Financial Risk Manager (FRM) Current Issues and Investment Risk Syllabus

Define the Sortino ratio and the Information ratio.

Sortino ratio: $\dfrac{E[R_p]-T}{\sigma_{\text{down}}}$, excess return over a target $T$ per unit of downside deviation. Information ratio: $\dfrac{E[R_p]-E[R_b]}{\text{TE}}$, active return over benchmark $b$ per unit of tracking error TE, measuring consistency of active management skill.

How do the standard '2 and 20' hedge fund fees, with high-water marks, create convexity in manager incentives?

With a 2% management fee plus 20% performance fee, the incentive fee resembles a call option on fund assets: the manager shares gains but not losses. This convex payoff (long an option) rewards volatility, incentivizing risk-taking, especially when far below the high-water mark or when seeking to recover.

What is a high-water mark and how does it affect risk-taking incentives?

A high-water mark is the peak NAV above which a manager must recover before earning new performance fees. After large losses, a fund deep below its high-water mark earns no incentive fee until recovery, which can encourage either excessive risk-taking ('gambling for resurrection') or closing the fund.

Why does the optionality of performance fees represent a 'convexity of incentives' problem for investors?

Because the manager holds option-like upside without symmetric downside, their optimal risk level exceeds the investor's. The convex (option) payoff means higher volatility raises expected fees, misaligning incentives; investors bear the full downside while managers capture a fixed share of the upside.

Why is valuation of illiquid alternative assets (private equity, real estate) prone to smoothing, and what is its effect on measured risk?

Infrequent, appraisal-based (stale) pricing causes reported returns to be serially correlated and smoothed. This artificially lowers measured volatility and correlation with public markets, overstating risk-adjusted performance (e.g., Sharpe ratios) and understating true market risk and tail exposure.

How can return smoothing in illiquid assets be detected, and how is volatility corrected?

Smoothing shows up as significant positive first-order autocorrelation in reported returns. An unsmoothing model (e.g., Geltner/Getmansky) recovers true returns; for an AR(1) with coefficient $\rho$, true variance is understated and the smoothed-to-true volatility relationship implies the reported $\sigma$ must be scaled up to reflect actual risk.

Distinguish physical climate risk from transition climate risk.

Physical risk is financial loss from climate-driven events: acute (storms, floods, wildfires) and chronic (sea-level rise, heat, drought) damaging assets and operations. Transition risk is loss from the shift to a low-carbon economy: policy/carbon pricing, technology change, market shifts, and reputation, which can strand high-carbon assets.

What are stranded assets in the context of transition climate risk?

Assets (e.g., fossil-fuel reserves, coal plants, carbon-intensive infrastructure) that suffer unanticipated or premature write-downs, devaluations, or conversion to liabilities because of the transition to a low-carbon economy through policy, technology, or demand changes before the end of their expected economic life.

What are the three categories of greenhouse-gas emissions used in climate risk disclosure?

Scope 1: direct emissions from owned/controlled sources. Scope 2: indirect emissions from purchased electricity, steam, heating/cooling. Scope 3: all other indirect emissions across the value chain (suppliers, product use, financed emissions), typically the largest and hardest to measure.

What does the term 'operational resilience' mean and how does it differ from traditional operational risk management?

Operational resilience is a firm's ability to prevent, adapt to, respond to, recover from, and learn from operational disruptions while continuing to deliver critical services within impact tolerances. Unlike traditional control-focused operational risk management, it assumes disruptions will occur and centers on continuity of important business services.

What is cyber risk classified as under Basel, and what makes it distinctive?

Cyber risk is a subset of operational risk (people, processes, systems, external events). It is distinctive for its potential to be systemic and highly correlated, fast-propagating, intentional/adversarial (active threat actors), difficult to quantify due to sparse loss data, and capable of producing severe tail losses and contagion across interconnected firms.

Define geopolitical risk and give examples of how it transmits to portfolios.

Geopolitical risk is the risk of adverse financial impact from political tensions, conflicts, sanctions, trade wars, and regime changes. Transmission channels include commodity and energy price shocks, currency and capital-flow volatility, sanctions/asset freezes, supply-chain disruption, and sudden repricing of country and credit risk.

How does supply chain disruption translate into financial and operational risk for firms?

Disruptions (pandemics, conflict, natural disasters, chokepoints) cause input shortages, production halts, inventory and working-capital strain, margin compression from cost spikes, lost revenue, and concentration risk when reliant on single suppliers or regions; they can cascade through interconnected firms, raising credit and earnings risk.

In machine learning, distinguish supervised, unsupervised, and reinforcement learning.

Supervised learning maps inputs to known labeled outputs (regression, classification). Unsupervised learning finds structure in unlabeled data (clustering, dimensionality reduction, anomaly detection). Reinforcement learning trains an agent to take actions maximizing cumulative reward through trial-and-error interaction with an environment.

What is the bias-variance tradeoff in machine learning, and how does it relate to overfitting?

Total expected error decomposes as $$E[(y-\hat{f})^2] = \text{Bias}^2 + \text{Variance} + \sigma^2_{\text{noise}}.$$ High bias (too simple) underfits; high variance (too complex) overfits, fitting noise and generalizing poorly. Overfitting is the high-variance regime; regularization and cross-validation manage the tradeoff.

What is cross-validation and why is it important in risk model development?

Cross-validation partitions data into training and validation folds (e.g., k-fold), repeatedly training on some folds and testing on the held-out fold to estimate out-of-sample performance. It guards against overfitting and gives a more reliable generalization estimate; for time series, walk-forward/expanding-window validation preserves temporal order.

