Diagnosing Excess Returns in a Daily Value-Weighted Portfolio
Article Quant Q&A · Author: Constantine Phoenix
Summary
The document describes a dissertation calculation of daily returns for a value-weighted portfolio of large corporations, using prior-day market values as weights to avoid using future information. It outlines normalizing market values across constituents, computing daily weighted returns, and compounding those returns into a holding-period return. The author reports that the portfolio’s cumulative return reaches roughly 100, compared with roughly 30 for an S&P benchmark, and asks why the result appears unusually high.
The posted code and sample market-value and return inputs provide material for diagnosing the calculation, but the document contains no accepted answer or confirmed correction. In particular, the discussion raises questions about whether the inputs are levels or returns, whether the market-value reconstruction is appropriate, and whether portfolio weights are aligned with the return dates. The reported comparison is not evidence of outperformance: without checking those conventions, corporate actions, constituent selection, and compounding, the result cannot be interpreted reliably.
Key ideas
- Value-weighted portfolio returns use constituent weights based on market values from the prior period.
- Portfolio weights should be normalized across assets at each rebalancing date.
- The document reports a much higher compounded return than its benchmark but does not establish the cause.
- Return definitions, market-value construction, and date alignment need checking before interpreting the result.
- A high holding-period return alone does not demonstrate a valid strategy or outperformance.
Tags
Full text
# Holding Period Return abnormally high
# Holding Period Return abnormally high
I've been doing my Dissertation and I was told to create a value - weighted portfolio on the 1979's 200 largest cap corporations (based on Market Value). I was also told that the correct way to build it would be to have today's returns weighted by yesterday's market values instead of today's because I can't use information from the future and I supposedly wouldn't have today's numbers available, ergo
Return(portfolio) = SUM( Return(today) * Market Value(yesterday))
I was also told that to have more accurate estimates of Market Values and isolate their variations from external factors, I should not use the stock Market Values (which I imported as MVp) but to create new ones based on the formula
MV t-1 = MV i, t-1 / SUMi=1N (MVi,t-1) where
MV i, t-1 = MV0 * PRODUCTj=1t-1(1+ri,j)
i = Denotes Stock, N = All stocks, j = Time Unit (here daily)
The problem is when I plot the holding period return, given the code below where I create a different value - weighted portfolio at every day depending on how the Market Value of each corporation changes, I get a HPR of about 100, which I was told is abnormally high compared to the SP base which is about 30.
```
import numpy as np
import pandas as pd
from matplotlib import pyplot as plt
#MVp, RIp are the imported matrices
#Compute Returns
RIp = RIp.pct_change(1)
#Do the shift so as to have TRI(t)*MV(t-1)
MVp = MVp.shift(1)
#To get initial MVs, as per the formula request
MV0 = MVp.iloc[[0]]
RIp += 1
initial = MV0*RIp;
