Comparing portfolio returns with benchmark

Let's say our portfolio has only one stock. At the purchase date, the price was

1import yahooquery as yq
2import datetime
3appl = yq.Ticker('aapl')
4print(appl.history(start=datetime.date(2023,1,1), end=datetime.date(2023,1,4)).close)

symbol  date      
aapl    2023-01-03    125.07
Name: close, dtype: float64

We can register this purchase in our ledger with

2023-01-03 * Buy appl
    assets:investments:stocks  1 aapl @ $125.07
    assets:cash

Then we can check our portfolio with,

1hledger -f portfolio.ledger bal acct:investments

              1 aapl  assets:investments:stocks
--------------------
              1 aapl  

How much the portfolio value now, can be computed if we have the price now.

The stock price fluctuates, and at the end of the year, the value is,

1import yahooquery as yq
2import datetime
3appl = yq.Ticker('aapl')
4print(appl.history(start=datetime.date(2023,12,28), end=datetime.date(2023,12,31)).close)

symbol  date      
aapl    2023-12-28    193.580002
        2023-12-29    192.529999
Name: close, dtype: float64

We can see, the stock closed December 29th at 192.53. We can get the stock price each month and record it in the ledger,

1python=~/.venv/general/bin/python
2$python -m investory.values --commodity aapl --begin 2023-01-01
3cat aapl.ledger

P 2023-01-31 "aapl" $143.487961
P 2023-02-28 "aapl" $146.814438
P 2023-03-31 "aapl" $164.233780
P 2023-04-28 "aapl" $168.994476
P 2023-05-31 "aapl" $176.778061
P 2023-06-30 "aapl" $193.453552
P 2023-07-31 "aapl" $195.926956
P 2023-08-31 "aapl" $187.622818
P 2023-09-29 "aapl" $170.984741
P 2023-10-31 "aapl" $170.545319
P 2023-11-30 "aapl" $189.949997
P 2023-12-29 "aapl" $192.529999

Now we want to know the performance of our portfolio. This means, how much our assets appreciated or depreciated in value. Of course, without considering contributions and withdrawls to our portfolio.

With hledger we can obtain the time-weighted return. For the first month, we get that we started with a cashflow event of 125.07. This represents the purchase, the value=then can only be obtained because we have --infer-market-price option, which will use the purchase price as market value on this date.

The TWR for the period is 14.73%. Which represents the increase in value without considering contributions/withdrawls. We can check with (/ (- 143.49 125.07) 125.07)0.14727.

1hledger -f portfolio.ledger -f aapl.ledger roi --inv investments --pnl "unrealized" --value=then --monthly --infer-market-price

+---++------------+------------++---------------+----------+-------------+--------++---------++------------+----------+
|   ||      Begin |        End || Value (begin) | Cashflow | Value (end) |    PnL ||     IRR || TWR/period | TWR/year |
+===++============+============++===============+==========+=============+========++=========++============+==========+
| 1 || 2023-01-01 | 2023-01-31 ||             0 |  $125.07 |     $143.49 | $18.42 || 463.54% ||     14.73% |  404.25% |
+---++------------+------------++---------------+----------+-------------+--------++---------++------------+----------+

We can get the TWR for each month by specifying the end date since we have price directives for each month end. We can see, some very positive months and some negatives as well.

1hledger -f portfolio.ledger -f aapl.ledger roi --inv investments --pnl "unrealized" --value=then --monthly --infer-market-price --end=2024-01-01

