**What is Modified Dietz?**

Modified Dietz refers to the measure which is used in order to determine the historical performance of the portfolio by dividing the actual cash flow net of the outflow with average capital, which uses the weight and value of the portfolio at the beginning. In a simple Dietz method, all the cash flows are assumed to be from the middle of the period, whereas that is not the case with the modified Dietz method.

### Formula

Modified Dietz Rate of Return can be defined using the following formula and each of the terms in it explained:

**ROR = (EMV – BMV – C) / (BMV + W*C)**

**ROR**(Rate of Return) – this is the term we are looking to calculate**EMV**(Ending Market Value) – This is the value of the portfolio after the end of the term we are looking for.**BMV**(Beginning Market Value) – This is the value of the portfolio from the date, which the returns are to be calculated**W**(Weight of each cash flow on the portfolio) – This is the weight of portfolio between zero and one, but only between the period they occurred and at the end of the period. This can be explained as the proportion of time between the point in time when the flow occurs and the end of the period. This can be calculated using the formula.**W = [C- D] / C**where D is the number of days from the start of the return period until the day on which the flow occurred.**C**– Cash flows during the period – This might not be a single number, but a series of cash flows that happened during the period.**W*C**= the sum of each cash flow multiplied by its weight. This is a summation of weighted cash flows.

### Examples

Below are some examples of the Modified Dietz method.

#### Example #1

Let us consider a very simple scenario with the following conditions:

- We have a portfolio worth 1 million USD at the beginning of the investment period.
- After two years, the portfolio’s worth has grown to 2.3 million USD.
- There was an inflow of 0.5 million USD after one year.

Now, we will calculate how the Modified Dietz method will be used to calculate the returns in this portfolio.

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- Actual profit = EMV (2.3 million USD) – BMV (1 million USD) – Cash flows (0.5 million USD Inflow)
- =$0.8

This brings a profit of 0.8 million USD.

Now let us see what the average capital in this case was.

- Average Capital = BMV (1 million USD) + W*C (0.5 million USD * 0.5 Time period)
- = 1.25

Therefore the rate of return will be –

- Rate of Return = Actual Profit / Average Capital
- = $0.8 / 1.25
- = 64%

#### Example #2

**Comparison of Modified Dietz to Time-Weighted Rate of Return**

Let us consider two investors with the following portfolios.

- Investor A started with a portfolio of
**250k USD**at the beginning of a year (Jan) and used his strategies to make it into**298k USD**by the end of the same year (Dec). However, he put up an additional capital of 25k USD during September. - Investor B started with a portfolio of
**250k USD**at the beginning of the year (Jan) and used his strategies but ended up with 2**51k USD**at the ending of the year. However, he withdrew 25K during September.

To a naked eye, or by using elementary mathematics in our minds, we can tell that Investor B is bad at investing than investor A. However, going deep into the calculations will give us another side of the story entirely.

**For Investor A:**

Actual Profit will be –

- Actual Profit= (298k USD – 250k USD – 25k USD )
- =23K USD

The average period will be –

- Average Period = 250k USD + (25k USD * 0.3)
- =258K USD

Modified Dietz Rate will be –

- Modified Dietz Rate = 8.7%

**For Investor B:**

Actual Profit will be –

- Actual Profit = (251k USD – 250k USD + 25k USD )
- =26K USD

The average period will be –

- Average Period = 250k USD + (-25K USD * 0.3)
- =242.5 k USD

Modified Dietz Rate will be –

- Modified Dietz Rate = 10.72%

The time-weighted rate of return for both the above will be around 9.5, but modified Dietz gave us different results. This is the reason this method is used by investors for reporting purposes.

### Advantages

- The main advantage of this method is that it does not require portfolio valuation on each date of the cash flow. This helps the analyst in asserting the value of returns easily, without reassessing each time.
- There are performance attributions that are unavailable with other time-weighing methods; during those cases, the Modified Dietz method is useful.
- Cases like Example 2, where the Time-Weighted Rate of Returns is not an appropriate measure.

### Limitations

- With the advance in computing, most of today’s returns are calculated on a continuous basis – these provide a better way of analyzing the returns and leave methods like Modified Dietz very naïve and basic.
- An assumption of all transactions taking place simultaneously at a single point in a period of time will lead to errors.
- It is very difficult to deal with negative or average-zero cash flows.

### Conclusion

As the regulations around the financial sector grow, investors need to take more care regarding how the investment and returns are calculated and how they are reported. This method of Modified Dietz provides reasonable confidence in the investment returns analysis.

The modified Dietz method just provides us with a measure of returns on investment portfolios, where there are multiple inflows and outflows. In the current day, with advanced computing and continuous returns management, this method is not useful. However, the basic concept behind the method is useful for understanding how returns and their calculations work.

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