Inevitably, the definition is somewhat mathematical but it's not too heavy. Take a time interval (0,t) over which we are monitoring performance. The terms “DV” and “MV” always refer to “discounted value” and “market value”, respectively.
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 payment dates until the end of the interval at the same rate of return (namely 100 j % pa).
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 but the above has been generalised.
Depending upon the form of the “f” operator, the DVRs may well not be chainable from interval to interval. In other words, taking 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.
