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hledger/Hledger/Cli/Commands/Roi.md
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@ -17,7 +17,7 @@ At a minimum, you need to supply a query (which could be just an
account name) to select your investments with `--inv`, and another
query to identify your profit and loss transactions with `--pnl`.
It will compute and display the internalized rate of return (IRR) and
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.
@ -36,31 +36,222 @@ https://github.com/simonmichael/hledger/blob/master/examples/roi-unrealised.ledg
More background:
ROI is return on investment. There are various ways to compute it.
IRR (internal/money-weighted rate of return) is one strategy.
TWR (time-weighted rate of return) is another.
hledger's "roi" command computes both IRR and TWR.
"ROI" stands for "return on investment". Traditionally this was
computed as a difference between current value of investment and its
initial value, expressed in percentage of the initial value.
If you have a single "incoming" cash flow (e.g. you put money in a savings account)
and a single "outgoing" flow (you extracted money + interest at the end of term)
then both IRR and TWR will be the same, and will be equal to the rate of return of your saving account.
However, this approach is only practical in simple cases, where
investments receives no in-flows or out-flows of money, and where rate
of growth is fixed over time. For more complex scenarios you need
different ways to compute rate of return, and this command implements
two of them: IRR and TWR.
But if you keep paying into your account at irregular intervals, then IRR and TWR will be different.
IRR assumes that periods between cash flows are equal, the more this assumption is violated the more "off" it will be.
TWR does not require time intervals to be equal and gives a much better estimate of how much your "average dollar" of investment grew.
However, IRR is wildly popular (possibly because Excel initially only had IRR, but not TWR), so it is included for completeness.
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 an annual rate of return that investment
is expected to generate.
Now, what about unrealized gains reporting ?
In order to compute IRR or TWR, you need to know (1) how much you paid in, (2) how much you withdrew, and (3) how much the investment has grown in value.
1 and 2 are your transactions (regular ones) and 3 is in "unrealized gains" transactions.
So 1, 2 and 3 together are the cashflows of your investment that could be used to compute IRR and TWR.
So "unrealized gains" transactions are one of the inputs for "roi".
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
transactions that involve account(s) matching `--inv` argument and NOT
involve account(s) matching `--pnl` argument.
https://blog.commonwealth.com/measuring-portfolio-performance-twr-vs.-irr has good small examples.
It also explains why both numbers can be problematic.
But in layman's terms:
Presumably, you will also record changes in the value of your
investment, and balance them against "profit and loss" (or "unrealized
gains") account. Note that in order for IRR to compute the precise
effect of your in-flows and out-flows on the rate of return, you will
need to record the value of your investement on or close to the days
when in- or out-flows occur.
- TWR will show you how well your investment is performing (even though you might be adding and removing cash from your investment along the way); so if you have different investments or investment strategies, you can use TWR to compare them.
- IRR will show you how much money you are actually making. So if you are comparing different pay-in/withdrawal schedules into the same investment trying to find one that is best for you, IRR is your tool.
Implementation of IRR in hledger should match the `XIRR` formula in
Excel.
If you squint just the right way, your pay-ins/withdrawals will have effect on IRR, and growth of investment will have effect on TWR.
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 and
out-flows to compute rate of return per each period and then a
compound rate of return. However, internal workings of TWR are quite
different.
In technical terms, IRR uses the same approach as computation of net
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.
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.
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)
* [Examples of computing IRR and TWR and discussion of the limitations of both metrics](https://blog.commonwealth.com/measuring-portfolio-performance-twr-vs.-irr)
More examples:
Lets say that we found an investment in Snake Oil that is proising to give us 10% annually:
```hledger
2019-01-01 Investing in Snake Oil
assets:cash -$100
investment:snake oil
2019-12-24 Recording the growth of Snake Oil
investment:snake oil = $110
equity:unrealized gains
```
For now, basic computation of the rate of return, as well as IRR and TWR, gives us the expected 10%:
```
$ hledger roi -Y --inv investment --pnl "unrealized"
+---++------------+------------++---------------+----------+-------------+-----++--------+--------+
| || Begin | End || Value (begin) | Cashflow | Value (end) | PnL || IRR | TWR |
+===++============+============++===============+==========+=============+=====++========+========+
| 1 || 2019-01-01 | 2019-12-31 || 0 | 100 | 110 | 10 || 10.00% | 10.00% |
+---++------------+------------++---------------+----------+-------------+-----++--------+--------+
```
However, lets say that shorty after investing in the Snake Oil we started to have second thoughs, so we prompty withdrew $90, leaving only $10 in.
Before Christmas, though, we started to get the "fear of mission out", so we put the $90 back in. So for most of the year, our investment was just $10 dollars,
and it gave us just $1 in growth:
```hledger
2019-01-01 Investing in Snake Oil
assets:cash -$100
investment:snake oil
2019-01-02 Buyers remorse
assets:cash $90
investment:snake oil
2019-12-30 Fear of missing out
assets:cash -$90
investment:snake oil
2019-12-31 Recording the growth of Snake Oil
investment:snake oil = $101
equity:unrealized gains
```
Now IRR and TWR are drastically different:
```
$ hledger roi -Y --inv investment --pnl "unrealized"
+---++------------+------------++---------------+----------+-------------+-----++-------+-------+
| || Begin | End || Value (begin) | Cashflow | Value (end) | PnL || IRR | TWR |
+===++============+============++===============+==========+=============+=====++=======+=======+
| 1 || 2019-01-01 | 2019-12-31 || 0 | 100 | 101 | 1 || 9.32% | 1.00% |
+---++------------+------------++---------------+----------+-------------+-----++-------+-------+
```
Here, IRR tells us that we made close to 10% on the $10 dollars that
we had in the account most of the time. And TWR is ... just 1%? Why?
