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Preliminary This wonderful question is directly connected to the necessity of precise definitions and carefully writing in academic research: The decomposition you are asking for has two different solutions, regarding to the framework you are using. So a superficial look to the literature and quickly comparing the formulas yields to confusion, especially in ...


8

Kenetic Component Analysis If I am to summarize the work of the authors from a broader view than that which is taken in the abstract, essentially the price process is decomposed into position, velocity and acceleration reminiscent of projectile motion in classical mechanics. I added this as an answer so that if @Pierre wants to accept it he may.


6

The idea of skipping a month was already in Jegadeesh and Titman 1993. The key academic paper in this area. Jegadeesh himself (without Titman) discovered a 1-month return REVERSAL effect in 1990, so it makes sense that he would take out 1 month in calculating returns in his later (1993) study. He already knew what happens to stocks that are up a lot ...


6

You may want to have a look at the papers by Jegadeesh & Titman (1993) Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency De Bondt & Thaler (1985) Does the stock market overreact? They are (afaik) the by far most cited publications on momentum (and the calendar-time-method to calculate momentum returns). You ...


6

Reading what I have, I can only offer a guess. 1: Let's say you're looking at 9 sectors compared to \$SPX on a daily chart. Foreach sector, compute relative closing price: 100 * Sector/\$SPX 2: It looks like the RS-Ratio is averaged over 14 periods. I say 14 because stockcharts.com shows RS-Ratio peaking after a lag (2-3wks), despite price peaking 2-3 ...


6

It kind of depends what your objective is. First, momentum 'bias' isn't well-defined. Are you looking to eliminate momentum exposure for some reason? Momentum itself isn't even well-defined really: momentum over the trailing 1 year? Trailing 6m? Looking over 3-5y periods where mean-reversion is more at play? Generally, in the absence of a clearer ...


5

I think the normalisation step is incorrect. Since we would like have 100 as our baseline, it should be 100 + ((value-mean)/stddev + 1). Then we get fairly realistic results. See the following Python function (code review welcome): def rs_ratio(prices_df, benchmark, window=10): from numpy import mean, std for series in prices_df: rs = (...


5

Quantopian provides both the fundamental data (from Morningstar), as well as the backtest platform to reproduce results from the books you mentioned. Here's the introduction to our fundamentals offering: https://www.quantopian.com/posts/fundamental-data-from-morningstar-now-available-for-backtesting (disclosure: I'm the ceo of quantopian)


5

The following paper gives you a range of different indicators and methods and, even better, unifies the whole concept: Which Trend Is Your Friend? by Levine, A., Pedersen, L. Abstract Managed-futures funds (sometimes called CTAs) trade predominantly on trends. There are several ways of identifying trends, either using heuristics or statistical ...


4

Non overlapping periods would make for a far smaller sample


4

I think, the following list answers your question. Even though the below list is exhaustive, there might be some recent changes. Try looking for additional sources, you might find some more useful information. ADX Average Directional Movement Index ADXR Average Directional Movement Index Rating APO Absolute Price Oscillator AROON Aroon ...


4

You need to compute the autocorrelation of the log returns $r_t$, not of the prices, $p_t$. The relationship of the log return series to the price series is $$ r_t = \log \frac{p_t}{p_{t-1}} $$ The price series is obviously very autocorrelated, since today's price is yesterday's price plus small delta.


4

The point of confusion may be in thinking that a predictable price process is synonymous with a mean-reverting process while using the definitions in these papers, it's actually the opposite! In the context of these papers, a random walk would be 100% predictable: the unpredictable component of a random walk (i.e. the period specific shock which has finite ...


3

You are right, the authors provide no strong justification for why their method works. They just show that "it would have worked well in the past". But we should be skeptical how well it will work in the future, especially when you consider what a big improvement this simple change makes in the strategy; it seems a little too good to be true. This is a ...


3

To answer your first question: You need to make all sharpe ratios annual, or quartely, or monthly to be comparable. All of them must have the same periodicity. To answer your second question: From the year returns, you can compute the monthly returns by making $(1+R_{t+2})/(1+R_{t+1})$ and then compute the monthly sharpe ratio, or alternatively, just ...


