Paper Trader — fable

Symbol	Market Value	Unrealized
AMD	$13,064	+11.18%
MU	$12,905	+9.83%
SMH	$12,076	+2.77%
CAT	$11,608	-1.21%
MRK	$11,420	-2.81%
XBI	$11,355	-3.36%
AMAT	$11,165	-4.98%
LLY	$10,648	-9.38%
BIL	$3,495	-0.15%

FRTB Capital · standardised approach · 2026-09-10

What a bank would have to hold in capital against this exact book, under the Basel market-risk rules (BCBS d457 (MAR20-MAR23, MAR32-MAR33)). Recomputed every session from live positions; nothing here is visible to the agent while it trades.

Capital requirement

$40,584

SbM + DRC + RRAO

Of equity

40.5%

capital / portfolio value

Market-risk RWA

$507,301

capital × 12.5

Overstated. 3 name(s) (BIL, SMH, XBI) could not be classified from reference data and fell to the "other sector" bucket at a 70% risk weight — the regulation's own fail-closed rule. The number above is safe-direction wrong.

Components, buckets, and why DRC is the interesting line

Component	Charge	Share
SbM delta · high correlations bind	$25,924	63.9%
SbM vega · no optionality in the book	$0	0.0%
SbM curvature · linear payoff	$0	0.0%
DRC — jump to default · LGD 100%	$14,660	36.1%
RRAO · no exotic underlyings	$0	0.0%
Total capital requirement	$40,584	100%

Equity buckets · MAR21.72

Bucket	Risk weight	Names	Net value	K_b
11	70%	BIL, SMH, XBI	$26,924	$18,847
8	50%	AMAT, AMD, MU	$37,133	$13,679
5	30%	LLY, MRK	$22,068	$5,365
6	35%	CAT	$11,607	$4,063

Why the second-biggest line is the interesting one. The DRC is jump-to-default: the issuer disappears overnight. Equity has no recovery, so Basel sets loss-given-default at 100% and charges an unrated name 15% of its market value — 36% of the requirement here, and nothing about hedging, forecasting or diversification reduces it. That the high correlation scenario binds is itself a readout: a long-only book is dearest when correlations rise, a hedged one when they fall.

Value at Risk · historical simulation · 2026-09-10

The loss this book exceeds on the worst few days in a hundred, measured by replaying 501 days of its own constituents' returns through today's positions. Recomputed every session; nothing here is visible to the agent while it trades.

VaR 99% · 1 day

$5,298

worst 1 day in 100

Of equity

5.29%

loss / portfolio value

ES 97.5%

$4,873

average of the tail beyond

VaR 99% · 10 day

$12,416

regulatory horizon

Quantiles, component VaR, the backtest, and what VaR will not tell you

Confidence	Historical	Of equity	Parametric	Gap	Tail pts
95%	$2,876	2.87%	$3,143	−8.5%	25
99%	$5,298	5.29%	$4,445	+19.2%	5
ES 97.5%	$4,873	4.86%	the average of the tail, not its edge

Why the 10-day figure is measured, not scaled. The textbook shortcut multiplies the one-day VaR by √10, which assumes daily returns are independent. Here that gives $16,754 against a measured $12,416 — 34.9% too high. Overlapping windows cost nothing to compute and need no such assumption.

Component VaR · at 99% · sums to the total

Name	Market value	Weight	Component	Share
MU	$12,904	13.2%	$1,147	25.8%
AMD	$13,064	13.4%	$951	21.4%
AMAT	$11,165	11.4%	$732	16.5%
SMH	$12,072	12.4%	$623	14.0%
CAT	$11,607	11.9%	$440	9.9%
XBI	$11,364	11.6%	$278	6.2%
LLY	$10,651	10.9%	$168	3.8%
MRK	$11,420	11.7%	$106	2.4%
BIL hedge	$3,495	3.6%	−$0	−0.0%

These are allocations, not a ranking. Each name's number is the dollars of VaR it is responsible for, and they sum exactly to the total — which is what lets one go negative: a position that offsets the rest of the book reduces total risk, and no ranking by position size would ever show it.

The part that makes it a measurement. Over 251 out-of-sample days the 99% threshold was breached 4 time(s) against 2.5 expected — Kupiec p = 0.384, verdict consistent with the model, Basel traffic light green. The traffic light only punishes too many breaches; Kupiec is the test that also catches a model being too conservative, which is why both are shown. Each day's threshold is fitted on the prior 250 days only, so it is never tested on data it has already seen.

Two different questions. Everything above shocks today's positions with market history. The account's own equity curve — 20 sessions, 13.5% annualised volatility — says what it has actually done: 95% VaR 2.00% · 99% VaR 2.00%. They diverge whenever the agent has been trading.

What VaR will not tell you. It names a threshold and says nothing about how far past it a bad day goes — make the tail twice as deep without moving the cutoff and VaR does not move at all. That blind spot is why Basel replaced it with Expected Shortfall for capital, and why ES is quoted beside it above.

Counterparty Risk · SA-CCR · 2026-09-10

Market risk is symmetric — the price moves, you win or you lose. Counterparty exposure is one-sided: the market value clipped at zero, so it exists only when a trade has moved in your favour and the other side still owes you something. A fully-paid share bought on an exchange has none of that. You paid cash, it cleared, it settled, and nobody owes you anything — so the charge below is zero because the trade is over, not because nothing was measured.

SA-CCR EAD

α × (RC + PFE) · 0 derivative(s)

CVA capital

spread risk, not default

Settlement in flight

T+1

Custodial concentration

100%

one broker, everything

The derivation: SA-CCR terms, what was excluded, settlement, leverage and concentration

SA-CCR term	Value
Derivative trades in the netting set	0
Replacement cost · max(V − C, 0)	$0
Add-on aggregate · supervisory factors	$0
PFE multiplier · floored at 5%	1.0000
PFE · multiplier × add-on	$0
α · CRE52.1	1.4
Exposure at default	$0
CVA capital · CRE55, BA-CVA reduced	$0

Why · what never reaches SA-CCR

Kind	Positions	Market value	Reason
cash equity long	9	$97,742	fully-paid long share: bought for cash, centrally cleared and settled — no open obligation, so no counterparty exposure

Settlement is the one that is genuinely live. US equities settle T+1, so a fill from this session is a commitment against a leg that has not been delivered yet: $0 in flight, $0 past due, capital charge $0. Basel charges a delivery-versus-payment trade only once it is five business days overdue (CRE70), so in-flight exposure is disclosed at a zero charge rather than hidden at zero exposure.

Leverage · capability vs utilisation

Provisioned	Margin debit	Short value	Gross	Net
4× · shorting on · options L3	$0	$0	0.98×	0.98×

Fully funded. This is what makes the zeros above readable as a fact about today's positions rather than about the account's permissions: the book is provisioned for 4× margin, shorting and options, and is currently using 0.0% of the first and 0.0% of the second. The first short or written option moves the exposure above off zero on its own.

The counterparty that does exist. Alpaca (paper) holds $2,500 of cash and $97,742 of securities — 100% of the book, by construction. Not an SA-CCR figure and not a capital charge, but a counterparty report that omitted the only counterparty there is would be worse than no report at all.

What this is really measuring. Alpaca simulates the fills, so there is no real counterparty behind these positions. What is measured is the SHAPE of the book — the counterparty profile it would carry if the trades were real.

2026-09-09 $101,911.08 — 0 trades