Risk Management Review

Risk Management Review

A disciplined, repeatable methodology for reviewing the risk of a portfolio, trading strategy, or single position — before sizing it, while running it, or when stress hits. It answers four questions, in order:

1. What is the loss distribution? (volatility, skew, fat tails, drawdown profile)
2. How big should the position(s) be? (Kelly, fractional Kelly, vol-targeting, Optimal f)
3. What is the right risk-adjusted return metric? (Sharpe / Sortino / Calmar / UPI — not raw return)
4. How does the portfolio fail? (concentration, correlation, regime, leverage, liquidity, tail)

The output is a blunt verdict banner, a numeric risk dashboard, a sizing review, a stress-test table, and concrete recommendations — backed by formulas the user can re-run.

Honest scope and limits. I reason over what you provide (returns series, positions/weights, leverage, scenario inputs). Without numbers, output is qualitative. Risk metrics describe history and assumed distributions — they do not predict the next regime shift. Not financial advice; size below your pain threshold.

When to Activate

Activate when the user:

• Asks "is this position too big?" or "how much should I risk on this trade?"
• Shares a returns series and asks for risk metrics (Sharpe, Sortino, MDD, VaR, ES).
• Wants a portfolio risk review ("am I diversified?", "what's my real downside?").
• Mentions any of: Kelly · fractional Kelly · vol targeting · drawdown · MDD · VaR · CVaR · Expected Shortfall · Sharpe · Sortino · Calmar · Ulcer Index · risk-of-ruin · position sizing · leverage cap · concentration · stress test · reverse stress test · risk parity · Optimal f.
• Wants to institutionalize a risk policy (single-name cap, factor cap, drawdown stop, leverage cap) for a fund / personal book / trading desk.

Step 1: Intake & Scope

Pin down what is being reviewed and what inputs you have before computing anything. A risk number without scope is theatre.

1. What is being reviewed?
   • (A) Single position — one symbol / one trade. Sizing is the dominant question.
   • (B) Strategy — a rule-set with a returns series (live or backtest). Risk-adjusted return + drawdown + tail are dominant.
   • (C) Multi-asset portfolio — multiple positions, possibly leveraged. Concentration + correlation + stress are dominant.
2. What inputs are available?
   • Returns series (daily / weekly / monthly): needed for σ, σ_d, MDD, UI, VaR, ES, Sharpe, Sortino, Calmar, UPI.
   • Positions / weights (per name): needed for concentration, top-N share, sector/factor exposure.
   • Leverage (gross and net): needed for risk-of-ruin and margin checks.
   • Pairwise correlations (or factor exposures): needed for "ρ → 1" stress.
   • Scenario inputs (vol shock, rate shock, liquidity haircut): for stress tests.
3. Capital, benchmark, risk policy.
   • NAV (so percentages map to dollars).
   • Benchmark (SPY / 60-40 / risk-free): so we can compute Information Ratio when relevant.
   • Existing risk policy (single-name cap, factor cap, leverage cap, max drawdown stop) — if absent, flag it as a Step-8 red flag.
4. Horizon and regime.
   • Holding period (intraday / daily / monthly).
   • Realized regime over the returns window (bull / bear / low-vol / crisis) — a 2017-only sample is not a risk model.

Do not proceed to a verdict until you know what is being reviewed, what inputs exist, and what the existing risk policy (if any) is.

Step 2: Loss Distribution & Metrics

Compute (or explain how to compute) every metric below. Use the formulas verbatim — the user should be able to re-run them.

Volatility & dispersion

• Standard deviation σ = sqrt( mean( (r_t − r̄)² ) ) — total dispersion; symmetric (treats upside = downside).
• Downside deviation σ_d = sqrt( mean( min(r_t − MAR, 0)² ) ) — only returns below the minimum acceptable return (often 0 or the risk-free rate) count. Used by Sortino.

