A portfolio’s dollar description and its risk description are different
objects. This note takes one hypothetical long/short book, ten large caps in the
US, six long and four short, gross 100% and net +30%, and decomposes it the way a
multi-manager risk desk decomposes a new manager’s positions. Weights are
constant and rebalanced daily; the daily return is regressed on the
Fama–French five factors plus Carhart momentum with Newey–West
standard errors.
Three things the dollars hide. Net exposure of +30% carries a realized market
beta of 0.56, roughly 1.9× the direction those dollars imply, because every
short is a low-beta defensive. NVDA is 16.0% of gross and 41.3% of variance, so a
book that counts as nine effective bets by dollars is far narrower by risk. And
61.4% of daily variance is factor, led by an Investment (CMA) beta of
−0.50, long aggressive growth against short conservative payers; that is a
style bet in the coat of a stock picker.
Sample, method and fit.
Measure
Value
Regression sample
5,405 trading days, 2005-01-04 to 2026-06-30
Model
Fama–French five factors plus Carhart momentum, Newey–West standard errors
Gross exposure (all position sizes, either side)
100% of capital
Net exposure (longs minus shorts)
+30% of capital
Variance explained by the six factors
61.4%
Idiosyncratic variance (specific to individual stocks)
38.6%
Residual alpha, annualized, in sample
+9.7%
t-statistic on residual alpha
4.49
Risk contribution method
annualized covariance of the positions
Value-at-risk sample
5,433 daily returns, historical simulation over one day, percent of capital
Stress method
realized returns compounded at constant weights across each window
The portfolio
Table 1. The portfolio: ten positions by side and weight.
Ticker
Side
Weight (% NAV)
NVDA
Long
16.0%
AAPL
Long
13.0%
MSFT
Long
12.0%
GOOGL
Long
9.0%
AMZN
Long
8.0%
JPM
Long
7.0%
XOM
Short
−9.0%
KO
Short
−9.0%
PG
Short
−9.0%
DUK
Short
−8.0%
Gross 100% · Net +30%
6 long / 4 short
10 names
Factor decomposition
Table 2. Factor exposures (the Fama–French five factors plus momentum).
Exposure
Book beta
Market (Mkt-RF)
+0.56
Size (SMB)
−0.03
Value (HML)
−0.17
Profitability (RMW)
−0.13
Investment (CMA)
−0.50
Momentum (Mom)
+0.03
Reading each exposure: intended or not.
Exposure
Beta
What it is
Verdict
Market (Mkt-RF, the market return minus the risk-free rate)
+0.56
The shorts are defensives with low beta, so netting dollars did not net out direction; about 1.9× more directional than the net book implies
Unintended
Investment (conservative minus aggressive, CMA)
−0.50
Long tech among the mega caps, with heavy reinvestment, funded by short conservative payers. A style bet, not stock selection
Unintended
Value (high minus low, HML)
−0.17
Net short value, long growth. A style bet, not stock selection
Unintended
Profitability (robust minus weak, RMW)
−0.13
Mildly short quality; the shorts are the profitable defensives. A style bet, not stock selection
Unintended
Size (small minus big, SMB)
−0.03
Negligible; both sides of the book are large caps, so the book is correctly size neutral
Intended (clean)
Concentration
Table 3. Concentration and volatility metrics.
Metric
Value
Largest position
NVDA at 16.0% of gross
Herfindahl (HHI, normalized by gross)
0.11
Effective number of bets (1/HHI)
9.3
Annualized book volatility
15.6%
Largest risk contributor
NVDA at 41.3% of variance
Table 4. Dollar weight versus risk contribution, by name.
Name
Dollar weight (% gross)
Share of risk
NVDA
16.0%
41.3%
AAPL
13.0%
18.6%
MSFT
12.0%
14.6%
AMZN
8.0%
13.0%
GOOGL
9.0%
12.0%
JPM
7.0%
7.7%
DUK
8.0%
−0.7%
KO
9.0%
−1.6%
PG
9.0%
−1.7%
XOM
9.0%
−3.2%
Loss
Value-at-risk is the loss exceeded on only 1% (or 5%) of days; expected
shortfall is the mean loss on the days that breach it.
Table 5. Historical value-at-risk and expected shortfall over one day.
Confidence
VaR over 1 day
Expected Shortfall over 1 day
99%
2.67%
3.29%
95%
1.57%
2.24%
Table 6. Historical stress windows.
Scenario
Window
Book return
Days
Worst single day
2008-09-29
−7.0%
1
Mean of 10 worst market days
2005–2026
−3.3%
10
Global Financial Crisis
2008-09-01 → 2008-12-31
−19.0%
85
COVID crash
2020-02-19 → 2020-03-23
−4.8%
24
The two crisis windows read against each other. The book gave back only
−4.8% peak-to-trough in the COVID crash because its low-beta shorts fell
alongside its longs; the −19.0% Global Financial Crisis loss is the same
hidden market beta biting once the shorts stopped hedging.
Fixes
Findings and remedies.
Issue
What the record says
Fix
Hidden market beta
0.56 market beta on +30% net dollars, roughly 1.9× more directional than the net book suggests, because every short is a defensive with low beta
Size to a beta target rather than a dollar target, substituting shorts with higher beta or overlaying an index short until realized beta matches the intended net
Risk concentrated in one name
NVDA is 16.0% of gross dollars but 41.3% of portfolio variance; 9.3 effective bets by dollars, far fewer by risk
Cap the risk contribution of a single name, not only its weight, trimming NVDA or adding an offsetting position
A style bet in the coat of a stock picker
Only 38.6% of daily variance is idiosyncratic; 61.4% is the six factors, led by an Investment (CMA) beta of −0.50
Neutralize the CMA/growth tilt if the thesis is selection of single names, or own it deliberately as the strategy and budget risk to it
What this does not claim
The book is hypothetical and illustrative, constructed to be taken apart
rather than traded, and is neither a real position nor a recommendation. Its
universe is large caps that are survivors today, so the history carries hindsight
about which names lived. Every in-sample figure, the residual alpha above all, is
an upper bound rather than a forecast, measured on the same data the model was
fitted to.
The teardown is the product. A book’s net exposure is easy
to quote; the work is showing that +30% net dollars carry a 0.56 market beta,
that 16.0% of gross is 41.3% of the risk, and that a book billed as stock
selection is 61.4% factor by variance.
References
Carhart, M. M. (1997). On Persistence in Mutual Fund Performance.
Journal of Finance, 52(1), 57–82.
Fama, E. F., and French, K. R. (2015). A Five-Factor Asset Pricing Model.
Journal of Financial Economics, 116(1), 1–22.
Newey, W. K., and West, K. D. (1987). A Simple, Positive Semi-Definite,
Heteroskedasticity and Autocorrelation Consistent Covariance Matrix.
Econometrica, 55(3), 703–708.