Based on the transactions in our journal, TWR "think" that we are buying back $90 worst of Snake Oil
at the same price that it had at the beginning of they year, and then after that our $100 investment
gets $1 increase in value, or 1% of $100. Let's take a closer look at what is happening here by
asking for quarterly reports instead of annual:
```
$ hledger roi -Q --inv investment --pnl "unrealized"
+---++------------+------------++---------------+----------+-------------+-----++--------+-------+
| || Begin | End || Value (begin) | Cashflow | Value (end) | PnL || IRR | TWR |
+===++============+============++===============+==========+=============+=====++========+=======+
| 1 || 2019-01-01 | 2019-03-31 || 0 | 10 | 10 | 0 || 0.00% | 0.00% |
| 2 || 2019-04-01 | 2019-06-30 || 10 | 0 | 10 | 0 || 0.00% | 0.00% |
| 3 || 2019-07-01 | 2019-09-30 || 10 | 0 | 10 | 0 || 0.00% | 0.00% |
| 4 || 2019-10-01 | 2019-12-31 || 10 | 90 | 101 | 1 || 37.80% | 4.03% |
+---++------------+------------++---------------+----------+-------------+-----++--------+-------+
```
Now both IRR and TWR are thrown off by the fact that all of the growth for our investment happens in
Q4 2019. This happes because IRR computation is still yielding 9.32% and TWR is still 1%, but
this time these are rates for three month period instead of twelve, so in order to get an annual rate
they should be multiplied by four!
Let's try to keep a better record of how Snake Oil grew in value:
```hledger
2019-01-01 Investing in Snake Oil
assets:cash -$100
investment:snake oil
2019-01-02 Buyers remorse
assets:cash $90
investment:snake oil
2019-02-28 Recording the growth of Snake Oil
investment:snake oil
equity:unrealized gains -$0.25
2019-06-30 Recording the growth of Snake Oil
investment:snake oil
equity:unrealized gains -$0.25
2019-09-30 Recording the growth of Snake Oil
investment:snake oil
equity:unrealized gains -$0.25
2019-12-30 Fear of missing out
assets:cash -$90
investment:snake oil
2019-12-31 Recording the growth of Snake Oil
investment:snake oil
equity:unrealized gains -$0.25
```
Would our quartery report look better now? Almost:
```
$ hledger roi -Q --inv investment --pnl "unrealized"
+---++------------+------------++---------------+----------+-------------+------++--------+--------+
| || Begin | End || Value (begin) | Cashflow | Value (end) | PnL || IRR | TWR |
+===++============+============++===============+==========+=============+======++========+========+
| 1 || 2019-01-01 | 2019-03-31 || 0 | 10 | 10.25 | 0.25 || 9.53% | 10.53% |
| 2 || 2019-04-01 | 2019-06-30 || 10.25 | 0 | 10.50 | 0.25 || 10.15% | 10.15% |
| 3 || 2019-07-01 | 2019-09-30 || 10.50 | 0 | 10.75 | 0.25 || 9.79% | 9.78% |
| 4 || 2019-10-01 | 2019-12-31 || 10.75 | 90 | 101.00 | 0.25 || 8.05% | 1.00% |
+---++------------+------------++---------------+----------+-------------+------++--------+--------+
```
Something is still wrong with TWR computation for Q4, and if you have been paying attention you know
what it is already: big $90 buy-back is recorded prior to the only transaction that captures the
change of value of Snake Oil that happened in this time period. Lets combine transactions from 30th
and 31st of Dec into one:
```hledger
2019-12-30 Fear of missing out and growth of Snake Oil
assets:cash -$90
investment:snake oil
equity:unrealized gains -$0.25
```
Now growth of investment properly affects its price at the time of buy-back:
```
$ hledger roi -Q --inv investment --pnl "unrealized"
+---++------------+------------++---------------+----------+-------------+------++--------+--------+
| || Begin | End || Value (begin) | Cashflow | Value (end) | PnL || IRR | TWR |
+===++============+============++===============+==========+=============+======++========+========+
| 1 || 2019-01-01 | 2019-03-31 || 0 | 10 | 10.25 | 0.25 || 9.53% | 10.53% |
| 2 || 2019-04-01 | 2019-06-30 || 10.25 | 0 | 10.50 | 0.25 || 10.15% | 10.15% |
| 3 || 2019-07-01 | 2019-09-30 || 10.50 | 0 | 10.75 | 0.25 || 9.79% | 9.78% |
| 4 || 2019-10-01 | 2019-12-31 || 10.75 | 90 | 101.00 | 0.25 || 8.05% | 9.57% |
+---++------------+------------++---------------+----------+-------------+------++--------+--------+
```
And for annual report, TWR now reports the exact profitability of our investment:
```
$ hledger roi -Y --inv investment --pnl "unrealized"
+---++------------+------------++---------------+----------+-------------+------++-------+--------+
| || Begin | End || Value (begin) | Cashflow | Value (end) | PnL || IRR | TWR |
+===++============+============++===============+==========+=============+======++=======+========+
| 1 || 2019-01-01 | 2019-12-31 || 0 | 100 | 101.00 | 1.00 || 9.32% | 10.00% |
+---++------------+------------++---------------+----------+-------------+------++-------+--------+
```