Drawdown family

• Max drawdown MDD = max_t (peak_t − value_t) / peak_t — the single number every retail trader should know.
• Average drawdown — mean of all drawdown episodes (each counted from peak to recovery).
• Drawdown duration — peak → trough → recovery in calendar time. A long flat -20% is often more painful than a fast -30% that recovers in a month; track duration, not just depth.
• Ulcer Index (Peter Martin, 1987): UI = sqrt( mean( drawdown_t² ) ) over the period. Captures depth × time underwater in one number — penalises sustained underwater periods.

Tail risk

• VaR_α — the loss that is not exceeded with confidence α. "95% daily VaR = $X" means the worst 5% of days lose at least $X. Computable via historical sim, parametric (normal), or Monte Carlo. VaR is NOT subadditive — combining two portfolios' VaRs can give the wrong answer.
• CVaR / Expected Shortfall ES_α = E[ loss | loss ≥ VaR_α ] — the average loss in the worst (1 − α) of cases. Coherent (subadditive, monotonic, translation-invariant, positive-homogeneous). Basel III moved banks from VaR to ES_97.5 — prefer ES for portfolio decisions.
• Risk of ruin — probability the equity curve hits a fatal threshold. Closed form exists for IID Bernoulli trades; otherwise simulate.
• Tail / kurtosis check — empirical returns are fat-tailed, not normal, almost always. Parametric-normal VaR therefore systematically understates tail loss. If you must use it, call out the assumption and cross-check against historical/ES.

Output these as a dashboard table (Step 9), not prose.

Step 3: Risk-Adjusted Return

Never quote raw return. Always pair it with one of these — and pick the one that matches the strategy shape.

Patterns that should make you suspicious

• Sharpe > 3 on a non-HFT strategy → likely over-fit, illiquidity smoothing, or hidden tail (short-vol). Treat as red flag, not a feature.
• Autocorrelated daily returns — inflates Sharpe artificially; check via the autocorrelation of r_t (a daily ρ of 0.2+ is suspicious for liquid markets).
• Sortino << Sharpe → the upside is the source of "return" (e.g. selling vol / picking up nickels in front of a steam roller). Drawdowns are larger than the symmetric vol implies.
• Calmar high but UPI low → the strategy avoided one giant DD but spends long stretches underwater (a slow bleed); investors will redeem.

Multiple-testing. If the strategy was selected from many candidates, Sharpe overstates skill. Cross-link the Viprasol trading-strategy-review skill to compute Deflated Sharpe (Bailey & López de Prado) and Probability of Backtest Overfitting before trusting the headline number.

Step 4: Position Sizing Review

What method is being used? Apply the right formula; flag missing or arbitrary sizing as a Step-8 red flag.

Kelly criterion

• Discrete bet with edge e and net odds b: f* = e / b.
• Continuous returns (the practical form):

  f* = (μ − r) / σ²
  

  where μ = expected return, r = risk-free rate, σ² = return variance.
• Why Kelly maximises long-run growth — and why pure Kelly is too aggressive in practice: parameter-estimation error (μ and σ are estimated, not known) → systematic over-sizing → catastrophic drawdowns when reality rhymes differently than the sample. Kelly also assumes IID stationary returns; real markets shift regime.
• Half-Kelly / quarter-Kelly is the practitioner default. Halving f* approximately halves volatility while keeping most of the geometric growth.

Volatility targeting

• Choose a target portfolio vol (e.g. 10–15% annualised). Size each position so its risk contribution matches the budget:

  notional_i = (target_vol × NAV) / σ_i
  

• Used by every CTA, risk-parity manager, and most multi-strat books — it turns regime-vol changes into stable risk contributions instead of stable dollars.

Risk parity (limits)

• Equal risk contribution, not equal weight: w_i × σ_i × ρ_{ip} = const. Works when correlations are stable; fails badly in crisis when everything correlates → 1.

Optimal f (Vince)

• Maximises geometric growth on the actual P&L distribution (not an assumed Gaussian). Closer to "empirical Kelly" — better than naive Kelly when payoffs are highly non-binary (options strategies, lumpy event trades).

