Datastream: Total Shareholder Return (TSR), average return

This is the change in price of a stock added with dividend on yearly basis.
Return index – datatype (RI)
A return index (RI) is available for individual equities and unit trusts. This shows a theoretical growth in value of a share holding over a specified period, assuming that dividends are re-invested to purchase additional units of an equity or unit trust at the closing price applicable on the ex-dividend date.
Total Return (datatype RI) on Datastream is cumulative as it adds any changes on to the previous day's value.

Average return, there are a few options here.
If you want to get the average between two specific dates then you would run a static request with the company codes in the series field and the expression as per below:
AVG#(X(RI),01/01/00,31/12/00)
Another option is to use a calendar average such as calendar monthly average in a time series request as per below:
CMA#(X(RI))
You would need to set the frequency to monthly and it will then provide an average of the company's RI for each complete calendar month in your time period (specified using the start and end date fields).
Alternatively, if you want to calculate the cumulative sum of all of the calendar monthly average datapoints between two dates, you can use the following:
CSUM#(CMA#(X(RI)))

. . .

For unit trusts, the closing bid price is used. For all countries except the USA and Canada detailed dividend payment data is only available on Datastream from 1988 onwards. Up to this time the RI is constructed using an annualised dividend yield.
From 1988 onwards (and from 1973 for US and Canadian stocks), the availability of detailed dividend payment data enables a more realistic method to be used in which the discrete quantity of dividend paid is added to the price on the ex-date of the payment.
Gross dividends are used where available and the calculation ignores tax and re-investment charges.
Adjusted closing prices are used throughout to determine price index and hence return index. At this point the RI is calculated back to the base date.

See also: functions and expressions in Datastream (link)
or creating list and find historical Beta