How is artificial intelligence applied to credit risk and fraud detection?

In credit: ML models (gradient boosting, neural nets) use traditional plus alternative data to score default probability, improving discrimination and including thin-file borrowers. In fraud: anomaly-detection and classification models flag unusual transaction patterns in real time, learning evolving fraud typologies that static rules miss.

What are the key model-risk and governance concerns when using AI/ML in finance?

Lack of interpretability (black-box models), data quality and representativeness, bias/discrimination and fair-lending compliance, overfitting and instability out-of-sample, concept drift, cyber/adversarial manipulation, and difficulty validating and explaining decisions to regulators, requiring strong model governance and explainability (XAI) tools.

What is meant by 'alternative data' in risk modeling, and give examples.

Alternative data is non-traditional information used to gain insight beyond standard financial statements and prices. Examples: satellite imagery, credit-card transactions, geolocation/foot traffic, web-scraping and social media sentiment, supply-chain shipping data, and IoT sensor data, used to improve forecasting, credit, and trading signals.

What are the '3 (or 5) Vs' that characterize big data?

Volume (vast quantity), Velocity (high speed of generation/processing), and Variety (structured, semi-structured, unstructured forms); often extended with Veracity (data quality/uncertainty) and Value (usefulness extracted).

What is distributed ledger technology (DLT) and how does a blockchain implement it?

DLT is a shared, synchronized database replicated across multiple nodes with no single central administrator, updated via consensus. A blockchain implements DLT by grouping transactions into cryptographically linked, time-stamped blocks (each containing the prior block's hash), making the chain append-only and tamper-evident.

Contrast permissionless (public) and permissioned (private) distributed ledgers.

Permissionless ledgers (e.g., Bitcoin, Ethereum) allow anyone to participate, validate, and read/write, relying on incentive-based consensus like proof-of-work or proof-of-stake. Permissioned ledgers restrict participation to vetted entities, offer greater control, privacy, and throughput, and are favored for regulated institutional/enterprise use.

What is a stablecoin, and what are the main types by collateralization?

A stablecoin is a crypto asset designed to maintain a stable value, usually pegged to a fiat currency. Types: fiat-collateralized (backed by cash/reserves, e.g., USDC, USDT), crypto-collateralized (over-collateralized with crypto, e.g., DAI), and algorithmic (uses supply rules/seigniorage to hold the peg, historically prone to de-pegging, e.g., TerraUSD).

What is a central bank digital currency (CBDC), and how does it differ from a stablecoin?

A CBDC is a digital form of sovereign (central-bank) money that is a direct central-bank liability and legal tender. Unlike a privately issued stablecoin (a private liability backed by reserves), a CBDC carries no issuer credit/de-peg risk; it can be retail (public) or wholesale (interbank settlement).

What is tokenization of assets, and what benefits does it offer?

Tokenization represents ownership rights in a real or financial asset as digital tokens on a distributed ledger. Benefits: fractional ownership of high-value/illiquid assets, improved liquidity, faster and cheaper settlement (potentially atomic/T+0), greater transparency, and programmability via smart contracts.

Why was LIBOR replaced, and what fundamental flaw did it have?

LIBOR was discontinued (most tenors after end-2021, remaining USD tenors mid-2023) because it relied on banks' subjective estimates of unsecured borrowing costs in a market with shrinking actual transactions, making it susceptible to manipulation (the LIBOR-rigging scandal) and unrepresentative of real funding conditions.

How do the new risk-free reference rates (e.g., SOFR) structurally differ from LIBOR?

RFRs like SOFR (USD), SONIA (GBP), and €STR are overnight, nearly risk-free rates based on large volumes of actual transactions (SOFR on overnight Treasury repo). Differences from LIBOR: they are secured/near-risk-free (no bank credit premium), backward-looking overnight (no term structure or forward-looking tenor), and far harder to manipulate.

What is a credit spread adjustment in the LIBOR-to-SOFR transition, and why is it needed?

Because LIBOR embeds bank credit and term premia that risk-free SOFR lacks, a fixed credit spread adjustment (e.g., ISDA's median 5-year historical LIBOR-minus-SOFR spread) is added to SOFR in fallback language so that legacy contracts transition without an economic value transfer between counterparties.

Define nonbank financial intermediation (shadow banking) and why it concerns regulators.

Shadow banking is credit intermediation involving entities and activities outside the regular banking system (money market funds, hedge funds, finance companies, securitization vehicles, repo markets). It concerns regulators because it can perform bank-like maturity/liquidity transformation and leverage without deposit insurance, lender-of-last-resort access, or full prudential oversight, posing systemic risk.

What bank-like risks do shadow banking entities create despite operating outside traditional regulation?

Maturity transformation (funding long-term assets with short-term liabilities), liquidity transformation, high leverage, and interconnectedness with banks. These create run risk (e.g., money-market fund and repo runs), fire-sale spillovers, and procyclical credit expansion/contraction that can amplify systemic instability, as seen in the 2007-09 crisis.

How does the convexity of an option-like incentive fee specifically encourage volatility-seeking by a manager near or below the high-water mark?

An incentive fee paid only on gains above the high-water mark is a call option on NAV; its value rises with volatility ($\text{vega} > 0$). When the fund is at-the-money or below the mark, increasing portfolio volatility raises the option's expected payoff at no symmetric cost to the manager, incentivizing higher risk to maximize expected fees rather than investor utility.