Output of this step

State the current sizing method (or "gut-feel — none documented" if so), the recommended sizing, and the constraint that should bind (the lower of half-Kelly, vol-target sizing, and the single-name cap from Step 5). Show the numbers.

Step 5: Concentration, Correlation & Leverage

Sizing is necessary but not sufficient — a properly-sized but concentrated portfolio still blows up.

• Single-position cap — practitioner default: 5–10% of NAV per single position. Tighter (1–3%) for illiquid names. >10–15% on one name = flag.
• Sector / factor concentration — sum exposures to any one factor (tech, oil, US-rates duration, EM-FX, momentum) and apply a hard cap. A "diversified" book of 8 tech names is one position.
• Top-N concentration — top-3 holdings > 40% of NAV = flag, regardless of vol; reads as "if any one of these breaks, the book breaks."
• Pairwise correlation stress — assume ρ → 1 in crisis for all risk-on assets and recompute portfolio vol. If realized vol explodes, the book is a single bet dressed up as diversification.
• Leverage — gross (sum of absolute exposures) vs net (long − short). Practitioner reads:
  • gross > 2× equity = elevated (intraday stops mandatory),
  • gross > 3× without stops = flag,
  • gross > 4× = institutional / margin-call territory (one bad day kills the fund).
• Liquidity — position size as a % of average daily volume (ADV). >1 ADV = "can't exit in one day at quoted prices"; price-of-exit is part of the risk model.

Step 6: Stress-Test Catalog

Apply at least 3 historical scenarios and 2 hypotheticals plus a reverse stress test. Report portfolio P&L per scenario, in dollars and as a percent of NAV.

Historical replays (apply each book to the move)

• 1987-Oct ("Black Monday") — SPX -22% in a day.
• 2008-Sep–Nov ("GFC") — SPX peak-to-trough ≈ -45%, credit spreads ×3, funding markets frozen, gold up, treasuries up.
• 2020-Mar ("COVID crash") — SPX -34% in 22 trading days, IG spreads ×3, HY ×4, oil briefly negative, VIX > 80, correlations → 1.
• 2022 bond rout — bonds and equities down together; 60-40 had its worst year since the 1930s.
• 2023-Mar ("SVB") — regional-bank stress, 2-yr UST fastest move in decades, repricing of duration.

Hypotheticals

• +1σ vol shock — multiply realised σ by ~1.7× (one standard deviation up on a vol-of-vol basis); does the leverage cap still hold?
• -10% equity / +200bp rates instant — concurrent shock to both legs.
• Correlation → 1 — every "diversifier" moves with risk; recompute portfolio vol on a correlation matrix of ones.
• 50% liquidity haircut — every exit price halves the bid; how big is the gap between mark and exit?

Reverse stress test

Ask the inverse question: what move kills the book? Solve for the combination of equity shock + vol shock + correlation shock + liquidity shock that drives the portfolio to a fatal drawdown (e.g. -50%). If the answer is "3% intraday on SPX", the book is too levered. If the answer is "1987 + 2008

• 2020 all at once and twice as big", it is robust.

Step 7: Risk-of-Ruin

Make the asymmetry explicit. Drawdown recovery is multiplicative, not additive.

required gain to recover from a drawdown of d  =  1 / (1 − d) − 1

  -25%  →  +33.3%
  -50%  →  +100%
  -75%  →  +300%
  -80%  →  +400%
  -90%  →  +900%

Asymmetry kills compounders. A strategy that compounds at 15% for ten years and gives back 80% in year eleven is a worse outcome than one that compounds at 6% with no -80% event.

Risk-of-ruin is high whenever sizing or leverage make a fatal drawdown a plausible path, not a tail. Triggers to call this out explicitly:

• Single position > 20% of NAV with σ_i > 50% annualised.
• Pure-Kelly (not fractional) sizing.
• Gross leverage > 3× without intraday stops.
• A stress-test row in Step 6 produces > -40% portfolio P&L.

