Dear Guldana,

The arithmetic monthly return is equal to P(t+1) / P(t) -1 where P(t+1) is the value of the Kazakhstan index at the end of month t and P(t) the value of the index at the end of month (t-1).

The logarithmic return is computed as LN ( P(t+1) / P(t) ).

BR

Sébastien

INDEX: Tracking changes of price and quantity over a time period. Need the following items: (i) price; (ii) quantity corresponding to price; and (iii) time consisting of reference time called based period (t0) and time at present (tn) or at point of analysis. Therefore, the price at the base period is P0, quantity at the base period is Q0; likewise, the price at observed period(now) is Pn and the corresponding quantity is Qn.

PROCEDURE: Below are step-by-step procedures on how to calculate index. Examples of 4 different types of index are attached in the excel  file below.

(i) Monthly Average. Since the data is in a daily format, we need to make it into monthly. One simple approach is to take the monthly average and tabulate a new table as monthly price and monthly quantity. NOTE: price is measured in thousand. Quantity is in million. Since there is a large disparity, we need to adjust the quantity by a factor of 1000 so divide quantity by 1000 so that the final result will be easy to read.

(ii) Select Base Period. Select the month that will be fixed as a base period. Here, the year 2007 has three running month, we are going to drop them and use January 2008 as a fresh start as the base period. Thus, P0 and Q0 is fixed at January 2008. Any thing else happened after January 2008 will be analyzed relative to January 2008. 

(iii) Select Type of Index to Use. There are several index types to use. In the attached excel file, I tabulated 4 different types of index and compare their result to verify whether their results are statistically significant---the verification by Z-score says no significant different under 0.95 confidence interval.

(iv) calculate the index. I tabulated 12 months in 2008. For subsequent months, just follow the steps. Remember to bring the monthly average of price and quantity from the first sheet. After that, just copy and paste column G onward.

I hope this has been helpful. Cheers.

REFERENCES:

(1) Fisher, I. The Making of Index Numbers: A Study of Their Varieties, Tests and Reliability, 3rd ed. New York: Augustus M. Kelly, 1967.

(2) Kenney, J. F. and Keeping, E. S. "Index Numbers." Ch. 5 in Mathematics of Statistics, Pt. 1, 3rd ed. Princeton, NJ: Van Nostrand, pp. 64-74, 1962.

Use of daily data or monthly data will usually depend upon the research you are undertaking. It is necessary to define the time period for your research context. In case you are considering a vast time period like many years, it may be difficult to work with voluminous data esp. if you take daily data. If that is the case, in a simple way, I would suggest you take data of the last day of the month and use it as monthly data of the time series. the variations within the month will of course not be captured in that case but in long term forecasting we are really not interested in day-to-day variations.

Sorry, but if you take the price of the last day of the month from the time series what changes?

If anything, I would worry to recover the closing price adjusted

the changes in the time series exist even when you take only the closing prices. you are only losing information of the variations within the month and this is acceptable when we use the time series for long range analysis and forecasts. In macroeconomic analysis, we also come across some economic parameters being put out as monthly data.

https://www.researchgate.net/publication/303830251_Macroeconomic_Determinants_of_the_Behavior_of_Dhaka_Stock_Exchange_DSE

Article Macroeconomic Determinants of the Behavior of Dhaka Stock Ex...