectional dispersion in mean returns for most holding periods, sigma 2 hat mu (k) continues.

Jegadeesh,., and. The results of our article are clearly dependent on the assumption that the mean returns of individual securities are constant during the periods in which the trading strategies are implemented. Note that barring the weekly and the 3-month strategies, the sigma 2 hat mu (k s lead to substantial losses to contrarian strategies. Moreover, the average t-statistics of all the medium-term bootstrap strategies are greater than 10 and each of the t-values are significant for each strategy in all the 500 replications. Given that this empirical decomposition is affected by measurement errors in mean returns, however, our inferences at this stage should be treated with caution. Sign In or Create an Account. Second, it is important to note that, regardless of whether a strategy is contrarian or momentum, the premise is that its success is based on the time-series behavior of asset prices. Hansen., 1982, Large Sample Properties of Generalized Method of Moments Estimators, Econometrica,. The results from the simulations are consistent with the hypothesis that the profits of momentum strategies are largely due to cross-sectional variation in mean returns. Appendix.1 Estimation of the components of profits The components of total profits see Equation (4) are estimated by allowing serial covariances (both own and cross) and the cross-sectional variance of mean returns of individual securities to be time dependent. The corresponding percentages are 26 and 191 for the limited-firms sample. The t - 1 subscript on hat mu_it - 1 (k) and hat mu_mt - 1 (k) simply denotes that these are the sample means of securities available at time t - 1 to form the trading strategy portfolios see Equation (1).

All profit estimates are multiplied by 100. Trading strategies that apparently beat the market date back to the inception of trading in financial assets. Most return-based trading strategies implemented in the literature rely exclusively on the existence of time-series patterns in returns. Karjalainen., 1993, Using Genetic Algorithms to Find Technical Trading Rules, working paper, University of Pennsylvania. Second, the cross-sectional distribution of the in-sample mean returns accurately measure the true cross-sectional variation in the mean returns. M., 1936, The General Theory of Employment, Interest, and Money, Harcourt, Brace., New York. Trading, to purchase short term access, please sign in to your Pdf Academic account above. The different holding period strategies can therefore contain different sets of securities. The numbers in parentheses below the implied estimates of the cross-sectional variation in mean returns are the minimum and maximum percentages of the profits of trading strategies reported in Table 1 for different time periods that can be explained by the implied estimates.

Although this portfolio method differs from ours, their results also suggest that cross-sectional variation in mean returns is importantthey find that the average profits of the simulated zero-investment strategy, though less than the actual profits, still constitute about 80 of profits in the real data. However, an advantage of evaluating the relative contribution of hat P(k) is that we can also determine the statistical significance of any profits to trading strategies due to predictable time-series patterns in asset prices. View Large.1 The random walk model Although Equation (4) provides a convenient decomposition of expected profits, we need a benchmark model for *an anatomy of trading strategies* the return-generating process of financial assets to interpret the two different potential sources of profits to trading strategies. We consider five time periods: 19621989; 19261989, and three equal-size subperiods within the period (January 1926April 1947, May 1947August 1968, September 1968December 1989). 11 Note that all estimates in Tables 2 and 3 are profits and not returns because the strategies are zero-investment strategies see Equation (2a). 12.3 Some additional evidence and interpretation The empirical decomposition and the simulation evidence suggest that cross-sectional differences in mean returns could play an important role in determining the profitability of return-based trading strategies.

If a security is included in a k-period strategy based on its past k-period performance, but it survives for less than k periods in the future (because it is delisted we use a (k - j) period. We simulate 500 such monthly series and implement the momentum trading strategy for the 3- to 12-month intervals for each set of returns. Since measurement errors are likely to have some effects on our references even using overlapping data, we address this issue in several alternative ways in Section 3 of the article. Yet only in less than half the cases (7 of the 15 long-term strategies ) are the price reversals able to overwhelm the losses from the cross-sectional variance in mean returns and lead to statistically significant net profits. Specifically, we generate a sample of 301 monthly returns for each stock in the sample by resampling with replacement from the actual monthly returns between (December) 1964 and (December) 1989. Table 3, panel B, contains the average profits, the average t-statistics, and the p-values denoting the proportion of times the 500 simulated mean returns are greater than the corresponding sample mean returns in the second column of the table. A momentum strategy is usually profitable at the medium (3- to 12-month) horizons: of the 20 medium-term strategies reported in Table 1, a momentum strategy is profitable in 15 of the cases. The unconditional probabilities of success of momentum and contrarian strategies are approximately equal: of the 55 statistically profitable strategies, 30 are momentum, while 25 are contrarian strategies.

