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DreamCard in a secure seamless transaction. Hence, we have considered overlapping portfolios for the four trading strategies. Therefore, in any given month, the strategies hold a series of portfolios that are selected in the current month as well as in the previous N-1 months, where N is the holding period. In this paper, we explain the methodology for 6 x 12 strategy for illustration purpose, although similar methodology has been used in other strategies as well. The analysis is performed using first six months data for portfolio formation and next twelve months for portfolio testing period i.
As the study uses months data from January to August , there are 86 winner and loser portfolios each for the testing period.
Formation PeriodIn case of a 6x12 strategy, if the portfolio has to be formed for the month of August , then the cumulative returns of the selected stocks for last 6 months are calculated and then arranged in a descending order. The portfolio formed at the end of June based on April -June returns would be held till December. Thus, in any given month t, the strategies hold a series of portfolios that are selected in the current month as well as in the previous n -1 months where n is the holding period. Suppose no news appears for ten minutes.
But, over this period, suppose that a buy order first comes in at Rs. This sequence of events makes it seem that the stock price has dropped by Rs. These changes are spurious. This problem is the greatest with illiquid stocks where the bid-ask spread is wide. In simple words, cumulative returns are the sum total of the logarithmic month-on-month returns of the stock prices in the past six months.
Based on the cumulative returns CR i , the stocks are arranged in descending order. Based on these rankings, ten decile portfolios are formed.
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Each decile portfolio consists of stocks weighed equally in that decile. Top decile portfolio forms winner portfolio and bottom decile portfolio forms loser portfolio. It is to be noted that a portfolio is constructed by going long on the winner portfolio and short on the loser portfolio. This is done on a monthly basis and the step is repeated 86 times for the period starting August and ending on August, as mentioned above.
Holding PeriodAfter the winner and loser portfolios are identified in a given month for a given formation period, the following calculations are to be done for the holding period.
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Step 1: Calculating month-on-month stock returns for all stocks selected in winner and loser portfolioThe first step involves calculating month-on-month returns for all candidate stocks in the winner and loser portfolio for each of the 12 months holding period i. Step 2: Calculating Average Return of Stocks AfterStep 1, average of the stock returns are calculated for each month of the month holding period for each winner and loser portfolio. This is illustrated in Matrix 1 where: ,9 ,R 1,10 i. Matrix 2 illustrates the average returns of all the winner portfolios.
Similar matrix needs to be constructed for the loser portfolio. Matrix: 2 Calculation of average returns of the 86 winner portfolios CAR 12,1 and CAR 12,86 are the Cumulative Average Returns for the 12 st month of the holding period for the 1 st and 86 th portfolios respectively. Step 4 AR 1,1 and AR 1,86 are the Average Returns for the 1 st month of the holding period for the 1 st and 86 th portfolios respectively. Let us understand this by following two possible scenarios.
Scenario 1: Market Goes UpIf the entire market goes up significantly say by 10 percent, both the winner as well as loser portfolios would generate positive returns.
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The only difference being that winner portfolio would outperform the market and may earn 12 percent returns whereas the loser portfolio would underperform the market and may earn only 8 percent. Therefore, the momentum portfolio i. Scenario Market Goes DownIf the entire market goes down by 10 percent, both the winner as well loser portfolios would expectedly generate negative returns. The only difference being that the winner portfolio would lose percent while the loser portfolio would underperform and may go down by 12 percent.
Therefore the momentum portfolio i. Thus, an important point to be noted is that irrespective of direction of market movement, the momentum portfolio W minus L would generate absolute positive return of 4 percent. This is also known as a zero beta or non-directional strategy. Mean Cumulative Average Returns TestMCAR t of a portfolio shows the cumulated returns of the portfolio till the t th month for example MCAR 3 denotes mean cumulative average returns of 86 winner and loser portfolios in the third month.
As shown in Table 1, the winner portfolio delivers a 1. Similarly, the MCAR of loser portfolio in the 1 st month of the testing period is 1. Column 3 of table 1 gives the mean cumulated average return of the long winner and short loser portfolio. The return on the momentum portfolio i. Interestingly in this 12 month IV. If we look at the the initial 5 months there is significantly high differential of winner and loser portfo contributed significantly to a particular months MAR for winner as well as loser portfolio independently.
Thus, from MCAR test, it becomes clear that irrespective of the market direction, the difference remains positive indicating that the strategy is market neutral minus MCAR L,t over the testing period for 6 x12 trading strategy V. Mean Average Test MAR of a portfolio denotes the mean of the average return of the portfolio in the t month of the testing period. If we look at the MAR of the winner portfolio see whether it is the winner portfolio or loser portfolio that runs out of momentum and b returns of which portfolio winner or loser are reversed in the first instance.
In the third month there is a strong fall in the MAR which becomes 0. After the sixth month there is a reversal and loser portfolio starts to rally see chart 4. Sixth month onwards the MAR of the portfolio increases to 1. To test whether the momentum profits do exist in shorter formation and holding period, the study is done for shorter duration formation and holding periods. The results for 3x3, 3x6 and 3x12 strategies are explained with the help of tables and charts in Annexure 2 and Annexure 3. Clearly, the momentum returns do exist for almost all the combinations of formation and holding periods.
It is also evident from the discussion of 6x12 strategy that though MCAR remains positive for the entire holding period, from seventh month onwards loser portfolio shows superior MAR to the winner portfolio, implying that the trend of winner portfolio outperforming loser portfolio is completely getting reversed. It shows that going by the results of this study, for a momentum portfolio formed using six months returns, it is better to have a holding period for six months rather than of 12 months.
Because one can see, that momentum loses steam from seventh month onwards. Having said that, it is worth mentioning here that this conclusion is based on the result of current study only. Implementation issuesMost studies on momentum investment strategies assume zero-cost portfolios, zero transaction costs, ability to short-sale the desired stocks and ignores the impact of block deals on prices and the constraints imposed by regulations.
However, these factors affect implementation of momentum-based investment strategies and have been classified as avoidable and unavoidable factors and examined in some detail. Large funds trading on momentum strategy execute block trades; however, the implicit price pressure costs of such trades reduce the expected returns from this strategy. In case a stock is recalled by the lender, the portfolio manager has to take up additional transaction costs to maintain his short position in the security, which reduces the return of the portfolio.
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The longer the period of short position the greater is the probability of the stock being recalled. Thus, the cost of borrowing stocks and the possibility of the borrowed stock being recalled by the lender makes it difficult for funds to exploit the short-selling possibilities. Futures marketFutures market provides another mechanism to short an individual stock. Advantages of futures market include low transaction costs and high liquidity and therefore low impact costs.
Roll-over costs come into picture when a short position has to be maintained beyond three months since the maturity period for futures contracts is three months. This point can be explained with the help of an example. In the strategy explained in this paper if during a month we have 90 stocks which have to be divided into ten deciles, it means that we will have nine stocks each in the winner and a loser portfolio.
In such a case, if we have to create equally weighted winner or loser portfolio as required by this strategy we need to put more 21 Many studies have documented significant price impact of large block trades. This constraint can however be avoided by creating portfolios of more than 10 stocks. Fund management characteristicsMutual funds can manage their portfolios using equally weighted investments or market capitalization-weighted investments.