Several methods exist for determining performance returns, each with its unique assumptions that should be understood when presenting results to clients. At Zoe, we employ the Time-Weighted Return (TWR) technique, a method encouraged by the Global Investment Performance Standards (GIPS) of the CFA Institute. Other frequently used return calculation methodologies include the simple return and dollar-weighted return, sometimes known as the money-weighted or internal rate of return.

These methods mainly differ in their handling of cash flows. Assuming an account experiences no cash flows, all three methodologies will yield identical results. However, it’s improbable that an account wouldn’t experience cash flows, and neglecting to consider these would lead to inaccurate and misleading results.

Our approach nullifies the impacts of cash flows, enabling us to evaluate an investment strategy’s performance. It facilitates the most direct comparison against benchmarks by isolating the return produced by the advisor’s decisions. No matter the size of an account or its monetary value, returns calculated using this method can be compared accurately.

TWR operates on the principle of establishing sub-periods when a cash flow occurs, valuing the portfolio on that day. Returns are calculated for each sub-period and then geometrically linked to compute a return for the entire period. For instance, if a cash flow transpires on June 15th, separate sub-period returns are computed for June 1-14 and June 15-30.

The general formula is as follows:

Where:

r1 = return for the first sub-period

r2 = return for the second sub-period

rn = return for the final sub-period

The return is calculated using this formula:

Where:

EMV = ending market value

BMV = beginning market value

CF = cash flow

Older systems often avoided calculating a sub-period for each cash flow due to time and computational constraints. They instead established a percentage threshold, creating a sub-period only if a cash flow exceeded 10% of the BMV, for example.

Zoe doesn’t rely on such inputs because we calculate daily returns and geometrically link them. Our ability to do this stems from our storage of daily price, transaction, and position information, as well as keeping a daily balance record.

Here’s a sample calculation:

Key assumptions to note:

Beginning and ending market values include dividend and interest accruals. Dividend accruals are part of the market value of positions starting on the ex-dividend date and ending the day before the payout date. For example, if a stock’s ex-dividend date is 7/25 and the payout date is 8/5, our market values will reflect the dividend value from 7/25 to 8/4.

Cash flows are assumed to be at the beginning of the day.

Cash flows encompass both cash and security transfers. Security transfers are calculated using end-of-day prices on the transfer date.

When you select a date range, the balance included in the calculation is the end-of-day balance. For instance, if you generate a custom report with the date range 1/1/19 – 6/30/19, the return on 1/1 won’t be included because the beginning market value is the closing balance on 1/1. For a year-to-date report, you should select 12/31/18, so the daily return on 1/1 is included.