Momentum analysis is mainly done to measure the rate of rise or fall in stock prices (Sehgal and Jain, 2011). It is a method to show the trend of daily stocks and prices over time. Momentum analysis is applied only on financial stock prices of companies or stock portfolios. The use of momentum analysis dates back to the early 1990s, when a paper analyzing the momentum of stock returns on U.S. equities was presented for the period 1963-1990.

Investors usually invest in the market on the basis of the growth and trend of the momentum of the stock prices. Momentum analysis therefore is an important indicator for the investors to invest in a specific company or a stock portfolio. Academicians also use momentum analysis to check the presence of momentum in the returns for various researches.

## Concepts surrounding momentum analysis

There are two main components of a momentum; holding and the formation period. The value for today usually forms the holding phase and the stock price n-days ago which forms the formation period. In other

The rate of fall or rise of stock returns is also possible to check using the Price Rate of Change Indicator (ROC) (Tsai and Wang, 2009). However, ROC is a momentum-based technical indicator that measures the percentage change in price between the current period and the price, a certain number of days ago. Fall or rise of stock returns can be checked by subtracting the holding period value from formation period value or by the use of the formula for ROC. In addition to ROC, other indicators such as the moving average convergence divergence (MACD), stochastics, and the relative strength index (RSI) help perform momentum analysis (Tsai and Wang, 2009).

## Need for momentum analysis

**To check the trend of fall and rise of daily stock returns: **This is basically done by subtracting the current stock by the stock purchased n-number of days back. Then the trend of the stocks is presented graphically.

M = V – Vx

Where:

V = latest price;

Vx = closing price;

x = number of days ago.

**To check the stocks that is best performing and worst performing:** This is usually done to check momentum investing by investors. This is done on the basis of the annualized momentum of the stock returns and then conducting t-test for each year. Analysis involves average annual returns for portfolios grouped by momentum. The t-test helps to check if there is momentum between the years, if not then investing will not be done by the investors.

Availability of momentum during a given period is done by the first method and then t-test is run between the formation and holding periods in the combinations of n-number of days. The availability of momentum is seen by ‘p-value’ whereby ‘p’ must be less than 0.05. If the p-value is more than 0.05 there is no momentum and if the p-value is less than 0.05, there exists momentum.

## Type of data used

Momentum data is found from the daily stock return values. To evaluate the daily stock returns use the respective formula from daily starting and closing prices of the stocks.

Stock return = {(P_{1}– P_{0}) + D / P_{0}}

Where, P_{1 }= Ending stock price; P_{0 }= Initial stock price; and D = Dividends

A misconception is momentum analysis is possible using annual stock returns or average annual stock returns. A time horizon is the key in conduction of momentum analysis. The time may comprise of short term or long term. Long term combination of daily stock returns remain calculated in months or years. On the other hand, the short term combinations remain conducted over a minimum of 10 days to 50 or 120 days.

## Average annualized returns data

The first type of data is the average annualized returns of the companies in a stock. In this case, the formation and holding period are stock before n-number of days as on 1^{st} Dec 2015 and current stock as on 31^{st} May 2016 in the short term period. In the long term period, the formation and holding period are stock before n-number of days as on 1^{st} Dec 2012 and current stock as on 31^{st} May 2016. This type of data is chosen to show the presence of momentum for a specific set of companies. Data can also be chosen while exploring the most profitable and the least profitable stocks amongst a group of stocks or stocks of companies.

## Average rate of returns of growth and value stock portfolios

Second type is average returns of growth and value stock portfolios. Initially the growth and value portfolios are classified on the basis of price-earnings (PE) ratio and price to book (PB) ratio and the companies remain divided accordingly. The average daily returns of the companies remain calculated for the chosen time period and then the formation and holding periods are chosen. Choose this type of data to check if there is any difference between the growth portfolios and value portfolios. In other words, choose this data type only when the companies in a stock index are classified into growth and value, and needs exploration of presence of momentum.