initial = initial.iloc[[0]]
newMV = initial.append(RIp)
newMV = newMV[~newMV.index.duplicated(keep='first')]
MV = newMV.cumprod()
RI = RIp.copy()
RI -= 1
#Calculating SUM(MV) and percentages
sum_cap = np.sum(MVp, axis=1)
p = MVp.divide(sum_cap, axis=0)
# R(p) = SUM(R(i,t) * p(i, t-1)|MV(t-1))
portfolio = RI.multiply(p)
portfolio = portfolio.sum(axis=1)
portfolio.dropna(inplace=True)
hdr = portfolio.add(1).cumprod().sub(1)
histogram = hdr.plot(title="Holding Period Returns over Time")
plt.show(histogram)
# Here I show for illustration the first and last 5 rows of my
# suspected abnormal file of HPR and of the benchmarked SP HPR
hdr.head().values =
[-0.02332244],
[-0.02610473],
[-0.0138813 ],
[-0.01069693],
[ 0.01453517]
hdr.tail.values() =
[91.92066528],
[91.76834481],
[93.28143382],
[93.36009697],
[92.3151313 ]]
SP.head().values =
[-0.00510591, 0.00718603, 0.0099281 , 0.03016258, 0.03110818]
SP.tail().values =
[25.16423819, 25.00973891, 25.56883386, 25.56212091, 25.17984093]
#Here I also provide some initial values of MVp, RIp BEFORE I do any
#Calculations with them (Data extracted from Thomson ReutersDataStream)
#two first rows of each original matrix, each row includes 200 corps
MVp = [[3.755470e+04, 2.498292e+04, 1.191806e+04, 1.145820e+04,
9.636620e+03, 7.412540e+03, 6.129630e+03, 5.897540e+03,
5.439700e+03, 5.226260e+03, 4.998420e+03, 4.843040e+03,
4.666410e+03, 4.482140e+03, 4.354520e+03, 4.262710e+03,
4.086790e+03, 3.856000e+03, 3.482870e+03, 3.447840e+03,
3.248250e+03, 2.865640e+03, 2.601440e+03, 2.480580e+03,
2.421320e+03, 2.374420e+03, 2.258650e+03, 2.238450e+03,
2.155060e+03, 2.129760e+03, 2.100110e+03, 2.064440e+03,
2.008780e+03, 1.929240e+03, 1.928700e+03, 1.790820e+03,
1.778960e+03, 1.743590e+03, 1.729600e+03, 1.709660e+03,
1.692570e+03, 1.616920e+03, 1.607260e+03, 1.591730e+03,
1.569670e+03, 1.516010e+03, 1.449150e+03, 1.442600e+03,
1.392930e+03, 1.357540e+03, 1.317370e+03, 1.256920e+03,
1.177400e+03, 1.137850e+03, 1.125640e+03, 1.069700e+03,
1.040250e+03, 1.038220e+03, 1.018250e+03, 1.003950e+03,
9.914800e+02, 9.907800e+02, 9.890100e+02, 9.862300e+02,
9.804600e+02, 9.760300e+02, 9.536700e+02, 9.364500e+02,
9.228900e+02, 9.128400e+02, 9.060200e+02, 8.711100e+02,
8.679000e+02, 8.614900e+02, 8.544900e+02, 8.351700e+02,
7.912500e+02, 7.698300e+02, 7.363900e+02, 7.192600e+02,
7.104100e+02, 6.990700e+02, 6.879700e+02, 6.814500e+02,
6.786100e+02, 6.740100e+02, 6.669200e+02, 6.577700e+02,
6.577000e+02, 6.564500e+02, 6.511000e+02, 6.507900e+02,
6.044600e+02, 5.890800e+02, 5.845100e+02, 5.668000e+02,
5.625900e+02, 5.460800e+02, 5.315100e+02, 5.311000e+02,
5.281300e+02, 5.273000e+02, 5.268400e+02, 5.245500e+02,
5.214500e+02, 5.068100e+02, 4.800800e+02, 4.576000e+02,
4.330200e+02, 4.070700e+02, 4.019400e+02, 3.935600e+02,
3.822100e+02, 3.751200e+02, 3.744500e+02, 3.531400e+02,
3.486700e+02, 3.429200e+02, 3.275400e+02, 3.219900e+02,
3.056700e+02, 2.976700e+02, 2.839400e+02, 2.683200e+02,
2.591500e+02, 2.585400e+02, 2.553100e+02, 2.498600e+02,
2.461800e+02, 2.429600e+02, 2.360200e+02, 2.357800e+02,
2.252700e+02, 2.240800e+02, 2.223800e+02, 2.215600e+02,
2.191300e+02, 2.189300e+02, 2.076600e+02, 1.994800e+02,
1.969900e+02, 1.746300e+02, 1.645000e+02, 1.635700e+02,
1.622000e+02, 1.596000e+02, 1.476200e+02, 1.405200e+02,
1.297500e+02, 1.290700e+02, 1.269100e+02, 1.263900e+02,
