There are several acceptable ways to calculate performance returns. It is important to understand the underlying assumptions in each of them as they inform how best to discuss returns with your clients. Atlas uses the time-weighted return (TWR) methodology because this is what the Global Investment Performance Standards (GIPS) set forth by the CFA Institute recommend. See our other articles where we explore other common approaches - the simple return and dollar weighted return (sometimes referred to as money-weighted or internal rate of return).
The key difference among the approaches is how cash flows are treated. If there are no cash flows in an account, all three methods will produce the same return calculation. Of course, it is unlikely that a cash flow would not occur, and it would be misleading and incorrect to not account for these.
With this approach, the effects of cash flows are eliminated so that one can evaluate the performance of an investment strategy. This approach allows for the most “apples to apples” comparison against things like benchmarks as it isolates the return generated by the advisor’s decisions. Regardless of how large or small an account is or how much money it has, returns calculated with this approach can be accurately compared.
The idea behind the TWR is that when there is a cash flow, the portfolio is valued on that day to create sub-periods. Returns are calculated for each sub-period and then geometrically linked to calculate a return for the whole period. For example, if a cash flow happens on June 15th, a sub-period return is calculated for the periods of June 1-14 and June 15-30.
The generalized formula looks like this:
where
r1 = return for the first sub period
r2 = return for the second sub period
rn = return for the final sub period
The return itself is calculated using the following formula:
where
EMV = ending market value
BMV = beginning market value
CF = cash flow
In older systems, it was considered too timely or computationally difficult to calculate a sub-period for each and every cash flow. A percentage threshold would be set where only if a cash flow is greater than 10% of the BMV, for example, a sub-period is created.
Atlas does not require this input because it calculates daily returns and geometrically links those. We are able to do this because we store daily price, transaction, and position information and maintain a daily record of balances.
Below we have a sample calculation:
Note some key assumptions:
Beginning and ending market values include dividend and interest accruals. Dividend accruals are included in the market value of positions beginning on the ex-dividend date and ending the day before the payout date. For example, if a stock has an ex-dividend date of 7/25 and payout date of 8/5, our market values will update for 7/25 through 8/4 to include the value of the dividend.
Cash flows are assumed to be beginning of day.
Cash flows include both cash and security transfers. Security transfers are calculated using end of day prices on the date of the transfer.
When you select a date range, the balance that is included in the calculation is the balance at the end of the day. For example, if you generate a custom report with the date range 1/1/19 - 6/30/19, the return on the day of 1/1 will not be included because the beginning market value is the closing balance on 1/1. For a year to date report, you would need to select 12/31/18 so that the daily return on 1/1 is included.