Lo and MacKinlay (1990) also define an identical profitability index. This article is also available for anatomy through DeepDyve. Journal of Finance 54:2143. Titman., 1995b, Short-Horizon Return Reversals and the Bid-Ask Spread, Journal of Financial Intermediation,. The profits in Equation (6) are realized simply because in a world where security prices follow random walks (with drifts following a momentum strategy amounts, on average, to buying high-mean securities using the proceeds from the sale of low-mean securities. Hence, the biases in the simulations appear to have a minor effect on the inferences because the profitability of trading strategies is very small if there is no cross-sectional variation in the mean returns of individual securities. The numbers in parentheses are z-statistics that are asymptotically N(0, 1) under the null hypothesis that the relevant parameter is zero and are robust to heteroscedasticity and autocorrelation, and account for any cross-correlation in the realized profits and the realized. 1, broadly speaking, these articles analyze two strategies, diametrically opposed in philosophy and execution: the contrarian strategy that relies on price reversals and the momentum strategy based on price continuations (or momentum in asset prices). (6) Equation (6) implies that as long as there are any cross-sectional differences in mean returns of individual securities, momentum strategies will generate profits equal to sigma 2 mu (k). The estimates in Table 1 are the time-series averages, for each k, of the profits at each time t, pi_t (k).

The numbers in parentheses are z-statistics that are asymptotically N(0, 1) under the null hypothesis that true profits are zero and are robust to heteroscedasticity and autocorrelation, and account for any cross-correlation in the realized profits of strategies within. Third, the dollar weights in Equation (1).e., w_1t - 1 (k ldots, w_Nt - 1 (k) lead to an arbitrage (zero cost) portfolio by construction sumlimits_i 1N w_it - 1 (k) 0quad forall k, (2a) and the. Journal of Finance 54(4 1325. In panel C, none of the mean profits are less than the corresponding real numbers reported in the second column of the table, and the p-values remain large, ranging from.60.00. Journal of Finance, 40: 793-805. The random walk model provides economic content to the time-series versus cross-sectional decomposition of the expected profits of return-based trading strategies. Specifically, given Equation (5), the expected profits from a momentum strategy applied to a trading horizon of periods and continuously compounded returns is given by see Equation (6) Epi_t (k) k2 sigma 2 mu (1) k2 Epi_t (1). Specifically, the cross-sectional component of the profits is both the predominant source of profits to the momentum strategy at medium horizons, and a major source of losses to contrarian strategies at long horizons.

The small-sample bias is potentially important, especially for longer horizons because we use k-period returns to calculate the k-period mean returns (that is, 12-month returns are used to calculate 12-month mean returns). C., 1988, On Contrarian Investment Strategy, Journal of Business,. This finding is noteworthy given that momentum and contrarian strategies are (as noted in the introduction) diametrically opposed in philosophy. References Alexander., 1961, Price Movements in Speculative Markets: Trends or Random Walks, Industrial Management Review, 2,. Momentum Investing and Business Cycle Risk: Evidence from Pole to Pole. The results of this Monte Carlo experiment are similar to the bootstrap evidence in panel. A momentum strategy is usually profitable at the medium 3- to months horizon, while a contrarian strategy nets statistically anatomy profits at long horizons, but only during the subperiod. To gauge the success of the momentum strategy at the medium horizon, we test for the joint significance of the 3- to 12-month strategies within each time period. However, the actual profits to the trading strategies implemented based on past performance contain a cross-sectional component that would arise even if stock prices are completely unpredictable and do follow random walks. This evidence is also consistent with the results of Fama and French (1988) and Kim, Nelson, and Startz (1991), who find that long-term mean reversion in the prices of portfolios of securities is peculiar to the prewar period.

Journal of *an anatomy of trading strategies* Finance and Quantitative Analysis, 24: 479-496. The panel also contains the t-statistics average of the 500 simulated t-values and the p-values, where these values denote the proportion of times the 500 simulated mean returns are greater than the sample mean profits of the actual strategy shown in the second column. Journal of Finance 52(3 1035. 2 Jegadeesh and Titman (1993) use a variant of this strategy in which securities are ranked based on their past performance and are then combined into 10 portfolios that are held for a specific period of time. Email alerts New issue alert. A number of practitioners and academics in the pre-market-efficiency era (i.e., pre-1960s) believed that predictable patterns in stock returns could lead to abnormal profits to trading strategies. As others have pointed out, time variation in expected returns could also lead to predictability in stock returns see,.g., Fama (1970, 1991 ). View Large Table 2 The decomposition of average profits to trading strategies Strategy interval hat Epi_t (k) hat P(k) - hat c_1 (k) hat o_1 (k) sigma 2 hat mu (k) hat P(k) sigma 2 hat mu (k) Panel. 5 For example, past research has demonstrated the abnormal profitability of trading strategies that use the Value Line timeliness rankings which are based on price momentum, determined by price performance over the past 12 months see Copeland and Mayers (1982) and Stickel (1985). However, their motivation is to deemphasize the role of sigma 2 mu (k) since it has a small effect on profits to trading strategies that use weekly returns (see also Tables 2 and 4 ). For brevity we implement strategies for which the length of the past performance evaluation periods and the future holding periods are identical. Summers., 1988, Mean Reversion inStock Prices: Evidence and Implications, Journal of Financial Economics, 22,. The contribution of sigma 2 hat mu (k) is again always statistically different from zero.