# Time-weighted vs money-weighted return

> Two honest ways to answer "what did I make", giving different numbers. One measures the investments, the other measures your timing. Here is which is which.

Ask what a portfolio returned and there are two defensible answers. They
disagree, sometimes dramatically, and neither is wrong.

**Time-weighted return** measures how the investments performed, ignoring when
you put money in. It is what you would compare against an index.

**Money-weighted return** measures how _you_ did, including the effect of when
you invested. It is what your bank balance experienced.

## Why they differ

Suppose you hold a fund that falls 50% and then doubles. Over the whole period
the fund is flat, and its time-weighted return is 0%.

Now suppose you invested a small amount at the start and a large amount at the
bottom, just before it doubled. Your money-weighted return is strongly
positive, because most of your money was present for the recovery and very
little of it was present for the fall.

Both statements are true. The fund went nowhere. You did well. Time-weighted
answers the first, money-weighted answers the second.

## How Gylder calculates money-weighted return

The money-weighted figure is an internal rate of return, solved from your
actual cashflows using the same convention as Excel's XIRR:

- Buys are money flowing in, entered as negative
- Sells and dividends are money flowing out to you, entered as positive
- The value at the start of the period counts as money in, the value at the end
  as money out

Gylder solves for the annual rate that makes those flows net to zero.

The equation only has a solution when there is at least one inflow and one
outflow. If your cashflows never change sign, or the data is pathological, the
figure shows a dash rather than a confident wrong number.

## Which to use

Use **time-weighted** when comparing against a benchmark, or judging a fund or
a strategy, since it removes the effect of contribution timing that has nothing
to do with the investment itself. Everything in the
[risk grid](/metrics/sharpe-ratio) is built from the time-weighted value
series for this reason.

Use **money-weighted** when asking what your actual money earned, especially if
you contribute regularly. For anyone paying in monthly, this is usually the
more honest answer to "how am I doing".

## A caveat

Holdings you entered by hand have no cashflow ledger, only the valuations you
typed. They are excluded from the contribution-based return rather than being
given invented flows, so a portfolio heavy in manual entries will have a
money-weighted figure covering less than all of it.