# How to calculate monthly momentum strategies J6K6?

I am doing PhD on momentum investment (Jegadeesh and Titman, 1993). My supervisor has some concerns over the momentum strategy that I know. Let me explain my steps in J6K6 momentum strategy, i.e. portfolios are formed on the basis of six months ($$j = 6$$) returns and then they are held for another six months ($$k = 6$$) in the portfolio).

Step 1 - I have calculated monthly stock returns of all the stocks listed on Malaysian stock market through a formula $$\frac{p_t - p_{t-1}}{p_{t-1}} \cdot100$$, where $$p_t$$ is the price of a share at the end of month $$t$$.

Step 2 - My formation period starts from 25/5/02 so I will take the average of returns from 25/5/02 to 25/11/02 in cell 25/11/02. this is 6 month formation period.

Step 3- After the formation period, I will rank the stocks in ascending order and separate the 10% winners and 10% of losers of total stocks available.

Step 4 - I will hold the same winners and losers for next 6 months (K6 - holding period). For this I will take the average returns in 25/5/03 cell. So it complete 12 months (25/5/02 to 25/5/03).

Step 5 - I took monthly averages of all the winners and losers and then subtract losers from winners.

Supervisor comment - Why I am taking just average of losers and winners? why my W-L average monthly returns are higher than the previous studies.

• Possible duplicate of quant.stackexchange.com/questions/34313/… – Alex C Dec 15 '18 at 19:20
• Another similar question quant.stackexchange.com/questions/36083/… – Alex C Dec 16 '18 at 2:44
• Dear Alex C - thank you very my much for editing my question and referring to some relevant questions. however, I am still confused. I would appreciate if you guide me through the steps I have mentioned above as I have understand them. If I try to understand the methodology in a general way, it makes me more confused. Please help me. – Z. A. Imran Dec 16 '18 at 3:39
• Step 4 confuses me, You need to start a new portfolio every month, and keep track of its month by month (not average) returns in the next 6 months. This means you have up to 6 portfolios running simultaneously. The returns to the strategy in any given month are found by averaging returns across the 6 pfolios in the given month. – Alex C Dec 17 '18 at 16:11

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.

1. 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, portfolio sorts and the calculation of their "high minus low" portfolio returns are a well known and common applied method in empirical finance. As a nonparametric technique it does not make any assumptions about the nature of the cross-sectional relations between the variables under investigation. Otherwise, you could also apply regression techniques like Fama/MacBeth (1973), which is applicable for controlling for a large set of other variables.

1. why my W-L average monthly returns are higher than the previous studies.

There are some details missing in your description of return calculation, so let me list some aspects, which may bias your returns:

• Your formula in step 1 does not take into account corporate finance decisions like dividends, share repurchases. Investors anticipate from these events, so you should calculate the total return, i.e. including dividends, etc.

• You do not mention any exclusion of your stocks, so your stock universe is the entire Malaysian stock market. As stated here, you should at minimum exclude banks and/or public utility firms, as their business model differs a lot from other companies. This is e.g. done by Fama/French (1992) by excluding firms with SIC codes between 6,000 and 6,999, which also exclude firms with negative book-values. Furthermore, illiquidity of a stock is positively related to its expected returns in both time series and cross section (see Amihud (2002)). Therefore, it is common to exclude illiquid stocks and following Ang et al. (2009), this is done by simply exclude the 5% of frims with the lowest market equity.

• You follow the approach in (Jegadeesh/Titman (1993) and define momentum for stock $$i$$ in month $$t$$ as the stock return during the (here) six month up to and including month $$t$$. However, the nowadays more common approach is to exclude the current month. This approach is driven by the desire to separate the medium-term momentum effect from the short-term reversal effect. Jegadeesh (1990) found, that stock returns over one month tend to have a negative cross-sectional relation with returns over the next month, i.e. a strategy of buying previous month "losers" and selling recent "winners" generates positive returns for the following month (2.20% p.m. with t-value of 15.63!). In fact, i suggest you to skip the last recent month for calculating momentum.

In summary, excluding the previous month for return calculation should further increase your portfolio returns, as the lowering short-term reversal effect is taken into account. However, in my opinion, the crucial bias towards higher returns may be small and illiquid firms, which you currently do not remove from your sample.

• Dear Skoestlmeier, I appreciate your help. Let me repeat what you said, I should excludes (i) Banks and public sector firms and (ii) stock which is less than $5 as (Jegadeesh and Titman, 2001) did. – Z. A. Imran Dec 18 '18 at 7:28 • Furthermore, you could try to 1) follow the approach of Ang (2009) and exclude firms with the lowest 5% of market valuation (and not only prices$<\$5$). 2) Exclude firms with negative book-value (common approach like e.g. in Fama/French (1992). Also, skip the most recent month for calculating momentum. I would appreciate if you could provide detailed numbers, i.e. what is you W-L portfolio return, t-value, etc.. Just try some of my suggestions and look how it affects the return - it will help you to get familiar with your data. If my answer is helpful, it would be kind if you accept/upvote. – skoestlmeier Dec 19 '18 at 8:03
• Dear Skoestlmeier, I am new on this website and even I am not much familiar with its options. I will surely accept or upvote you, as you are very helpful and kind person, but let me figure it out how to do it. Can I have your email ID, I can share my whole Excel file with you. You can see the data and the method. It would be kind to talk to you personally. My email ID is "imran.0033@gmail.com" thank you. – Z. A. Imran Dec 20 '18 at 9:48
• Then warmly welcome @Z.A.Imran on Quantitative Finance SE! To get familiar with this site, i recommend you to read what topics are discussed on this site and further information here. This is a professional Q&A site, so please shape your answer and provide/share information and details on what you are asking here. Therefore, i am not content to give personal consulting outside this community but i would like to encourage you to edit your question and provide some summary statistic details. – skoestlmeier Dec 20 '18 at 11:03
• Put that code in an edit and please use proper code formatting. – Bob Jansen Dec 23 '18 at 10:27