Modified Dietz Return¶

1. Calculation Name¶

Modified Dietz Money-Weighted Return

2. Description and Mathematical Formula¶

The modified Dietz method measures the money-weighted return over a period while accounting for the timing and size of external flows. Each flow is weighted by the proportion of the period that capital is invested.

Let:

\( B \) = beginning market value
\( E \) = ending market value
\( F_j \) = external flow \( j \) occurring on day \( d_j \) (where \( d_j = 0 \) is the period start)
\( T \) = total number of days in the period
\( w_j = \frac{T - d_j}{T} \) = weight applied to flow \( j \)

The modified Dietz return \( R_{\text{MD}} \) is

\[ R_{\text{MD}} = \frac{E - B - \sum_j F_j}{B + \sum_j w_j F_j} \]

3. Input Sample Data¶

Event	Date	Cash Amount (USD)	Notes
Beginning Market Value	2024-01-01	1,000,000	Portfolio opening balance
Contribution	2024-01-05	50,000	Client top-up (day 4)
Withdrawal	2024-01-15	-20,000	Mid-month rebalance (day 14)
Contribution	2024-01-25	10,000	Income sweep (day 24)
Ending Market Value	2024-01-31	1,080,000	Valuation after fees

4. Mathematical Solution¶

Total flows: \( 50{,}000 - 20{,}000 + 10{,}000 = 40{,}000 \)
Weighted flows:
\( 50{,}000 \times \frac{26}{30} = 43{,}333.33 \)
\( -20{,}000 \times \frac{16}{30} = -10{,}666.67 \)
\( 10{,}000 \times \frac{6}{30} = 2{,}000.00 \)
Sum of weighted flows \( = 34{,}666.67 \)
Numerator: \( 1{,}080{,}000 - 1{,}000{,}000 - 40{,}000 = 40{,}000 \)
Denominator: \( 1{,}000{,}000 + 34{,}666.67 = 1{,}034{,}666.67 \)
Return: \( R_{\text{MD}} = \frac{40{,}000}{1{,}034{,}666.67} = 0.03866 \) → 3.87%

5. Sample Python and R Code¶

Python

import pandas as pd

data = pd.DataFrame(
    {
        "event": ["BOP", "Flow", "Flow", "Flow", "EOP"],
        "date": pd.to_datetime(
            ["2024-01-01", "2024-01-05", "2024-01-15", "2024-01-25", "2024-01-31"]
        ),
        "amount": [1_000_000, 50_000, -20_000, 10_000, 1_080_000],
    }
)

start = data.loc[0, "date"]
end = data.loc[len(data) - 1, "date"]
period_days = (end - start).days

flows = data.iloc[1:-1].copy()
flows["days"] = (flows["date"] - start).dt.days
flows["weight"] = (period_days - flows["days"]) / period_days

B = data.loc[data["event"] == "BOP", "amount"].iloc[0]
E = data.loc[data["event"] == "EOP", "amount"].iloc[0]

weighted_flows = (flows["amount"] * flows["weight"]).sum()
net_flows = flows["amount"].sum()

return_md = (E - B - net_flows) / (B + weighted_flows)
print(f"Modified Dietz return: {return_md:.4%}")

R

library(dplyr)
library(lubridate)

data <- tibble::tibble(
  event = c("BOP", "Flow", "Flow", "Flow", "EOP"),
  date = as_date(c("2024-01-01", "2024-01-05", "2024-01-15", "2024-01-25", "2024-01-31")),
  amount = c(1000000, 50000, -20000, 10000, 1080000)
)

start <- data$date[1]
end <- data$date[n()]
period_days <- as.numeric(end - start)

flows <- data %>%
  slice(2:(n() - 1)) %>%
  mutate(
    days = as.numeric(date - start),
    weight = (period_days - days) / period_days
  )

B <- data$amount[1]
E <- data$amount[n()]

weighted_flows <- sum(flows$amount * flows$weight)
net_flows <- sum(flows$amount)

return_md <- (E - B - net_flows) / (B + weighted_flows)
scales::percent(return_md, accuracy = 0.01)

6. Output Table¶

Metric	Value
Modified Dietz Return	3.87%
Net External Flows	40,000
Weighted Capital Base	1,034,666.67

7. Conclusion¶

The modified Dietz template captures capital-weighted performance while respecting cash flow timing. Use this structure when you need a quick sanity check against custodial money-weighted returns or when documenting validation test cases in FinFacts.