Define MV_0 and MV_t to be the portfolio market value at time 0 and time t, respectively. For simplicity, I shall initially exclude cashflows. Suppose that the “DVR” to be assessed is 100 j % pa.
Define “f” to be a singlevalued operator such that, at time u, we define DV_u by
DV_u = f{MV_u , j}.
Then, if there are no cashflows, we require
DV_0 * ((1+j) ^t ) = DV_t .
Any net cashflows (benefits paid or contributions receivable) can be accommodated by accumulating from the respective payable dates until the end of the interval at the same rate of return.
In practice, for bonds, “f” would take the form of an amortisation formula, allowing for capital and interest. For equities, something along similar lines could be adopted. In the UK, but nowhere else, such formulae have been commonly adopted in the past. Other parameters may well be needed, such as dividend growth or capital growth, but the above has been generalised.
Depending upon the form of the “f” operator, the DVRs may well not be chainable from one interval to the next. In other words, over the single years 1999, 2000 and 2001, the geometric mean DVR will not be the same as the DVR calculated for the 3 years as a whole (where only the beginning and end figures are taken into account).
