Stock Asset Returns Are Predictable Part 2

5. DATA SOURCES, METHODOLOGY AND VARIABLE CONSTRUCTION

5.1. Return Calculation

There are two ways to calculate stock returns

5.1.1. Continuous Return

This is the percentage return that would be earned by an investor who bought the stock at the end of a particular day/month t-1 and sold it at the end of the following day/month. For day t and stock A, the day return R At is defined as

R At = { In (P At/P A, t-1)}*100

The stock paid a dividend in day t, the total return would be

R At = {In (P At +Divt /P A, t-1)}*100

5.1.2. Discrete Return

An alternative method to calculate stock returns is defined as

R At = {(P At/P A, t-1)-1}*100

5.1.3. Continuous Compounded versus Discrete Returns

Using continuously compounded rate of return, it is assumed that Pt = Pt-1 ert where rt is the rate of return during the period (t-1,t) and where Pt is the price at time t. If r1, r2,….,r12 are the returns for12 months, then the price of the stock at the end of the 12 months will be

P12 = P0 e r1 +r2 +….+r12

This representation of prices and returns allows to assume the average daily or monthly returns is r = (r1, r2,….,r12)/ 12.Since we can assume that the return data for the 12 months represent the distribution of the returns for the coming month, it follows that the continuously compounded return is the appropriate return measure, and not discretely compounded return. (Benninga, 2008)

5.2. TESTS OF RETURN PREDICTABILITY

In this research study, methodology consists of four sections based on information set of return predictability. Information set can be defined as the past history of stock prices, time patterns, market characteristics and firm characteristics .The first section consists of short-term return predictability based on past hi...

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...r ARIMA model, the next step is to see whether the selected model is appropriate. One test of the chosen model is to see if the estimated residuals from the model are white noise thereby the chosen model fits the data reasonably well. Box and Jenkins(BJ) methodology suggests some diagnostic checks to determine whether an estimated model is statistically appropriate or not; if “Yes” then go for the last stage i.e. forecast; if “Not” then go back for the first stage and repeat the procedure from identification and estimation of parameters to diagnostic checking until there is a good final model.

5.2.2.2.1. D) Stage 4: Forecasting

One of the reasons of the widely accepted ARIMA models is its success in forecasting. The forecasting made by this method is more authentic than those made from other econometric models particularly for short run forecasts (Gujarati, 2003).