Compute, when given the inputs, the probability of breaching a drawdown threshold (e.g. -50%) over the holding horizon — via the closed-form ruin formula for IID trades or a quick Monte Carlo.

Step 8: Red-Flag Quick Scan

Any one of these moves the verdict toward 🟠 / ⛔.

• Sharpe > 3 on a non-HFT strategy → over-fit or hidden tail.
• Single position > 10–15% of NAV.
• Top-3 positions > 40% of NAV.
• MDD < 5% on 6+ months of live data → fat-tail risk hidden (likely a short-vol / sell-tail payoff).
• Leverage gross > 3× without intraday stops.
• Undefined max loss / no stop / no position cap in the strategy doc.
• "Sizing by gut-feel" — no Kelly, vol target, or fixed-fractional rule documented.
• Correlation → 1 in stress ignored — book is implicitly one factor.
• Sortino << Sharpe — upside is the source of "return"; downside fat-tail hidden.
• Parametric-normal VaR on fat-tailed returns — VaR systematically understates; pair with ES_97.5 and historical sim.
• No drawdown duration tracked — only depth. Long flat losses get under investors' skin.

Step 9: Output Format — the Risk Report

Lead with a verdict banner, then the dashboards, the sizing review, the stress-test table, the risk-of-ruin call-out (when relevant), the recommendations, and the disclaimer.

Verdict banner (pick one)

• ✅ WITHIN RISK POLICY — caps respected, sizing methodical, stress tests within tolerance, no red flags.
• 🟡 CAUTION — within caps but one or two yellow flags (concentration creep, high but not fatal leverage, missing reverse stress test, Sortino noticeably below Sharpe).
• 🟠 OVER-RISK — at least one hard cap breached (single-name > 15%, top-3 > 40%, gross > 3× without stops, MDD path > 30% in stress). Reduce before doing anything else.
• ⛔ LIKELY-RUIN PATH — sizing or leverage make a fatal drawdown a plausible path, not a tail (pure Kelly + 3×, all-in one factor, stress row

  -40%). Cut size now.

Follow the banner with one sentence explaining why.

Risk dashboard

Position dashboard

Sizing review

State the current method (or "none — gut-feel"), the Kelly / half-Kelly / vol-target recommended sizes (with formulas and plugged-in numbers), the binding cap, and the recommended size in dollars and % NAV.

Stress-test table

Risk-of-ruin call-out (when triggered)

State the path, the recovery math (+X% needed to recover -Y%), and the probability of breaching the user's drawdown threshold over the horizon if a closed-form or quick Monte Carlo gives it.

Recommendations

Concrete and numbered. Examples:

1. Cut single-name X from 18% → 8% (single-name cap).
2. Replace 3× ETF with the underlying to remove embedded leverage.
3. Add a tail hedge: SPX 5-delta puts, 1% of NAV per month.
4. Cap gross leverage at 2× with an intraday -2% NAV hard stop.
5. Switch sizing from gut-feel to vol-target 12% annualised with a half-Kelly override per position.

Disclaimer (always include)

Educational risk-management guidance — not financial, legal, or investment advice, and not a guarantee of safety. I reason only over the data you provide; without numbers, output is qualitative. Risk metrics describe history and assumed distributions; they do not predict the next regime shift. Risk-of-ruin is real — size below your pain threshold. Markets do things that have never happened before. Consult a qualified risk or investment professional for live decisions.

Related Viprasol Skills

• trading-strategy-review — backtest failure-modes (look-ahead, overfitting, survivorship, slippage) and Deflated Sharpe / PBO. Pair with this skill before trusting a headline Sharpe.
• options-strategy-analyzer — Greeks, payoff diagrams, and closed-form max-loss / max-profit / break-even for defined-risk option structures. Use before plugging an options strategy's σ and DD into this review.

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