## What is Modified Dietz?

The term “modified Dietz” (M.D) refers to the algebraic method that is used in the calculation of the rate of return of an investment portfolio on the basis of the cash inflows and outflows of the portfolio. This method takes cognizance of the timing of the cash flows and this is where this method overcomes the issue of the simple Dietz method, wherein it is assumed that all cash flows occur in the middle of the reporting period.

### Explanation for Modified Dietz

Modified Dietz return is considered to be the most accurate reflection of an investment portfolio’s rate of return. The calculation of M.D return takes into account the market value of the portfolio at the start of the period and at the end of the period along with all the cash inflows and outflows during that period and the associated period of investment of each cash flow event. In some cases, the result of modified Dietz is known as the Modified Internal Rate of Return (MIRR), which is a frequently used metric of capital budgeting.

### Formula for Modified Dietz

The formula for M.D return can be expressed in terms of the value of the portfolio at the start and end of the reporting period, cash inflow and outflow during the period, and effective investment period (ratio of time to end of the reporting period to overall reporting period). Mathematically, it is represented as,

**Modified Dietz return = (V _{1} – V_{0} – ∑CF_{i} ) / ( V_{0} ∑w_{i} * CF_{i})**

- where V
_{0}= Market value of the portfolio at the start of the period - V
_{1}= Market value of the portfolio at the end of the period - CF
_{i}= Cash flow at interval I during the period - w
_{i}= Weightage of i^{th}cash flow

### Examples of Modified Dietz

Following examples are given below:

#### Example #1

Let us take the simple example of an investment portfolio to illustrate the calculation of M.D return. Let us assume that the portfolio was worth $1,000,000 at the start of the calendar year and by the end of December the portfolio has grown up to become $1,250,000. During the year there was a cash inflow of $100,000in April and a cash outflow of $150,000 in October. Calculate the return of the portfolio based on the M.D method.

**Solution:**

- Given, V
_{0}= $1,000,000 - V
_{1}= $1,250,000 - CF
_{1}= $100,000 - CF
_{2}= – $150,000 - w
_{1}= (12 – 3) / 12 = 0.75 [Since April is the 4^{th}month of the year] - w
_{2}= (12 – 9) / 12 = 0.25 [Since October is the 10^{th}month of the year]

Now, the M.D return of the portfolio can be calculated using the above formula as,

**Modified Dietz Return = (V _{1} – V_{0} – ∑CF_{i} ) / ( V_{0} ∑w_{i} * CF_{i})**

- Modified Dietz Return = ($1,250,000 -$1,000,000 -($100,000 – $150,000)) / ($1,000,000 + (0.75* $100,000 – 0.25* $150,000))
- Modified Dietz Return =
**28.9%**

Therefore, using the M.D method the return of the portfolio has been calculated to be 28.9%.

#### Example #2

Let us take the example of two portfolios and compare their returns using the M.D method.

**Portfolio I:** The market value of the portfolio at the start of the year was $2,000,000, which reached $3,000,000 by the end of the year. During the year, there was an infusion of additional capital of $500,000 during September.

**Portfolio II:** The market value of the portfolio at the start of the year was $2,000,000, which reached $2,200,000 by the end of the year. During the year, there was a withdrawal of $500,000 during September.

##### Portfolio I

- Given, V
_{0}= $2,000,000 - V
_{1}= $3,000,000 - CF
_{1}= $500,000 - w
_{1}= (12 – 8) / 12 = 0.33 [Since September is the 9^{th}month of the year]

Now, M.D return of the portfolio I can be calculated using the above formula as,

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**Modified Dietz Return = (V _{1} – V_{0} – ∑CF_{i} ) / ( V_{0} ∑w_{i} * CF_{i})**

- Modified Dietz Return = ($3,000,000 – $2,000,000 – $500,000) / ($2,000,000 + (0.33 * $500,000))
- Modified Dietz Return =
**23.1%**

##### Portfolio II

- Given, V
_{0}= $2,000,000 - V
_{1}= $2,100,000 - CF
_{1}= -$500,000 - w
_{1}= (12 – 8) / 12 = 0.33 [Since September is the 9^{th}month of the year]

Now, modified Dietz return of the portfolio II can be calculated using the above formula as,

**Modified Dietz Return = (V _{1} – V_{0} – ∑CF_{i} ) / ( V_{0} ∑w_{i} * CF_{i})**

- Modified Dietz Return = ($3,000,000 – $2,000,000 + $500,000)/($2,000,000 – (0.33 * $500,000))
- Modified Dietz Return =
**32.7%**

Therefore, in the above example, it can be seen that even though at first it might seem that portfolio I generated better returns, after taking into account the cash flow movement it is clear that portfolio II has produced better results. This is how M.D return helps in the calculation of portfolio return.

### Importance of Modified Dietz

In the financial industry, both regulators and investors have been increasing their focus toward a greater level of transparency with regard to the calculation and reporting of investment returns. Now, a stream of cash inflows and outflows is a very frequent occurrence in an investment portfolio, which makes it difficult to track how much profit has been actually generated by the portfolio. Consequently, the M.D method was developed to calculate the portfolio return while keeping track of the magnitude as well as the timing of the cash flows occurring during the investment period.

### Advantages

Some of the major advantages of Modified Dietzare as follows:

- It doesn’t need the value of the portfolio on each day of the cash flow.
- A time-weighted rate of return facilitates more accurate results.

### Disadvantages

Some of the major disadvantages of M.D are as follows:

- Given the advancement witnessed in the field of computing, most of return calculation tools used nowadays allow continuous monitoring of the performance, which makes the method of Modified Dietz look very basic and naive.
- The assumption that all transactions will take place at the same time may lead to erroneous results.

### Conclusion

So, it can be seen that the modified Dietz method helps us measure returns on portfolios involving multiple cash inflows and outflows. Although the underlying principle of the method is very useful, it is difficult for this method to find use in today’s world owing to the rapid progress made in the field of computing that facilitates monitoring with higher frequency.

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