Simple Dietz method: Difference between revisions

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{{notability|date=November 2010}}

The '''simple Dietz method''' is a means of calculatingmeasuring an approximation ofhistorical investment portfolio performance during a period of external cash flows into/out of the portfolio.<ref>Dietz, Peter O. ''Pension Funds: Measuring Investment Performance''. Free Press, 1966.</ref> It addresses some of the weakness of the [[internal rate of return]] (IRR) calculation.

The simple Dietz method calculates performance as follows:

The formula for the simple Dietz method calculatesreturn performanceis as follows:

<math>R=\frac{M_2 -M_1 -C}{M_1 +\frac{C}{2}}</math>

<math>R=\frac{M_2EMV -M_1BMV -C}{M_1BMV +\frac{C}{2}}</math>

Where <math>M_1</math> is the starting value of the portfolio, <math>M_2</math> is the ending value of the portfolio, <math>R</math> is the portfolio rate of return, and <math>C</math> is the total external cash flows during the period (cash flows out of the portfolio are negative and cash flows into the portfolio are positive). This method assumes that all such cash flows are made mid-way through the period of analysis.

This method is somewhat more computationally tractable than IRR. However, the assumption that all cash flows are made at precisely the middle of the evaluation period remains troubling. This deficiency was the inspiration for the modified Dietz method, a clear improvement for the general case where there are cash flows which are not made at the midpoint of the period being analyzed.

where <math>BMV</math> is the starting value of the portfolio,

Like the more general [[modified Dietz method]], the simple Dietz method is only an approximation. The only precisely correct means of calculating returns in the presence of external cash flows is to use the [[true time-weighted rate of return]].

<math>EMV</math> is the ending value of the portfolio,

<math>R</math> is the portfolio rate of return, and

<math>C</math> is the net external inflow during the period (flows out of the portfolio are negative and flows into the portfolio are positive).

It is based on the assumption that all external flows occur at the half-way point in time within the evaluation period (or are spread evenly across the period, and so the flows occur on average at the middle of the period).

==Discussion==

1) The simple Dietz method is a variation upon the simple rate of return, which assumes that external flows occur either at the beginning or at the end of the period. The simple Dietz method is somewhat more computationally tractable than the [[internal rate of return]] (IRR) method.

2) A refinement of the simple Dietz method is the [[modified Dietz method]], which takes available information on the actual timing of external flows into consideration.

3) Like the [[modified Dietz method]], the simple Dietz method is based on the assumption of a simple rate of return principle, unlike the internal rate of return method, which applies a compounding principle.

4) Also like the [[modified Dietz method]], it is a money-weighted returns method (as opposed to a time-weighted returns method). In particular, if the simple Dietz returns on two portfolios over the same period are <math>R_1</math> and <math>R_2</math>, then the simple Dietz return on the combined portfolio containing the two portfolios is the weighted average of the simple Dietz return on the two individual portfolios:

<math>R = w_1 \times R_1 + w_2 \times R_2</math>

The weights <math>w_1</math> and <math>w_2</math> are given by:

<math>w_i = \frac{BMV_i +\frac{C_i}{2}}{BMV_1 + BMV_2 +\frac{C_1+C_2}{2}}</math>

== References ==