1.249000e+02, 1.230400e+02, 1.209200e+02, 1.195200e+02,
1.164400e+02, 1.111200e+02, 1.023800e+02, 1.007200e+02,
1.000300e+02, 9.685000e+01, 9.321000e+01, 9.026000e+01,
8.602000e+01, 7.606000e+01, 7.286000e+01, 7.034000e+01,
6.442000e+01, 6.298000e+01, 6.043000e+01, 5.485000e+01,
4.970000e+01, 4.962000e+01, 4.680000e+01, 4.414000e+01,
4.398000e+01, 4.300000e+01, 4.249000e+01, 4.231000e+01,
4.203000e+01, 4.143000e+01, 4.100000e+01, 4.061000e+01,
3.951000e+01, 3.583000e+01, 3.388000e+01, 3.211000e+01,
3.083000e+01, 2.902000e+01, 2.756000e+01, 2.729000e+01,
2.634000e+01, 2.566000e+01, 2.446000e+01, 2.407000e+01,
2.201000e+01, 2.151000e+01, 1.219000e+01, 1.177000e+01],
[3.646087e+04, 2.441641e+04, 1.134599e+04, 1.103382e+04,
9.273380e+03, 7.084380e+03, 6.129630e+03, 5.809510e+03,
5.326770e+03, 5.089560e+03, 4.888160e+03, 4.690270e+03,
4.601590e+03, 4.295380e+03, 4.226980e+03, 4.170050e+03,
4.038530e+03, 3.825870e+03, 3.387150e+03, 3.423980e+03,
3.184090e+03, 2.747000e+03, 2.601440e+03, 2.352400e+03,
2.380420e+03, 2.344070e+03, 2.224600e+03, 2.182020e+03,
2.155060e+03, 2.129760e+03, 2.045260e+03, 2.049740e+03,
1.920320e+03, 1.942420e+03, 1.822040e+03, 1.759590e+03,
1.760930e+03, 1.718460e+03, 1.689380e+03, 1.626370e+03,
1.674170e+03, 1.570150e+03, 1.556500e+03, 1.494430e+03,
1.553650e+03, 1.508200e+03, 1.404750e+03, 1.433040e+03,
1.320700e+03, 1.377210e+03, 1.308820e+03, 1.250640e+03,
1.156920e+03, 1.160390e+03, 1.125640e+03, 1.030720e+03,
1.033170e+03, 1.024850e+03, 1.013160e+03, 1.006910e+03,
9.737700e+02, 1.000160e+03, 1.001370e+03, 9.625200e+02,
9.665300e+02, 9.954200e+02, 9.536700e+02, 9.364500e+02,
9.228900e+02, 9.128400e+02, 9.112000e+02, 8.793700e+02,
8.136600e+02, 8.385600e+02, 8.440000e+02, 8.231300e+02,
7.764600e+02, 7.644100e+02, 7.144100e+02, 7.146700e+02,
7.016700e+02, 6.682800e+02, 6.660800e+02, 6.700300e+02,
6.636400e+02, 6.919800e+02, 6.506500e+02, 6.208400e+02,
6.641400e+02, 6.707200e+02, 6.511000e+02, 6.444100e+02,
6.044600e+02, 5.723700e+02, 5.756300e+02, 5.623400e+02,
5.340400e+02, 5.386200e+02, 5.315100e+02, 5.187500e+02,
5.076300e+02, 4.986400e+02, 5.145000e+02, 5.056800e+02,
5.077300e+02, 4.841200e+02, 4.800800e+02, 4.534700e+02,
4.306600e+02, 4.031900e+02, 3.947600e+02, 3.888200e+02,
3.637700e+02, 3.722500e+02, 3.613900e+02, 3.471600e+02,
3.433600e+02, 3.364500e+02, 3.157300e+02, 3.104600e+02,
3.087300e+02, 2.849200e+02, 2.853400e+02, 2.590700e+02,
2.439600e+02, 2.595800e+02, 2.393500e+02, 2.394500e+02,
2.439200e+02, 2.364400e+02, 2.360200e+02, 2.271500e+02,
2.196900e+02, 2.240800e+02, 2.198700e+02, 2.130400e+02,
2.222900e+02, 2.168000e+02, 2.179900e+02, 1.994800e+02,
1.900500e+02, 1.643600e+02, 1.633000e+02, 1.608900e+02,
1.599500e+02, 1.584000e+02, 1.448500e+02, 1.397500e+02,
1.263100e+02, 1.273900e+02, 1.256100e+02, 1.191300e+02,
1.249000e+02, 1.210500e+02, 1.125800e+02, 1.175300e+02,
1.176900e+02, 1.086000e+02, 9.788000e+01, 1.007200e+02,
9.900000e+01, 9.685000e+01, 9.412000e+01, 9.026000e+01,
8.271000e+01, 7.606000e+01, 6.831000e+01, 6.937000e+01,
6.401000e+01, 6.166000e+01, 5.951000e+01, 5.548000e+01,
4.920000e+01, 4.657000e+01, 4.517000e+01, 4.365000e+01,
4.277000e+01, 4.200000e+01, 4.174000e+01, 4.164000e+01,
4.203000e+01, 4.143000e+01, 4.195000e+01, 3.998000e+01,
3.805000e+01, 3.583000e+01, 3.297000e+01, 3.158000e+01,
