In the previous article, different data types and challenges faced while conducting momentum of daily returns remain presented. There are different methods of calculating the momentum of stock prices. Each type of calculation depends on the type of data being used. Stock exchange experts use different tools to find the momentum of stocks, however, MS Excel is one of the best methods. Apart from that, the STATA software package can be used for the assessment of momentum investing.

## Type 1: rate-of-change method

This is a three-step method. It is conducted to find the security of price momentum. In this process, use the rate-of-change method. In this process, the momentum is found by comparing the current prices with the price n-periods ago. MS Excel can be used to calculate the data.

- Step 1: Present the dataset in the MS Excel sheet in one column
- Step 2: Divide or consider a period, like 10 days period
- Step 3: Divide today’s closing price by the closing price 10 days ago
- Step 4: Multiply the value by 100

M = (Price Today/Price 10 Days Ago) x100

The baseline in this method is 100. If the M-value is lower than 100, then the momentum is low and if the value is greater than 100, the momentum is high. Therefore, the value will implicate if the momentum price is accelerating or decelerating.

## Type 2: Subtraction method of the rate of change in price movement

This method is the most common and the simplest form of

The below presents a list of daily returns from
11^{th} April to 21^{st} April, which is a period of 10 days.

11 Apr | 12 Apr 2016 | 13 Apr | 14 Apr | 15 Apr | 16 Apr | 17 Apr | 18 Apr | 19 Apr | 20 Apr | 21 Apr |

0.719 | 0.234 | 1.736 | 2.983 | 0.235 | 0.972 | 0.193 | 1.762 | 1.992 | 1.103 | 0.773 |

**Step 1:**Choose the latest price and the price 10 days ago. Latest price is 0.773 and the price 10 days ago is 0.719.**Step 2:**Choose the formula M = V-Vx, where V is the latest price and Vx is the price 10days ago.**Step 3:**Continue this process for the complete dataset chosen and extract the latest price and closing price for the complete dataset.**Step 4:**The next latest price after 11^{th}April will be 10^{th}April and the price 10 days ago will be 1st April 2016. Ascend the calculation for the period of the number of days. It will help in the formation of trend line.

Measuring the price differences over a set period shows the rates at which the stock price is rising or falling. Momentum shows trend lines of fall and rise of prices of stock. Distinct trend lines develop as the stock price increases, and a rising momentum plot line above zero indicates an uptrend is firmly developing.

## Type 3: Using the Size–value and Size momentum Sorted Portfolios method

This method is different from the ones used normally and is typical. This method was developed by Fama and French in 1993 and is widely used by academicians while using the size–value and size–momentum sorted portfolios to find momentum of stock prices. Start this method by creating a

For instance, keep a three-month gap from the closing of the financial year to the portfolio formation with an assumption that financial statement may reach the investors’ hand only after three months from the end of the financial year.

**Step 1:**Now group the stocks into three categories based on Price to Book (P/B) ratio which is the measure of company value and name them as low (L), neutral (N) and growth (G). The portfolios are S/L, S/N, S/G and B/L, B/N, B/G.**Step 2:**Calculate SMB or small minus big portfolio that shows returns in relation to company size and it is computed by subtracting monthly simple weighted average returns and subtracting monthly simple weighted average returns on three big stock portfolios.

SMB = (S/L + S/N + S/G)/3 - (B/L + B/N + B/G)/3

**Step 3:**Now calculate low minus high portfolio that includes returns in relation to company value by subtracting monthly simple weighted average returns on two growth stock portfolios.

LMH = (S/L + B/L)/2 - (S/G + B/G)/2

**Step 4:**Now regress monthly average returns on portfolios for monthly average returns on market portfolio for the whole sample period and run CAPM regression.

R_{pt}– R_{ft}= a + b (R_{mt}– R_{ft}) + e_{t}

Where, *R _{pt} – R_{ft} *is
excess returns on portfolio (portfolio returns are reduced by risk-free rate,

*R*is excess returns on market portfolio (market returns are reduced by risk-free rate, a is abnormal returns (portfolio returns in excess of returns on market portfolio), and b is portfolio’s responsiveness to market factor (beta coefficient).

_{mt}– R_{ft}**Step 5:**Run Fama and French three-factor model.

R_{pt}
– R_{ft} = a + b (R_{mt} – R_{ft}) + sSMB_{t} +
lLMH_{t} + e_{t}

Where, s and l are the portfolio’s responsiveness to (sensitivity coefficients) SMB and LMH factors.

**Step 6:**Now if the momentum asks for momentum investing, conduct WML or winner minus loser portfolio whereby risk factor in returns in relation to the momentum factor.

WML = (SW - SL)/2 + (BW - BL)/2

**Step 7:**Repeat the CAPM assessment as in step 5 and find the portfolio that proxies for momentum factor in returns.

Average returns on portfolios formed on the basis of size–value show up the presence of strong size and value effects in

stock market. Moreover, average returns on size– momentum sorted portfolios exhibit the strong or weak momentum effect in stock returns as the average return on SW portfolio outperforms other portfolios by giving the highest returns. Lastly, CAPM will show eithergrossly failure or success to capture the average returns on size–value and size–momentum sorted portfolios.

## Type 4: The growth and value portfolio method

This method is used to identify the companies under the growth and value stocks of the S&P index and if they have momentum. This method is best performed in MS Excel but is time taking. The chances of incorrect construction of the formation and holding period of the daily returns

**Step 1:**Find the data for all the companies in the stock index.**Step 2:**Find the Price-Earning (P/E) ratio and Price to Book (P/B) ratio of the chosen companies and divide them on the basis of growth and value portfolio.- Step 3: Categorize stocks whose prices were 25 times higher than their earnings and book values, were included in the growth portfolio. Stocks, whose prices were higher by 10 times or less than 10 times their earnings and book values, were included in the value portfolio.
- Step 4: Find the daily returns of the companies for the value and growth stocks and present the average daily returns of the stocks of growth and value portfolios.
- Step 5: Choose the formation and holding period (same as mentioned in the type 2 method). They may be short term or long term.
- Step 6: Use the formula mentioned in step 2 of the type 2 method of momentum analysis of stock prices.
- Step 7: Conduct a T-test to find the presence of momentum in the growth and value stocks. The T-test can be done by using the ‘Data Analysis’ option provided in the Data tool of MS Excel.
**Step 8:**Conduct risk assessment of the value and growth stocks by using the CAPM beta formula mentioned in step 4 of type 3 methods of momentum analysis.

The next article presents a detailed method and steps to conduct the CAPM regression and the risk of the value portfolio and the growth portfolio. In addition, it explains the stepwise method of variance-covariance formula to calculate beta. The risk assessment will indicate which stocks the investors should be investing in.

### Avishek Majumder

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