 # Modified Dietz Return

An algebraic method used to calculate the rate of return of an investment portfolio based on the cash flows of the portfolio

## What is the Modified Dietz Return?

The Modified Dietz Return is an algebraic method used to calculate the rate of return of an investment portfolio based on the cash flows of the portfolio. The method also accounts for the timing of when the cash flows come in and out of the portfolio. Unlike the Modified Internal Rate of Return and the Internal Rate of Return (IRR), the Modified Dietz Return is not an expected return and is backward-looking, doesn’t use expected value, and calculates the realized return of the portfolio.

### Why was the Modified Dietz Return Created?

The Modified Dietz formula was created to better understand and provide more transparency for the return an investment portfolio made. Investment portfolios constantly see cash flows coming in and going out, making it easy to lose track of how much money the portfolio made. Thus, the Modified Dietz Return formula was made to keep track of the timing and magnitude of the cash flows throughout the entire investment horizon.

### Formula for the Modified Dietz Return Where:

• V(0) = Value of portfolio at start date
• V(1) = Value of portfolio at end date
• CF’s = Cash flows throughout the investment horizon
• T = Length of the investment horizon
• t = Time of cash flow
• CF(t) = Cash flow at certain time

One of the main components of the formula is its ability to account for the timing of cash flows. The formula accounts for such a fact by taking the sum of the weighted cash flows, weighted by when they occurred throughout the investment horizon.

It is achieved by taking the difference of the length of the investment horizon (T) and the timing of the cash flow (t) and dividing the difference by the investment horizon (T), then by multiplying the result by the magnitude of the cash flow that happened at t; the product will be the weighted cash flow.

### Practical Example

An individual invests \$1,000 in an investment portfolio for one year. At the end of the year, the portfolio rose in value to \$1,200. During the investment horizon, at the end of the first three months, the investor deposited \$500 into the portfolio.

However, at the end of the nine-month period, the investor withdrew \$800. To understand the portfolio’s performance, the investor must calculate the rate of return that accounts for the timing of the withdrawals and deposits made.  Thus:

• V(0) = 1000
• V(1) = 1200
• CF25 = 500
• CF75 = -800
• T = 1 year ### Disadvantages of the Modified Dietz Return

The Modified Dietz Return formula exhibits disadvantages when one or more large cash flows occur during the investment period or when the investment is very volatile, and experiences returns that are significantly non-linear. Another disadvantage is that the investor needs to know the value of the investment both at the beginning and end of the investment horizon.

Additionally, the investor must adopt a way to keep track of the cash flows coming in and out of the portfolio. It is important to know when to use the Modified Dietz Return to get an accurate understanding of how the investment portfolio performed.