Modified Dietz Return vs Time Weighted Return

CFA General
#1

Hi,

Reviewing my firm’s performance data and calculations, I found that our software uses the modified dietz method to calculate returns. After a little research, it looks like it is basically the time wieghted return, but allows the total holding period to have a greater effect on the performance number? This can be seen with the two formulas: (A=start value B=end value)

The modified Dietz return is the solution R {\displaystyle R} R to the equation:

B = A × ( 1 + R ) + ∑ i = 1 n F i × ( 1 + R × T − t i T ) {\displaystyle B=A imes (1+R)+\sum _{i=1}^{n}F_{i} imes (1+R imes {\frac {T-t_{i}}{T}})} {\displaystyle B=A imes (1+R)+\sum _{i=1}^{n}F_{i} imes (1+R imes {\frac {T-t_{i}}{T}})}

Compare this with the (unannualized) internal rate of return (IRR). The IRR (or more strictly speaking, an un-annualized holding period return version of the IRR) is a solution R {\displaystyle R} R to the equation:

B = A × ( 1 + R ) + ∑ i = 1 n F i × ( 1 + R ) T − t i T {\displaystyle B=A imes (1+R)+\sum _{i=1}^{n}F_{i} imes (1+R)^{\frac {T-t_{i}}{T}}} {\displaystyle B=A imes (1+R)+\sum _{i=1}^{n}F_{i} imes (1+R)^{\frac {T-t_{i}}{T}}}

I’m having trouble understanding what this means for our performance numbers. Does anyone have experience with the modified dietz method? Or can someone explain how it differs vs the IRR and what the advantages/disadvantages might be.

Thanks

#2

Modified Dietz is a Time weighted return, not an IRR. This means is less affected by external cash flows than IRR.

It is modified because is taking into account the timing of each CF and is weighting it over time.