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@ -4469,14 +4469,295 @@ At a minimum, you need to supply a query (which could be just an account
name) to select your investments with \f[C]--inv\f[R], and another query
to identify your profit and loss transactions with \f[C]--pnl\f[R].
.PP
It 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.
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.
.PP
An example:
Note, in some cases this report can fail, for these reasons:
.IP \[bu] 2
Error (NotBracketed): No solution for Internal Rate of Return (IRR).
Possible causes: IRR is huge (>1000000%), balance of investment becomes
negative at some point in time.
.IP \[bu] 2
Error (SearchFailed): Failed to find solution for Internal Rate of
Return (IRR).
Either search does not converge to a solution, or converges too slowly.
.PP
Examples:
.IP \[bu] 2
Using roi to report unrealised gains:
https://github.com/simonmichael/hledger/blob/master/examples/roi-unrealised.ledger
.PP
More background:
.PP
\[dq]ROI\[dq] stands for \[dq]return on investment\[dq].
Traditionally this was computed as a difference between current value of
investment and its initial value, expressed in percentage of the initial
value.
.PP
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.
.PP
Internal rate of return, or \[dq]IRR\[dq] (also called
\[dq]money-weighted rate of return\[dq]) 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.
.PP
As mentioned before, in-flows and out-flows would be any cash that you
personally put in or withdraw, and for the \[dq]roi\[dq] command, these
are transactions that involve account(s) matching \f[C]--inv\f[R]
argument and NOT involve account(s) matching \f[C]--pnl\f[R] argument.
.PP
Presumably, you will also record changes in the value of your
investment, and balance them against \[dq]profit and loss\[dq] (or
\[dq]unrealized gains\[dq]) 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.
.PP
Implementation of IRR in hledger should match the \f[C]XIRR\f[R] formula
in Excel.
.PP
Second way to compute rate of return that \f[C]roi\f[R] command
implements is called \[dq]time-weighted rate of return\[dq] or
\[dq]TWR\[dq].
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.
.PP
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\[aq]t done discounted cash flow analysis before.
.PP
TWR represents your investment as an imaginary \[dq]unit fund\[dq] where
in-flows/ out-flows lead to buying or selling \[dq]units\[dq] of your
investment and changes in its value change the value of \[dq]investment
unit\[dq].
Change in \[dq]unit price\[dq] over the reporting period gives you rate
of return of your investment.
.PP
References: * Explanation of rate of return * Explanation of IRR *
Explanation of TWR * Examples of computing IRR and TWR and discussion of
the limitations of both metrics
.PP
More examples:
.PP
Lets say that we found an investment in Snake Oil that is proising to
give us 10% annually:
.IP
.nf
\f[C]
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
\f[R]
.fi
.PP
For now, basic computation of the rate of return, as well as IRR and
TWR, gives us the expected 10%:
.IP
.nf
\f[C]
$ hledger roi -Y --inv investment --pnl \[dq]unrealized\[dq]
+---++------------+------------++---------------+----------+-------------+-----++--------+--------+
| || 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% |
+---++------------+------------++---------------+----------+-------------+-----++--------+--------+
\f[R]
.fi
.PP
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 \[dq]fear of mission
out\[dq], 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:
.IP
.nf
\f[C]
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
\f[R]
.fi
.PP
Now IRR and TWR are drastically different:
.IP
.nf
\f[C]
$ hledger roi -Y --inv investment --pnl \[dq]unrealized\[dq]
+---++------------+------------++---------------+----------+-------------+-----++-------+-------+
| || 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% |
+---++------------+------------++---------------+----------+-------------+-----++-------+-------+
\f[R]
.fi
.PP
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?
.PP
Based on the transactions in our journal, TWR \[dq]think\[dq] 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\[aq]s take a closer look at what is happening here by asking for
quarterly reports instead of annual:
.IP
.nf
\f[C]
$ hledger roi -Q --inv investment --pnl \[dq]unrealized\[dq]
+---++------------+------------++---------------+----------+-------------+-----++--------+-------+
| || 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% |
+---++------------+------------++---------------+----------+-------------+-----++--------+-------+
\f[R]
.fi
.PP
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!
.PP
Let\[aq]s try to keep a better record of how Snake Oil grew in value:
.IP
.nf
\f[C]
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
\f[R]
.fi
.PP
Would our quartery report look better now?
Almost:
.IP
.nf
\f[C]
$ hledger roi -Q --inv investment --pnl \[dq]unrealized\[dq]
+---++------------+------------++---------------+----------+-------------+------++--------+--------+
| || 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% |
+---++------------+------------++---------------+----------+-------------+------++--------+--------+
\f[R]
.fi
.PP
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:
.IP
.nf
\f[C]
2019-12-30 Fear of missing out and growth of Snake Oil
assets:cash -$90
investment:snake oil
equity:unrealized gains -$0.25
\f[R]
.fi
.PP
Now growth of investment properly affects its price at the time of
buy-back:
.IP
.nf
\f[C]
$ hledger roi -Q --inv investment --pnl \[dq]unrealized\[dq]
+---++------------+------------++---------------+----------+-------------+------++--------+--------+
| || 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% |
+---++------------+------------++---------------+----------+-------------+------++--------+--------+
\f[R]
.fi
.PP
And for annual report, TWR now reports the exact profitability of our
investment:
.IP
.nf
\f[C]
$ hledger roi -Y --inv investment --pnl \[dq]unrealized\[dq]
+---++------------+------------++---------------+----------+-------------+------++-------+--------+
| || 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% |
+---++------------+------------++---------------+----------+-------------+------++-------+--------+
\f[R]
.fi
.SS stats
.PP
stats