+-------++------------+------------++---------------+----------+-------------+---------++---------++------------+----------+
|       ||      Begin |        End || Value (begin) | Cashflow | Value (end) |     PnL ||     IRR || TWR/period | TWR/year |
+=======++============+============++===============+==========+=============+=========++=========++============+==========+
|     1 || 2023-01-01 | 2023-01-31 ||             0 |  $125.07 |     $143.49 |  $18.42 || 463.54% ||     14.73% |  404.25% |
|     2 || 2023-02-01 | 2023-02-28 ||       $143.49 |        0 |     $146.81 |   $3.33 ||  34.82% ||      2.32% |   34.85% |
|     3 || 2023-03-01 | 2023-03-31 ||       $146.81 |        0 |     $164.23 |  $17.42 || 274.39% ||     11.86% |  274.20% |
|     4 || 2023-04-01 | 2023-04-30 ||       $164.23 |        0 |     $168.99 |   $4.76 ||  41.58% ||      2.90% |   41.60% |
|     5 || 2023-05-01 | 2023-05-31 ||       $168.99 |        0 |     $176.78 |   $7.78 ||  69.92% ||      4.61% |   70.00% |
|     6 || 2023-06-01 | 2023-06-30 ||       $176.78 |        0 |     $193.45 |  $16.68 || 199.44% ||      9.43% |  199.34% |
|     7 || 2023-07-01 | 2023-07-31 ||       $193.45 |        0 |     $195.93 |   $2.47 ||  16.14% ||      1.28% |   16.15% |
|     8 || 2023-08-01 | 2023-08-31 ||       $195.93 |        0 |     $187.62 |  $-8.30 || -39.95% ||     -4.24% |  -39.96% |
|     9 || 2023-09-01 | 2023-09-30 ||       $187.62 |        0 |     $170.98 | $-16.64 || -67.69% ||     -8.87% |  -67.70% |
|    10 || 2023-10-01 | 2023-10-31 ||       $170.98 |        0 |     $170.55 |  $-0.44 ||  -2.98% ||     -0.26% |   -3.02% |
|    11 || 2023-11-01 | 2023-11-30 ||       $170.55 |        0 |     $189.95 |  $19.40 || 271.02% ||     11.38% |  271.10% |
|    12 || 2023-12-01 | 2023-12-31 ||       $189.95 |        0 |     $192.53 |   $2.58 ||  17.22% ||      1.36% |   17.24% |
+-------++------------+------------++---------------+----------+-------------+---------++---------++------------+----------+
| Total || 2023-01-01 | 2023-12-31 ||             0 |  $125.07 |     $192.53 |  $67.46 ||  54.30% ||     53.94% |   53.94% |
+-------++------------+------------++---------------+----------+-------------+---------++---------++------------+----------+

If we multiply the TWR change factor¹ for each month, we can get the cummulative return for the year,

 1import numpy as np
 2monthly_returns_perc = np.array([
 3    14.73,
 4    2.32,
 5    11.86,
 6    2.90,
 7    4.61,
 8    9.43,
 9    1.28,
10    -4.24,
11    -8.87,
12    -0.26,
13    11.38,
14    1.36,
15])
16
17accumulated_return = np.prod(monthly_returns_perc / 100 + 1)
18print(f"Performance year: {(accumulated_return - 1)*100:.2f}%")

Performance year: 53.94%

With hledger we can also obtain this performance by asking for the yearly value,

1hledger -f portfolio.ledger -f aapl.ledger roi --inv investments --pnl "unrealized" --value=then --yearly --infer-market-price --end=2024-01-01

+---++------------+------------++---------------+----------+-------------+--------++--------++------------+----------+
|   ||      Begin |        End || Value (begin) | Cashflow | Value (end) |    PnL ||    IRR || TWR/period | TWR/year |
+===++============+============++===============+==========+=============+========++========++============+==========+
| 1 || 2023-01-01 | 2023-12-31 ||             0 |  $125.07 |     $192.53 | $67.46 || 54.30% ||     53.94% |   53.94% |
+---++------------+------------++---------------+----------+-------------+--------++--------++------------+----------+

We can compare to a benchmark in many different ways. One way is to check how much the index grew during the year.

1import yahooquery as yq
2import datetime
3spx = yq.Ticker('^spx')
4print(spx.history(start=datetime.date(2023,1,1), end=datetime.date(2023,1,4)).close)
5print(spx.history(start=datetime.date(2023,12,29), end=datetime.date(2023,12,31)).close)

symbol  date      
^spx    2023-01-03    3824.139893
Name: close, dtype: float64
symbol  date      
^spx    2023-12-29    4769.830078
Name: close, dtype: float64

We can then compute the growth for one share of the index,

1year_return = (4769.830078 - 3824.139893) / 3824.139893
2print(f"Performance year: {(year_return)*100:.2f}%")

Performance year: 24.73%

We can also use hledger to compute the performance of the index for the same period as our portfolio. With this we can get the same data points as our porfolio. To do that, we need the a hypotetical portfolio with the index share.

