Time Weighted Return Calculation

Accurately measure portfolio performance by eliminating cash flow distortions

Period 1: First Cash Flow Event

Period 2: Second Cash Flow Event (Optional)

Period 3: Third Cash Flow Event (Optional)

Understanding the true performance of an investment portfolio can be challenging when money is constantly moving in and out. This guide explores the time weighted return calculation, the industry-standard method for evaluating investment manager performance independently of client withdrawals and deposits.

What is Time Weighted Return (TWR)?

Time Weighted Return (TWR) is a method of calculating investment returns that eliminates the distorting effects of cash inflows (deposits) and outflows (withdrawals). By breaking the total investment period into smaller sub-periods based on when cash flows occur, TWR provides a clearer picture of how well the underlying assets performed.

Unlike the Simple Return or Money Weighted Return (IRR), the time weighted return calculation treats every dollar invested equally, regardless of when it was invested. This makes it the preferred metric for:

• Investment Managers: To demonstrate skill without being penalized for the timing of client cash flows.
• Mutual Funds: To report standardized performance data (GIPS compliant).
• Individual Investors: To compare their portfolio performance against market benchmarks like the S&P 500.

Time Weighted Return Formula and Explanation

The core concept of TWR is "geometric linking." We calculate the Holding Period Return (HPR) for each sub-period between cash flows and then multiply them together.

The Mathematical Steps:

1. Separate periods: Create a new sub-period every time a cash flow occurs.
2. Calculate HPR for each sub-period ($r_n$):
   Formula: $r_n = \frac{End\ Value – Start\ Value}{Start\ Value}$
   Note: The "End Value" here is the portfolio value immediately before the cash flow occurs. The "Start Value" is the value immediately after the previous cash flow.
3. Chain the returns:
   Formula: $TWR = [(1 + r_1) \times (1 + r_2) \times \dots \times (1 + r_n)] – 1$

Variable	Meaning	Unit
$V_{Start}$	Portfolio value at the beginning of a sub-period	Currency ($)
$V_{End}$	Portfolio value at the end of a sub-period (before cash flow)	Currency ($)
$CF$	Cash Flow (Deposit or Withdrawal)	Currency ($)
$r_n$	Return for sub-period $n$	Percentage (%)

Practical Examples: TWR in Action

Example 1: The Lucky Timing (Why TWR matters)

Imagine an investor starts with $10,000.
Period 1: The market drops 50%. The portfolio is now worth $5,000.
Cash Flow: The investor deposits $95,000. New Balance: $100,000.
Period 2: The market jumps 10%. The portfolio grows to $110,000.

Simple Calculation (Incorrect): Start $10k, Add $95k, End $110k. Profit $5k. It looks positive.
Time Weighted Return Calculation:
Period 1 Return: $(5,000 – 10,000) / 10,000 = -0.50$ (-50%)
Period 2 Return: $(110,000 – 100,000) / 100,000 = 0.10$ (+10%)
TWR: $(1 – 0.50) \times (1 + 0.10) – 1 = 0.5 \times 1.1 – 1 = -0.45$ (-45%)

The TWR correctly shows that the investment strategy lost 45% of value, even though the account balance is higher due to the large deposit.

How to Use This Calculator

Our tool simplifies the geometric linking process. Follow these steps:

1. Enter Initial Value: The value of the portfolio on Day 1.
2. Enter Sub-Period Data: For every date you added or removed money, enter the portfolio's value just before that transaction, and the amount of the transaction.
3. Enter Final Value: The current value of the portfolio today.
4. Review Results: The "Cumulative TWR" tells you the compound growth rate of your underlying assets.

Key Factors That Affect TWR Results

When performing a time weighted return calculation, consider these six factors:

• Valuation Frequency: TWR is most accurate when valuations are available daily. Less frequent valuations during volatile periods can introduce small errors.
• Cash Flow Magnitude: Large cash flows relative to the portfolio size (like in Example 1) create the biggest divergence between TWR and Money Weighted Return.
• Market Volatility: High volatility between cash flow dates impacts the sub-period returns significantly.
• Fees and Expenses: Ensure "Ending Values" are net of management fees to calculate a net-of-fee TWR.
• Timing of Flows: Deposits made just before a market rally do not improve TWR, though they increase total wealth.
• Inflation: TWR is a nominal figure. To get real return, you must adjust the final TWR for inflation over the same period.

Frequently Asked Questions (FAQ)

1. What is the difference between TWR and IRR?

Internal Rate of Return (IRR) is money-weighted; it accounts for the timing and size of cash flows. TWR ignores them. Use IRR to judge your personal wealth growth, and TWR to judge your fund manager's skill.

2. Can TWR be negative while total profit is positive?

Yes. If you have a small balance during a big loss period, and a huge balance during a small gain period, you might make money in dollars (positive profit) while the TWR remains negative.

3. Is TWR the same as CAGR?

Not exactly. TWR is the cumulative growth. CAGR (Compound Annual Growth Rate) is the annualized version of TWR. If you annualize the TWR result, you get CAGR.

4. How do I handle dividends?

If dividends are reinvested, they are not treated as external cash flows. They are part of the portfolio's growth. If they are withdrawn, treat them as a negative cash flow.

5. Why do professionals prefer TWR?

It allows for fair comparison. A fund manager cannot control when a client deposits money. TWR levels the playing field so managers aren't penalized for client behavior.

6. Does this calculator handle daily valuations?

This specific tool uses the "Modified Dietz" approximation style logic by linking discrete periods. For true daily TWR, you need daily data for every single day, which requires specialized software.

7. What constitutes a "Cash Flow"?

Only external money moving in or out. Deposits, withdrawals, and transfers. Internal trades, dividends received within the account, and fees deducted are usually not external flows (unless calculating Gross of Fees).

8. Can I use TWR for real estate?

Yes, but it is difficult because obtaining accurate market valuations for real estate before every cash flow (renovation cost, rent withdrawal) is impractical. IRR is often preferred for real estate.