Dear Srikanth Potharla

First, find the price level of the chosen index on the first and last trading days of the period you're evaluating. Be sure to use the opening price on the first day and the closing price on the last in order to make sure your calculation is as accurate as possible.

Next, subtract the starting price from the ending price to determine the index's change during the time period.

Finally, divide the index's change by the starting price, and multiply by 100 to express the index's return as a percentage.

so formula could be

Return = (Ending Price - starting price)100/Starting Price

Dear Srikanth ji, the formula is very simple= Index value at the end minus index in beginning of year divided by index in beginning. For percentage multiply with 100. OR compute daily return and find sum. Most books of security analysis as well as numerous research papers describes the procedure for determining stock returns. Just take a pain to refera book: Security Analysis and Portfolio Management authored either by Prasanna Chandra, or by Francis or by Brealey Myers and so on . Further on determining daily return you can determine annualised return

thank you Prof. Bhag Singh Bodla for your suggestion.

the formula, you have mentioned is for holding period return.

I am not asking about the computation of holding period return. It is as simple as such and it is a elementary level calculation of return.

I am interested in computing a representative measure of return for the year. the information content of holding period return is very poor.

You have to annualise the returns from the daily returns - then average

ok there is the wikipedia way of doing this which is wrong in my opinion which is to raise the daily returns to the power 365

The finance way of doing this is as follows:

In practice returns follow a log normal (we could debate that) distribution

Because of that you should estimate daily returns using the following formula - Ln(day+1 /Day 0), ln(day2/Day1) etc -ie natural log

As prices could go up and down over the year it wouldn't be right to compound them over 365 days to get an annulaized return. some days would go up and others down with a log normal return

Cannot rememeber the theory (see Hull and white options and other derivatives etc) but we multiply the log return by the squareroot of t to get the annualised returns (t=365 for daily to year or 12 for month to year) . In the markets I deal with I assume that there are 252 trading days (note not 365) so i would multiply the log return by sqrt of 252 ie 16 if you were using monthly log returns you would use the sqrt of 12

Get all of the annualised daily returns and average them -

I think that's what you want to do -

you might want to look at this as an example https://www.youtube.com/watch?v=PtoUlt3V0CI

Gary

Hopefully that made sense

thank prof. Gary Howorth for your most valuable answer.

i understood the procedure explained by you.

but, my more specific doubt is how to handle extreme values in computation of the average of the annualized returns. becuase, they undermine the representativeness of the average value.

some measures like DFBETAS, leverage points etcs can be computed for regression.

But, i have to compute simple arithmetic mean. In this process, how to identify the outliers and remove them in computation of best possible representative mean value of the returns.

thanks in advance

You need to be very careful with removing data. They may not be outliers..

techiques. You could use would be

1/histogram. of daily points e.g. Values vs freq. does it have a nice shape can you visualize outliers from this. Would expect the histogram to be log normal

2/Bollinger bands. E.g. 3x sigma say. What points lie outside 3 sigma

assumrs normal distribution though

3/Inter quartile ranges. Exclude say 1.5-2 times IQR

4/Box and whisker diagrams. - visual look for outliers

and so on

You cannot use arithmetic means to calculate average return. A simple counter-example is:

a stock performed 5% in day one but loss 5% in the second day. The average mean of those two would be zero. But if you calculate the two-days performance of this stock, this would be 100%*1,05*0,95=99,75% (negative performance of 0,25%, NOT 0% !!!).

You need geometric average rather than arithmetic average. For daily performance samples from a particular year: P_1, ..., P_250; the average daily return is 250-th root of the product of P_i.

But you want to calculate yearly performance (not daily). The yearly return is just all of daily returns, which can be calculated by the product of P_i. This is the exact return of the period april2016 until march2017.

Averaging makes any sense if your data is less than one-market-year (

Presumably you are seeking the annual geometric (i.e. compounded) return for a specific time period of an index, in this instance the TR on the NSE Nifty-50 Index. There are two simple ways to compute this accurate for any time period using a daily series:

(1) ((Value2/Value1)^(1/((Date2-Date1)/365.25)))-1

(2) (LN(Value2/Value1)) / ((Date2-Date1)365.25)

Natural Logarithms are often used as the best approximate for average return over any time period e.g. an index moves from 50 to 100 points, is that a +50% rise (100-50)/100 or a +100% gain (100-50)/50? Both methods are mathematically correct. Tradition and convention states that the denominator is the 'starting' value, but this is rote learning from school. So instead we use Natural Logs to give the best estimate LN(100/50)=0.693.

The above formulae are easy to use in MS-Excel. I would use method (1) for short time periods such as up to 1-year, and method (2) for longer time horizons such as multi-year periods. Also use 365.25 to account for 'Leap' years, especially over longer time horizons. In Excel each date is stored as a numeric value e.g. 2016-04-01 (using YYY-MM-DD format that all computers use internally) has a value of 42461, whereas 2017-03-31 has a value of 42825 in Excel. The difference between these two dates is 364 days (not exactly 1-year), which you could divide by 365 or 365.25, either way is approximately 0.9966 years.

I mention this latter point because if you are happy with these two specific dates (or other dates) then no worries, the formula works great, however, if you are looking for a time period of exactly 1-year, then you might consider revising your chosen start/end dates.

Dear Srikanth Potharla,

Hope all is well.

You need to use the geometric mean (compound return) instead of arithmetic mean, this is because:

Ø The arithmetic average return answers the question: “What was your return in an average year over a particular period?”

Ø The geometric average return answers the question: “What was your average compound return per year over a particular period?”

• When should you use the arithmetic average and when should you use the geometric average?
• The arithmetic average tells you what you earned in a typical year.
• The geometric average tells you what you actually earned per year on average, compounded annually.
• When we talk about average returns, we generally are talking about arithmetic average returns.
• For the purpose of forecasting future returns:

Best Regards

Prof. Dr. Mazin A. M. Al Janabi

Full Professor of Finance & Banking and Financial Engineering

Tecnologico de Monterrey, EGADE Business School,

Santa Fe Campus, Mexico City, Mexico.

I've been trading stocks with no criteria. Hopefully it will still work.