Time-weighted and money-weighted rates of return: A comparison

There are many different ways to measure your portfolio’s performance. In this article we’ll provide a quick overview of time-weighted and money-weighted rates of return to help you understand how the performance of your investments is measured. 

Account Performance is a tool offered by Investor’s Edge that lets you see how your accounts are performing by providing a time-weighted and money-weighted rate of return calculation. The time-weighted rate of return measures your account’s performance over a period of time while ignoring certain factors like cash flow. The money-weighted rate of return measures your account’s performance, taking into consideration both the timing and size of cash flow. Both calculations use various complex mathematical formulas to arrive at a final rate of return for your account. 

Let’s take a closer look at these calculations and how they can provide valuable information about your account’s performance.

Time-weighted rate of return (TWRR) measures your account’s performance over a certain period of time. TWRR ignores the effects of timing and size of cash flow from contributions and withdrawals in or out of your portfolio, which gives you a view of how well your investments in the account have performed over time. Cash flow includes any assets, cash or securities that you add or remove from your account, for example: transactions you make at your discretion that are not related to existing portfolio investments. TWRR is useful for comparing the performance of your account investments against a fund or index as a benchmark, as it focuses primarily on the underlying securities while filtering out the impacts of the investor’s cash flow decisions.

Let’s look at a simplified example to understand how investment choices can impact TWRR:

Jack and Kevin both invest $10,000 in the same fund in January. The fund steadily grows 10% by June. In March, Jack added $50,000 to this existing holding, while Kevin redeemed half of his investments in the fund. 

Without any calculations, it’s clear that Jack’s decision to add $50,000 made his total portfolio value higher than Kevin’s at the end of June. However, both have a TWRR of 10%  because TWRR strips out the impact of their cash flows.

TWRR is calculated based on daily valuation for each market day. The daily valuations are then geometrically linked together to give a rate of return over a longer period of time. Performance is driven by the daily changes in account values over time and these daily time periods are given equal weighting in the calculation. 

Let’s take a look at another simplified example to see how this is calculated at an account level:

Jane has $200,000 in her investment account on January 1. The underlying investments do well and by August 30, the balance is $220,000, an increase of 10%. Jane then adds $50,000 to the account on September 1, taking her balance to $270,000. By December 31 her investment account has a balance of $300,000, an increase of 11.11%. To calculate TWRR, the first step is to perform a separate valuation of the account’s performance for each sub-period within the year. The sub-periods are when the deposits or withdrawals happened in the account. In Jane’s account there are two sub-periods: January 1 to August 30 and September 1 to December 31.

For the sub-period January 1 to August 30, Jane did not make any deposits or withdrawals, and the investments generate a return of 10%. 

For the sub-period September 1 to December 31, we take the account balance as of September 1, including the deposit of $50,000, to calculate the return for the entire period until December 31. In this sub-period, Jane’s account balance increased by $30,000, from $270,000 to $300,0000 , which is 11.11% of the $270,000 starting balance. 

To summarize:

Sub-period 1 return = 10% from January 1 to August 30

Sub-period 2 return = 11.11% from September 1 to December 31

Next, the rates of return for both sub-periods are combined. This can be done using the geometric linking method. Here’s the calculation:

TWRR = [(1 + sub-period 1 return) × (1 + sub-period 2 return)] −1

= [(1 + 10%) × (1 + 11.11%)] − 1

= [(1.10) × (1.11)] − 1

= 1.22 − 1

= 0.22, or 22%

Since the deposit was made on September 1, Jane’s first sub-period is 8 months, January to August, and the second sub-period is 4 months, September to December. If there were more deposits or any withdrawals, there would be more sub-periods to incorporate into the calculation. For example, if Jane made a withdrawal 3 weeks after her September 1 deposit, it would have been necessary to perform a separate account valuation for that 3-week period, resulting in 3 rather than 2 sub-periods.

The formula is based on finding the rate of return for a specific time period that sets the present value of the portfolio’s ending value, including all cash flow changes, equal to the present value of the investments at the start of the time period you’re reviewing. 

In other words, the MWRR sets the present value of the initial value of your investments, based on the time period you’re reviewing, equal to the present value of all future cash flows such as cash deposits and withdrawals, security purchases, and sales and dividends.

You can use both calculations to track your account performance and make your own decisions about how you’d like to invest in the future.