3

Let me start with a general point: Why do you want to use these datapoints if it is so hard to understand how they are constructed? First of all 4) I am not familiar with testing momentum strategies but you should be aware that the datapoints given are not normal assets you can invest in at the end of the day because at the end of each time period they are ...


3

By mean reversion, people usually mean to say that some price process is second order stationnary -- even though they do not always know the technical term for it. It's only vague in the sense that this defines a class of processes, but doesn't pin down any specific process. By momentum, people usually mean a process which follows trends: upward movements ...


2

As a simple example: if stock A went up a lot in 2014 and also went up a lot in 2015 it could be: (a) that Stock A is a high Beta stock and the market was up in both years. This is the cross sectional property of expected returns. Some stocks, in this case high beta stocks go up more than others when the market goes up. (b) Somehow the fact that Stock A went ...


2

With the information given I would not expect that the denominators differ. $MA_{90}$ tells you the long term price (the moving average should remove noise) while $MA_{45}$ gives you the more recent price (noise removed). Then $M = MA_{45} - MA_{90}$ gives you momentum in terms of price level. You can downscale this momentum by using $M/\sigma$ and $\sigma$...


2

Your steps are well written and correct in general, but it seems like there are some details to clarify, which may cause your results being slightly different from previous studies. Why I am taking just average of losers and winners? Well, that's exactly what (Jegadeesh/Titman (1993) did in Table 3 of this seminal paper. As stated in my answer here, ...


2

Market sensitivity is beta of your portfolio returns to market return, momentum sensitivity is beta against your momentum returns. You'd likely want to run a multiple regression of your portfolio returns against market returns and momentum returns to get those betas/sensitivities.


2

From Daniel-Moskowitz ("Momentum Crashes") you can see that equity CSMOM has negative skewness. However, this is less clear for other asset classes. From their table 11 you can see that commodity momentum has essentially zero skewness (they report a mildly positive skewness). Also e.g. this paper (Menkhoff, L., Sarno, L., Schmeling, M. and Schrimpf,...


2

You are right: the "factors" stemming from the literature of CAPM anomalies and the "components" of PCA are not of the same nature as you underlined: factors are meant to have an economic sense (even if you have a factor like "betting against the beta", that are not that clear and have more a behavioral interpretation). whereas ...


2

Thanks to @user42108 and @amdopt for yours answers! I solved in this way: I've finding functions momentum and ROC of TTR package. In that package there are a lot of function to implement momentum strategies. I've downloaded time series with tseries and I've calculated momentum on adjusted prices. Then I putted the vector of momentum values and the 'zoo' ...


1

ACF plot suggests there is autocorrelation which lasts for long time. The series is clearly not stationary. You may try differencing once - return time series, then plot boathouse ACF and PACF.


1

Vayanos & Woolley have proposed a unified theory of momentum & reversal due to institutional fund flows, but their analysis appears to be limited to stocks. To quote: Our explanation of momentum and reversal is as follows. Suppose that a negative shock hits the fundamental value of some assets. Investment funds holding these assets realize low ...


1

I think there is not the exact replication of the momentum strategy you proposed in your question above. Anyway, in Gao, Han, Li & Zhou (2015) the authours suggested a methodology that can be used to develop a momentum strategy model on the basis of your hypothesis. Shown below the reference suggested: GAO, Lei, et al. Intraday momentum: The first ...


1

Barroso and Santa-Clara recommend that for risk management reasons you "scale the leverage" of the WML strategy over time, and they provide a formula for doing so. Let's say you manage 1 million dollars. Sometimes you short 0.2 million of L stocks against long 0.2 million of W stocks, at other times when circumstances are more favorable you short 2 million ...


1

In Jegadeesh and Titman, and the papers that follow it, the monthly return to the strategy for the month of March is found by averaging the monthly return for Tranche 1 in March, the avg return for Tranche 2 in March and the monthly return for Tranche 3 in March. As shown in the diagram Tranche 1 consists of those stocks bought at the end of December and ...


1

To be fair, their description is awful but you're making this way more complicated than it is. The author is assessing two signals, one short-term and another medium-term. He has a sample universe he's pulling return time-series for and calculating a ST (short-term) and MT (medium-term) indicator for each security, which, to short-hand, represents the ...


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