Cumulative return

Cumulative Return is the percent change in the value of your investment over a given time period, adjusted to remove the effect of any deposits or withdrawals you've made. It tells you how your investments performed independent of cash you moved in or out.

This metric appears at both the account level (your overall portfolio) and at the symphony level (each individual strategy you're invested in).

An example

Let's say you invest $10,000 in your account and the market goes up 20%, bringing your portfolio value to $12,000. Then you deposit another $50,000 and the market drops 10%, leaving your portfolio at $55,800.

Previously, Composer calculated Cumulative Return using a simple return formula:

Simple Return = (Portfolio Value − Net Deposits) / Net Deposits

Using this formula, ($55,800 − $60,000) / $60,000 = −7%. The simple return calculation would make it look like your investments are losing money because the large deposit right before the dip dominates the calculation.

But your investments actually made money. Your first $10,000 grew 20% and then declined 10%, which is a net gain of 8%. The $50,000 only experienced a 10% decline.

Cumulative Return uses a time-weighted method that evaluates each period independently and then chains them together: (1 + 20%) × (1 − 10%) − 1 = +8%. This metric reflects how your investments actually performed independent of your deposits and withdrawals.

Why use the time-weighted return instead of the simple return?

The simple return formula works fine if you make one deposit and never touch your account again. But the moment you add or withdraw money, the number becomes unreliable.

As the example above shows, a large deposit right before a market dip can make it look like you're losing money when your investments are actually up. The reverse is also true. A well-timed withdrawal can artificially inflate your apparent return.

Cumulative Return using a time-weighted methodology removes the effect of cash flows and captures the true performance of your investments.

What is the formula?

Composer uses the Modified Dietz method to calculate each day's return:

Daily Return = (Ending Value − Starting Value − Cash Flows) / (Starting Value + Time-Weighted Cash Flows)

Then each day's return is compounded together to produce your Cumulative Return:

Cumulative Return = (1 + Day 1 Return) × (1 + Day 2 Return) × ... × (1 + Today's Return) − 1

A Cumulative Return of 15% means that $1 invested at the start of the investment period would now be worth $1.15, regardless of any deposits or withdrawals made along the way.

What is the step-by-step calculation?

Here's how Composer calculates Cumulative Return, step by step:

Step 1: For each day, gather the inputs.

Start with your portfolio's value at the end of the previous day (the "starting value").
Get your portfolio's value at the end of the current day (the "ending value").
Identify any deposits or withdrawals that happened during the day, along with when during the day they occurred.

Step 2: Weight each cash flow by how much of the trading day it was invested.

The key insight underpinning the Modified Dietz method is that a deposit arriving at 10:00 AM has almost the full trading day to participate in market movements, while a deposit arriving at 3:30 PM only has 30 minutes of exposure. Each cash flow gets a time weight between 0 and 1 based on when it occurred during the day.

For equities, the trading day runs from 9:30 AM to 4:00 PM ET (6.5 hours). A deposit received at 11:00 AM has about 77% of the day remaining, so it gets a weight of roughly 0.77.

For users who were invested in crypto symphonies or hybrid stock and crypto symphonies when Composer offered them, there are additional considerations. For crypto, since markets run 24/7, the day is treated as a full 24-hour period from midnight to midnight ET. And if your account held both equities and crypto on a given day, the weight is blended based on the proportion of your portfolio in each asset class.

Deposits and withdrawals that occur outside trading hours (evenings, weekends, holidays) are treated as arriving at the next market open with a full day's weight.

Step 3: Calculate the daily return using the Modified Dietz formula.

Subtract the starting value and the total cash flows from the ending value — this gives you the gain or loss attributable to investment performance.
Divide by the starting value plus the time-weighted cash flows — this gives you the return as a percentage.

Step 4: Chain daily returns into a cumulative figure.

Multiply each day's return factor (1 + daily return) together across all days.
Subtract 1 from the result.
The result is your Cumulative Return.

An example

Your portfolio starts the day at $100,000 and the market returns 2%. You deposit $50,000 at 2:00 PM ET and end the day with a value of $152,000.

The Modified Dietz method recognizes that the $50,000 was only invested for the last portion of the day, weights it accordingly, and produces a daily return of approximately 1.73%, which is close to the true 2%.

What about symphony-level returns?

Cumulative Return is also calculated for each individual symphony in your portfolio. The methodology is the same, but the inputs differ:

Portfolio value is the value of the holdings within that specific symphony.
Cash flows are the buys into, sells from, and liquidations of that symphony (not your overall account deposits).
Internal trades within a symphony (buying and selling between assets as part of the strategy logic) are not treated as cash flows. They're treated as investment activity, not money moving in or out of the symphony.

This means you can evaluate each symphony's performance independently, even if you've added or removed money from it at various times.

Charting cumulative return vs. value

Composer lets you chart your portfolio and symphony in two ways:

% Cumulative Return (Performance): shows how your investments performed, independent of cash flows. This is the best way to evaluate how well your portfolio and symphonies are doing.
$ Portfolio Value: shows the actual dollar value of your account and symphonies over time, including the effect of deposits and withdrawals. This is useful for seeing your total amount invested, but it doesn't tell you how well your investments performed.

You can toggle between these views using the % and $ controls on your portfolio and symphony charts.

Industry use

The Modified Dietz method is a well-established standard in the investment management industry and is used by institutional portfolio managers, pension funds, endowments, wealth management firms, and financial advisors as one of the primary methods for calculating time-weighted returns.

This methodology was originally developed for the Bank Administration Institute (BAI), which sets standards for the banking and financial services industry.

It’s explicitly recognized as an accepted calculation methodology under the Global Investment Performance Standards (GIPS), maintained by the CFA Institute. GIPS is the global standard for how investment firms calculate and present performance to clients, adopted by thousands of firms across more than 40 countries and referenced by regulators such as the SEC and FINRA.

Known limitations

The Modified Dietz method provides a close approximation to the "true" time-weighted return, which would require capturing the value of the entire portfolio at the exact moment of every cash flow. For most accounts, this produces results very close to the exact time-weighted return. The approximation is less precise on days with very large cash flows relative to portfolio size.

On the day of your initial deposit, the Cumulative Return is 0%. That’s because there's no prior value to compare against, so there's no meaningful return to calculate yet.

Some common scenarios that can cause confusion

"My portfolio went up in dollar value, but my Cumulative Return is negative." This can happen if you made a large deposit and the market subsequently declined. Your portfolio value is higher because of the new money, but the investments themselves lost value. Cumulative Return correctly shows the negative investment performance.

"My Cumulative Return is positive, but my portfolio is worth less than what I deposited." This typically happens when you've withdrawn money. Cumulative Return reflects that your investments grew while they were invested, even if you've since taken money out.

"My Cumulative Return doesn't match the return I'd calculate from my starting and ending balance." That's expected and it's exactly why the time-weighted return methodology exists. A simple starting-vs-ending calculation is distorted by cash flows in and out of your investment. Cumulative Return gives you the true investment performance.

If you have any other questions about your return values, contact us at [email protected].