Reynolds operator

The simple Dietz method is a means of measuring historical investment portfolio performance during a period of external flows into/out of the portfolio. The formula for the simple Dietz return is as follows:

$R={\frac {EMV-BMV-C}{BMV+{C/2}}}$

where

• $BMV$ is the starting value of the portfolio,
• $EMV$ is the ending value of the portfolio,
• $R$ is the portfolio rate of return, and
• $C$ 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 $R_{1}$ and $R_{2}$, 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: $R=w_{1}\times R_{1}+w_{2}\times R_{2}$. The weights $w_{1}$ and $w_{2}$ are given by: $w_{i}={\frac {BMV_{i}+{\frac {C_{i}}{2}}}{BMV_{1}+BMV_{2}+{\frac {C_{1}+C_{2}}{2}}}}$.

See also

• Internal rate of return
• Modified Dietz method
• Rate of return

References

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