;doc:roi: mention annualization differences, clean up TWR section

hledger/Hledger/Cli/Commands/Roi.md

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