Rate of return

For a balance that had nothing added and nothing withdrawn, the return is the closing value minus the opening value, divided by the opening value. $50,000 that ends the year at $55,500 returned 11%.

A contribution or a withdrawal breaks that sum. The closing balance now includes money that was deposited, not earned, and the deposit was invested for only part of the period. Two conventions handle it. A time-weighted return splits the period at each flow, works out the return of each piece from its own opening value, and chains the pieces together, so the timing and size of the flows drop out. A money-weighted return, the internal rate of return, is the single rate that would grow each dollar from the day it arrived to the closing value, so a large deposit just before a good stretch counts more than one just before a bad one.

The two answer different questions. The time-weighted figure describes how the holdings did, whatever was paid in; the money-weighted figure describes how the investor's dollars did, timing included. A fund reports the first.

A brokerage account opens the year at $50,000. On June 30 it stands at $53,000. On July 1 a $10,000 contribution brings it to $63,000, and on December 31 it closes at $66,000.

The plain change is $16,000 on $50,000, or 32%, but $10,000 of that arrived as a deposit. Taking the contribution out leaves $6,000 of gain, which is 12% of the opening balance. Even that overstates it, because the extra $10,000 was invested for only half the year: on the average capital of $55,000 the gain is 10.9%, close to the money-weighted figure.

Time-weighted, the year is two halves. The first half took $50,000 to $53,000, a factor of 1.06. The second took $63,000 to $66,000, a factor of 1.0476. Chained, 1.06 × 1.0476 is 1.1105, so the return is 11.0%. Against the 32% the raw change suggests, the account grew by about 11%.

Opening balance, Jan 1

$50,000

Contribution, Jul 1

+ $10,000

Closing balance, Dec 31

$66,000

Change, $16,000 ÷ $50,000

32%

Gain, $16,000 − $10,000 contribution

$6,000

Time-weighted, 1.06 × 1.0476 − 1

11.0%

A balance grows for two reasons, deposits and market movement, and the raw change does not say which. In the example, $10,000 of a $16,000 rise was paid in. A household that saves steadily adds to its investment balance every month, and the return is what says how much of the change the holdings earned.

The convention matters when returns are compared. Two accounts with the same holdings but different deposit schedules show different money-weighted returns and the same time-weighted return, so a comparison of holdings uses the time-weighted figure, and a question about what an investor's own dollars did uses the money-weighted one.

The Investments page in Taiga Finance shows no rate of return: no return figure, time-weighted or money-weighted, and no comparison against an index.

The nearest figure is the change beside the “Holdings” total in the Investments rail, which reads as an arrow, a dollar amount and a percentage over the window picked in the toolbar, “7d”, “30d” or “90d”: the closing value minus the value at the start of the window, divided by that starting value. It is a change in balance, so a deposit or a withdrawal in the window moves it as much as the market does. Below it, “Balance over time” draws the balance through the window, stacked by portfolio.

The Investments page shows value and composition: each group's total and its change over the window, “Allocation” by asset class, a portfolio's “Current → Target” strip with an “On target” or “Off target” verdict, and in a holding's drawer a Lots table with a “Gain $” column, the unrealized gain of each lot against its cost.