edits: 2025-08-03
When dealing with investments made through monthly installments, the Compound Annual Growth Rate (CAGR) might not be the most suitable metric due to the issues you've mentioned. Instead, you might want to consider using the Modified Dietz Method or the Time-Weighted Rate of Return (TWRR). Let me explain these concepts in detail:
The Modified Dietz Method is a way to calculate the return on an investment portfolio that accounts for cash flows (like your monthly installments) during the period. Here's a simplified explanation:
- Identify Cash Flows: List all the cash flows (monthly investments) and their timing.
- Calculate the Holding Period Return: Determine the return for the period, taking into account the cash flows.
- Adjust for Cash Flows: Adjust the return to account for the timing and amount of each cash flow.
The formula for the Modified Dietz Method is:
[ \text{Modified Dietz Return} = \left( \frac{\text{Ending Value} - \text{Beginning Value} - \text{Net Cash Flows}}{\text{Beginning Value} + \sum (\text{Cash Flow} \times \text{Weight})} \right) \times 100 ]
modDietz = ((end_val - beg_val - net_cash_flows)/(beg_val + sum(cash_flow * weight))) * 100
Where:
- Ending Value is the value of the investment at the end of the period.
- Beginning Value is the value of the investment at the beginning of the period.
- Net Cash Flows is the sum of all cash flows during the period.
- Weight is the fraction of the period that the cash flow was invested.
The Time-Weighted Rate of Return (TWRR) is another method that can be useful for investments with regular cash flows. TWRR measures the compound growth rate of an investment over time, but it removes the effect of cash flows by breaking the period into sub-periods and calculating the growth rate for each sub-period.
- Divide the Period into Sub-Periods: Break the investment period into sub-periods based on the timing of cash flows.
- Calculate the Growth Rate for Each Sub-Period: Determine the growth rate for each sub-period.
- Combine the Growth Rates: Combine the growth rates for all sub-periods to get the overall TWRR.
The formula for TWRR is:
[ \text{TWRR} = \left( \prod_^{n} (1 + r_i) \right) - 1 ]
TWRR = subPeriodGrRate_array.reduce((ac, ak) => ac = ac * (1 + ak)) -1
Where:
- ( r_i ) is the growth rate for each sub-period.
- ( n ) is the number of sub-periods.
- Gather Data: Collect all the data on your monthly investments, including the amount and timing of each investment.
- Choose a Method: Decide whether to use the Modified Dietz Method or TWRR based on your specific needs and the complexity of your investments.
- Calculate the Return: Use the chosen method to calculate the return on your investments.
- Analyze the Results: Interpret the results to understand the performance of your investments.
Let's say you have the following data:
- Beginning Value: $10,000
- Monthly Investments: $1,000 at the beginning of each month
- Ending Value: $25,000
- Period: 12 months
Using the Modified Dietz Method:
- Net Cash Flows: $1,000 \times 12 = $12,000
- Weight: Since the cash flows are at the beginning of each month, the weight for each cash flow is approximately 1 (assuming the cash flow is invested for the entire period).
- Modified Dietz Return:
[ \text{Modified Dietz Return} = \left( \frac{25,000 - 10,000 - 12,000}{10,000 + (12,000 \times 1)} \right) \times 100 = \left( \frac{3,000}{22,000} \right) \times 100 \approx 13.64% ]
This gives you an annualized return that accounts for your monthly investments.
By using these methods, you can more accurately assess the performance of your investments made through monthly installments.