Daykin (1976) suggested a method of evaluating the rate of return achieved over a past period which did not depend directly on the market value at the end of the period in question. This was intended to avoid the volatility in the results of an assessment based on market values and sought to give a more reliable indication of the underlying rate of return which had been achieved.

If the general problem in relation to equities is considered, an investment of 1 at the beginning of year M will roll up with reinvestment of dividends to give an accumulated investment, XN, at the end of year N, in terms of ‘units’ in an index P, of:

(1)