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;doc:roi: mention annualization differences, clean up TWR section
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@ -15,9 +15,11 @@ could be an empty query (`--pnl ""` or `--pnl STR` where `STR` does
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not match any of your accounts).
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This command will compute and display the internalized rate of return
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(IRR) and time-weighted rate of return (TWR) for your investments for
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the time period requested. Both rates of return are annualized before
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display, regardless of the length of reporting interval.
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(IRR, also known as money-weighted rate of return) and time-weighted
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rate of return (TWR) for your investments for the time period
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requested. IRR is always annualized due to the way it is computed, but
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TWR is reported both as a rate over the chosen reporting period and as
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an annual rate.
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Price directives will be taken into account if you supply appropriate
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`--cost` or `--value` flags (see [VALUATION](https://hledger.org/hledger.html#valuation)).
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@ -125,15 +127,15 @@ different ways to compute rate of return, and this command implements
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two of them: IRR and TWR.
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Internal rate of return, or "IRR" (also called "money-weighted rate of
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return") takes into account effects of in-flows and out-flows.
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Naively, if you are withdrawing from your investment, your future
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gains would be smaller (in absolute numbers), and will be a smaller
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percentage of your initial investment, and if you are adding to your
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investment, you will receive bigger absolute gains (but probably at
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the same rate of return). IRR is a way to compute rate of return for
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each period between in-flow or out-flow of money, and then combine
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them in a way that gives you a compound annual rate of return that investment
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is expected to generate.
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return") takes into account effects of in-flows and out-flows, and the
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time between them. Investment at a particular fixed interest rate is
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going to give you more interest than the same amount invested at the
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same interest rate, but made later in time. If you are withdrawing from
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your investment, your future gains would be smaller (in absolute
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numbers), and will be a smaller percentage of your initial investment,
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so your IRR will be smaller. And if you are adding to your investment,
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you will receive bigger absolute gains, which will be a bigger
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percentage of your initial investment, so your IRR will be larger.
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As mentioned before, in-flows and out-flows would be any cash that you
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personally put in or withdraw, and for the "roi" command, these are
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@ -152,25 +154,28 @@ present value, and tries to find a discount rate that makes net
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present value of all the cash flows of your investment to add up to
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zero. This could be hard to wrap your head around, especially if you
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haven't done discounted cash flow analysis before. Implementation of
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IRR in hledger should produce results that match the `XIRR` formula in
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IRR in hledger should produce results that match the `=XIRR` formula in
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Excel.
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Second way to compute rate of return that `roi` command implements is
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called "time-weighted rate of return" or "TWR". Like IRR, it will also
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break the history of your investment into periods between in-flows,
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out-flows and value changes, to compute rate of return per each period
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and then a compound rate of return. However, internal workings of TWR
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are quite different.
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called "time-weighted rate of return" or "TWR". Like IRR, it will
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account for the effect of your in-flows and out-flows, but unlike IRR
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it will try to compute the true rate of return of the underlying
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asset, compensating for the effect that deposits and withdrawas have
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on the apparent rate of growth of your investment.
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TWR represents your investment as an imaginary "unit fund" where in-flows/
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out-flows lead to buying or selling "units" of your investment and changes in
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its value change the value of "investment unit". Change in "unit price" over the
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reporting period gives you rate of return of your investment.
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TWR represents your investment as an imaginary "unit fund" where
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in-flows/ out-flows lead to buying or selling "units" of your
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investment and changes in its value change the value of "investment
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unit". Change in "unit price" over the reporting period gives you rate
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of return of your investment, and make TWR less sensitive than IRR to
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the effects of cash in-flows and out-flows.
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References:
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* [Explanation of rate of return](https://www.investopedia.com/terms/r/rateofreturn.asp)
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* [Explanation of IRR](https://www.investopedia.com/terms/i/irr.asp)
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* [Explanation of TWR](https://www.investopedia.com/terms/t/time-weightedror.asp)
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* [IRR vs TWR](https://smartasset.com/investing/time-weighted-return)
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* [Examples of computing IRR and TWR and discussion of the limitations of both metrics](https://blog.commonwealth.com/measuring-portfolio-performance-twr-vs.-irr)
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