## Daily returns of companies

One last type of data used is daily returns of companies for a specific period of time, where the average annual returns for portfolios grouped by momentum are considered. Then the winner minus loser portfolio will be calculated to ascertain the profitability of the momentum strategy. This type of data is used to identify if the investors must invest in a set of stocks or to find if the investors invested in profitable or losing stocks on the presence of momentum.

## Challenges related to momentum

### 1. Time

The most important challenge is the time spent on choosing the formation and the holding combinations. In case of a daily returns data for a company between the financial year 2010-2011 and 2017-2018, the number of entries is in thousands. Now choosing the current price and price before n-number of days will take a lot of time to form the combinations manually. For 8 week time, the number of days is 56 days. So, manually choose the current price and price before 56 days. Then again present them as combinations.

### 2. Price difference in holding and formation period

Secondly, a common mistake made by researchers is the stock price consideration for current and price before then n-number of days. In general, current price on 20^{th} August 2017 is 225 and its prices before 10 days on 10^{th} Aug 2017 are 117. But, mistakes made is vice versa. It means the current price on 10^{th} Aug 2017 are 117 and prices for 10 days on 20^{th} August 2017 is 225. According to the formula, momentum is the latest price or current price minus closing price n-number of days ago.

### 3. Formation of portfolio

According to a study by Balakrishnan, (2016), every momentum study must be conducted using constructions of portfolio in value and growth momentum combinations. However, majority of studies avoid formation of portfolio in value and growth stocks. Without forming portfolio in value and growth momentum combinations, it is difficult to assess which set of companies perform good and which do not. Other strategies of momentum returns are not wrong, but do not provide accurate findings with respect to momentum investing and the investors end up investing in losing stocks.

### 4. Formula to use

Another challenge is confusion over the use of formula. As identified before, the momentum is used in different cases; one may face the issue of using different methods and formula. For instance, momentum on the basis of company stocks needs to use the daily reruns for each company and the conduct momentum analysis. On the other hand, momentum on the basis of the stock portfolio will include average daily returns of the portfolios.

### 5. Volume of data

Lastly, limitations of using short term and long term periods to identify the presence of momentum. Short term holding and formation period starts with a minimum of 10 days and may extend to a year or more. In many cases one may use 1 year holding and formation period which is termed as long term momentum investment. In case of medium term momentum, one may use 3 to 8 months of holding and formation period. Short term momentum starts from 10 days to 120 days period. Short term investment will use 10-120 days of holding and formation period, whereas long term investing will use 1 or more year of holding and formation period. However, even if one uses long term period, the data will always be daily, annualized data will not be used. For instance if the formation period is 31^{st} March 2015 and the holding period is 1^{st} April 2017, daily returns data will be used for choosing the formation and holding period and not find the average of 31^{st} March 2015 to 1^{st} April 2016 and then again 2^{nd} April 2016 to 1^{st} April 2017.

#### References

- Asness, C.S., Frazzini, A., Israel, R. and Moskowitz, T.J., 2014. Fact, fiction and momentum investing.
*Journal of Portfolio Management, Fall*. - Balakrishnan, A., 2016. Size, value, and momentum effects in stock returns: Evidence from India.
*Vision*,*20*(1), pp.1-8. - Fama, E.F. and French, K.R., 2012. Size, value, and momentum in international stock returns.
*Journal of financial economics*,*105*(3), pp.457-472. - Lewellen, J., 2002. Momentum and autocorrelation in stock returns.
*The Review of Financial Studies*,*15*(2), pp.533-564. - Sehgal, S. and Jain, S., 2011. Short-term momentum patterns in stock and sectoral returns: evidence from India.
*Journal of Advances in Management research*,*8*(1), pp.99-122. - Singh, A. 2018. Momentum and Contrarian Investment Strategies– A Study from NSE, India.
*International Journal of Business and Management Invention (IJBMI)*. 7(1), pp.78-90. - Tsai, C.F. and Wang, S.P., 2009, March. Stock price forecasting by hybrid machine learning techniques. In
*Proceedings of the International MultiConference of Engineers and Computer Scientists*(Vol. 1, No. 755, p. 60).

### Avishek Majumder

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