2023-01-03 * Benchmark portfolio
    assets:investments:stocks  1 ^spx @ $3824.139893
    assets:cash

Then we need the price of the index² at the end of each month,

1python=~/.venv/general/bin/python
2$python -m investory.values --commodity ^spx --begin 2023-01-01
3cat ^spx.ledger

P 2023-01-31 "^spx" $4076.600098
P 2023-02-28 "^spx" $3970.149902
P 2023-03-31 "^spx" $4109.310059
P 2023-04-28 "^spx" $4169.479980
P 2023-05-31 "^spx" $4179.830078
P 2023-06-30 "^spx" $4450.379883
P 2023-07-31 "^spx" $4588.959961
P 2023-08-31 "^spx" $4507.660156
P 2023-09-29 "^spx" $4288.049805
P 2023-10-31 "^spx" $4193.799805
P 2023-11-30 "^spx" $4567.799805
P 2023-12-29 "^spx" $4769.830078

With this price at the end of each month we can compute the performance monthly or yearly. Let's check the yearly change for the index. We can see that we get the same value as before for the year change.

1hledger -f benchmark.ledger -f ^spx.ledger roi --inv investments --pnl "unrealized" --value=then --yearly --infer-market-price --end=2024-01-01

+---++------------+------------++---------------+--------------+--------------+-------------++--------++------------+----------+
|   ||      Begin |        End || Value (begin) |     Cashflow |  Value (end) |         PnL ||    IRR || TWR/period | TWR/year |
+===++============+============++===============+==============+==============+=============++========++============+==========+
| 1 || 2023-01-01 | 2023-12-31 ||             0 | $3824.139893 | $4769.830078 | $945.690185 || 24.88% ||     24.73% |   24.73% |
+---++------------+------------++---------------+--------------+--------------+-------------++--------++------------+----------+

We can track the performance at the end of each year with a percentage change for the portfolio and index. Like we did, our portfolio at the year os 2023 grew 53.94% and the index only grew 24.73%. This means that our allocation of assets (only Apple in this case) in our portolio beat the market (US).

However would be nice to have a track of performance over time with monthly acummulated returns. For instance,

1. First month our portfolio increased in 14.73%, then we check how much the index changed this month.
2. Second month, our portolio increased (* (- (* 1.1473 1.0232) 1) 100)17.39. Which is the accumulated over the two first returns.

And repeating for the whole period, plotting the accumulated return each month.

We can do that by saving the monhthly TWR for the portfolio and for the benchmark,

1hledger -f portfolio.ledger -f aapl.ledger roi --inv investments --pnl "unrealized" --value=then --monthly --infer-market-price --end=2024-01-01 > portfolio-twr.txt
2hledger -f benchmark.ledger -f ^spx.ledger roi --inv investments --pnl "unrealized" --value=then --monthly --infer-market-price --end=2024-01-01 > benchmark-twr.txt

Then we can just load that with python and plot the cummulated value,

 1import matplotlib.pyplot as plt
 2import figtex; figtex.style()
 3import pandas as pd
 4
 5files = {
 6    "portfolio-twr.txt": dict(label="portfolio", linewidth=2),
 7    "benchmark-twr.txt": dict(label="S\&P500", linewidth=6, alpha=.3, color="black"),
 8}
 9
10fig, ax = plt.subplots(figsize=(4, 3))
11for file, params in files.items():
12    # read the ascii formatted table
13    # regex: 
14    # \s* matches one or more spaces
15    # \|\|? matches one or two |
16    df: pd.DataFrame = pd.read_csv(file,
17                                   sep=r'\s*\|\|?\s*',
18                                   skipfooter=4, skiprows=1, engine='python', skipinitialspace=True)
19    # remove columns with no data
20    df = df.drop(['Unnamed: 0', 'Unnamed: 1', 'Unnamed: 11'], axis=1)
21    # remove row with no data
22    df = df.drop([0], axis=0)
23    print(df)
24
25    end_dates: pd.Series = pd.to_datetime(df["End"], format="%Y-%m-%d").rename("end_dates")
26    twr: pd.Series = df["TWR/period"].rename("twr")
27    twr = twr.str.replace('%', '').astype(float)
28    twr = twr / 100 + 1
29
30    # get the cumulative product which aggregates the result for the period
31    ax.plot(end_dates.values, twr.cumprod(), **params)
32
33ax.set(xlabel="Date",
34       ylabel="Accumulated TWR")
35ax.legend()

We can see that the S&P500 is larged influenced by the Apple stock movement.