3.011000e+01, 2.989000e+01, 2.756000e+01, 2.691000e+01,
2.596000e+01, 2.566000e+01, 2.243000e+01, 2.358000e+01,
2.201000e+01, 2.151000e+01, 1.219000e+01, 1.177000e+01]]
RIp = [[ 99.27, 191.97, 365.84, 90.35, 212.05, 271.67, 80.55,
71.14, 93.73, 48.33, 199.29, 68.43, 147.77, 139.67,
89.96, 59.38, 134.24, 82.52, 140.3 , 273.98, 755.38,
111.22, 130.25, 272.72, 134.92, 231.25, 103.86, 112.82,
112.15, 56.31, 482.73, 93.89, 105.45, 191.54, 299.77,
276.96, 119.5 , 58.89, 244.59, 148.39, 112.28, 593.15,
90.2 , 89.24, 158.49, 175.58, 42.82, 165.3 , 845.84,
135.91, 153.93, 92.76, 58.27, 86.71, 124.23, 574.32,
249.63, 88.86, 104.64, 210.75, 61.82, 207.45, 118.87,
105.59, 193.09, 130. , 142.18, 137.71, 64. , 122.95,
141.22, 113.79, 150.12, 360.03, 100.27, 162.94, 115.39,
131.31, 127.04, 50.02, 173.76, 246.45, 107.3 , 127.25,
86.89, 69.9 , 142.67, 616.3 , 106.73, 127.17, 97.73,
94.94, 115.37, 55.02, 759.08, 282.18, 622.75, 116.26,
83.27, 117.99, 441.66, 120.06, 109.76, 210.99, 260.46,
187.72, 95.74, 173.29, 159.29, 122.37, 167.7 , 68.85,
90.11, 334.02, 305.74, 114.66, 156.3 , 188.23, 68.4 ,
295.47, 86.67, 631.55, 216.47, 689.58, 701.61, 69.41,
194.77, 233.46, 50.8 , 363.41, 44.54, 30.84, 182.97,
146.01, 235.51, 67.93, 105.96, 224.2 , 145.76, 96.7 ,
160.09, 256.83, 240.02, 138.9 , 46.52, 128.23, 373.23,
115.26, 208.97, 188.09, 252.86, 303.93, 69.86, 57.78,
966.67, 139.54, 148.98, 468.61, 1779.62, 267.86, 109.04,
253.42, 148.56, 176.16, 278.77, 151.44, 469.13, 151.17,
123.51, 274.48, 114.99, 39.55, 90.77, 234.62, 125.87,
60.76, 504.62, 124.94, 102.15, 589.2 , 159.82, 290.07,
409.97, 50.95, 280.37, 46.48, 20.88, 111.11, 65.81,
133.59, 514.93, 61.97, 45.16, 114.52, 21.82, 534.35,
91.94, 314.1 , 54.79, 148.44],
[ 96.37, 187.61, 348.28, 87. , 204.05, 259.65, 80.55,
70.08, 91.78, 47.07, 194.9 , 66.27, 145.72, 133.85,
87.33, 58.09, 132.65, 81.87, 136.44, 272.08, 740.46,
106.61, 130.25, 258.63, 132.64, 228.3 , 102.29, 109.98,
112.15, 56.31, 470.12, 93.22, 100.81, 192.85, 283.19,
272.13, 118.29, 58.04, 238.9 , 141.17, 111.06, 575.99,
87.36, 83.78, 156.87, 174.68, 41.51, 164.2 , 801.98,
137.88, 152.93, 92.29, 57.26, 88.43, 124.23, 553.39,
247.94, 87.72, 104.12, 211.37, 60.71, 209.42, 120.36,
103.05, 190.35, 132.59, 142.18, 137.71, 64. , 122.95,
142.02, 114.87, 140.74, 350.45, 99.04, 160.59, 113.23,
130.39, 123.25, 49.7 , 171.63, 235.59, 103.88, 125.12,
84.98, 71.76, 139.19, 581.7 , 107.78, 129.93, 97.73,
94.01, 115.37, 53.46, 747.54, 279.96, 591.14, 114.68,
83.27, 115.24, 424.52, 113.53, 107.19, 203.4 , 253.61,
179.31, 95.74, 171.73, 158.42, 121.2 , 164.71, 68.02,
85.76, 331.47, 295.08, 112.71, 153.92, 184.68, 65.93,
284.89, 87.54, 604.49, 217.54, 665.8 , 660.48, 69.69,
182.59, 223.73, 50.33, 353.66, 44.54, 29.71, 178.43,
146.01, 232.86, 65.32, 107.49, 222.02, 149.15, 96.7 ,
154.45, 241.72, 238.27, 136.63, 45.87, 127.26, 366.24,
114.63, 203.42, 185.65, 250.28, 286.46, 69.86, 56.84,
900. , 137.21, 150.58, 457.96, 1701.39, 267.86, 107.91,
253.42, 150. , 176.16, 268.05, 151.44, 439.81, 149.08,
122.71, 268.77, 113.24, 40. , 89.85, 220.19, 121.5 ,
60.07, 490.73, 122.03, 100.34, 579.92, 159.82, 290.07,
419.51, 50.16, 269.99, 46.48, 20.31, 109.26, 64.28,
137.64, 514.93, 61.1 , 44.52, 114.52, 20. , 523.52,
91.94, 314.1 , 54.79, 148.44]]
```Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.