283
hledger/hledger.info
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@ -3798,14 +3798,239 @@ your investments or withdrawals.
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
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.
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.
An example:
Note, in some cases this report can fail, for these reasons:
* Error (NotBracketed): No solution for Internal Rate of Return
(IRR). Possible causes: IRR is huge (>1000000%), balance of
investment becomes negative at some point in time.
* Error (SearchFailed): Failed to find solution for Internal Rate of
Return (IRR). Either search does not converge to a solution, or
converges too slowly.
Examples:
* Using roi to report unrealised gains:
https://github.com/simonmichael/hledger/blob/master/examples/roi-unrealised.ledger
More background:
"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.
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.
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.
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.
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.
Implementation of IRR in hledger should 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 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 * Explanation of IRR *
Explanation of TWR * Examples of computing IRR and TWR and discussion of
the limitations of both metrics
More examples:
Lets say that we found an investment in Snake Oil that is proising to
give us 10% annually:
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:
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:
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:
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% |
+---++------------+------------++---------------+----------+-------------+------++-------+--------+

File: hledger.info, Node: stats, Next: tags, Prev: roi, Up: COMMANDS
@ -4290,30 +4515,30 @@ Node: rewrite vs print --auto133861
Ref: #rewrite-vs.-print---auto134040
Node: roi134596
Ref: #roi134694
Node: stats135805
Ref: #stats135904
Node: tags136692
Ref: #tags136790
Node: test137309
Ref: #test137417
Node: Add-on commands138164
Ref: #add-on-commands138281
Node: ui139624
Ref: #ui139712
Node: web139766
Ref: #web139869
Node: iadd139985
Ref: #iadd140096
Node: interest140178
Ref: #interest140285
Node: ENVIRONMENT140525
Ref: #environment140637
Node: FILES141622
Ref: #files-1141725
Node: LIMITATIONS141938
Ref: #limitations142057
Node: TROUBLESHOOTING142799
Ref: #troubleshooting142912
Node: stats146904
Ref: #stats147003
Node: tags147791
Ref: #tags147889
Node: test148408
Ref: #test148516
Node: Add-on commands149263
Ref: #add-on-commands149380
Node: ui150723
Ref: #ui150811
Node: web150865
Ref: #web150968
Node: iadd151084
Ref: #iadd151195
Node: interest151277
Ref: #interest151384
Node: ENVIRONMENT151624
Ref: #environment151736
Node: FILES152721
Ref: #files-1152824
Node: LIMITATIONS153037
Ref: #limitations153156
Node: TROUBLESHOOTING153898
Ref: #troubleshooting154011

End Tag Table

239
hledger/hledger.txt
View File

@ -3230,13 +3230,240 @@ COMMANDS
count 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
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.
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.
An example: https://github.com/simonmichael/hledger/blob/master/exam-
ples/roi-unrealised.ledger
Note, in some cases this report can fail, for these reasons:
o Error (NotBracketed): No solution for Internal Rate of Return (IRR).
Possible causes: IRR is huge (>1000000%), balance of investment be-
comes negative at some point in time.
o Error (SearchFailed): Failed to find solution for Internal Rate of
Return (IRR). Either search does not converge to a solution, or con-
verges too slowly.
Examples:
o Using roi to report unrealised gains: https://github.com/simon-
michael/hledger/blob/master/examples/roi-unrealised.ledger
More background:
"ROI" stands for "return on investment". Traditionally this was com-
puted as a difference between current value of investment and its ini-
tial value, expressed in percentage of the initial value.
However, this approach is only practical in simple cases, where invest-
ments receives no in-flows or out-flows of money, and where rate of
growth is fixed over time. For more complex scenarios you need differ-
ent 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 percent-
age of your initial investment, and if you are adding to your invest-
ment, 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 pe-
riod 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.
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.
Presumably, you will also record changes in the value of your invest-
ment, and balance them against "profit and loss" (or "unrealized
gains") account. Note that in order for IRR to compute the precise ef-
fect 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.
Implementation of IRR in hledger should match the XIRR formula in Ex-
cel.
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 * Explanation of IRR * Ex-
planation of TWR * Examples of computing IRR and TWR and discussion of
the limitations of both metrics
More examples:
Lets say that we found an investment in Snake Oil that is proising to
give us 10% annually:
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:
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 buy-
ing 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 compu-
tation 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:
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:
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% |
+---++------------+------------++---------------+----------+-------------+------++-------+--------+
stats
stats