Ch7. FRM Financial Risk Manager — Investment Management Risk & ALM

Investment Management Risk Overview

The Risk Management and Investment Management section of FRM Part II focuses on risk management for institutional investors: portfolio managers, pension funds, insurance companies, and endowments. Core topics include performance attribution, hedge fund risk, asset-liability management (ALM), and economic capital.

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Hedge Fund Risk Analysis

Unique Hedge Fund Risk Factors

Risk Type	Description
Leverage risk	Amplification of gains and losses
Liquidity risk	Illiquid assets + investor redemption pressure
Model risk	Quantitative model failure in atypical markets
Concentration risk	Heavy exposure to few positions
Counterparty risk	OTC derivative and prime broker exposure

Return Manipulation Risk

Smoothed Returns: Artificially smoothing valuations for illiquid assets understates volatility and VaR — a form of return manipulation common in PE and real estate funds.

Backfilling Bias: Funds enter databases only after showing good results → past returns overstate expected performance.

Lock-up periods and liquidity gates: FRM frequently tests these in the context of liquidity risk for fund managers.

Performance Attribution — Factor Models

Fama-French 3-Factor Model:

• R_p − R_f = α + β_M(R_M − R_f) + β_SMB·SMB + β_HML·HML + ε

Carhart 4-Factor (adds momentum):

• • β_MOM · MOM

True alpha (α) is the return remaining after controlling for all factor exposures.

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Asset-Liability Management (ALM)

Purpose of ALM

Banks, insurers, and pension funds must manage the interest rate, liquidity, and currency mismatch between:

• Assets (how they deploy capital)
• Liabilities (obligations they must meet)

Interest Rate Gap Analysis

Re-pricing Gap = Rate-sensitive assets − Rate-sensitive liabilities (in a given maturity bucket)

GAP > 0 (asset-sensitive): NIM improves when rates rise

GAP < 0 (liability-sensitive): NIM deteriorates when rates rise

Duration Gap

Duration Gap = D_A − (L/A) × D_L

• D_A: Asset duration
• D_L: Liability duration
• L/A: Liability-to-asset ratio

Change in economic equity: ΔE = −Duration Gap × A × Δr

Example: Duration Gap = +2 years, Assets = $1B, Rate rise = 1→ ΔE = −2 ×$1B × 0.01 = −$20M

Immunization

Setting Duration Gap = 0 protects equity value regardless of interest rate movements.

Full Immunization Conditions:

1. Duration match: D_A = D_L
2. Value match: PV(Assets) = PV(Liabilities)
3. Convexity condition: C_A > C_L (ensures assets outperform liabilities for large rate moves)

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Economic Capital

Definition

Economic capital = Internal capital required to cover unexpected losses at a specified confidence level.

Regulatory vs. Economic Capital:

Feature	Regulatory Capital	Economic Capital
Set by	Basel/regulator	Internal management
Purpose	Regulatory compliance	Business risk coverage
Approach	Standardized/internal model	Fully internal
Confidence	99.9% (Basel)	99.9%–99.97%

RAROC (Risk-Adjusted Return on Capital)

RAROC = (Revenue − Costs − Expected Loss) / Economic Capital

• Expected Loss is already priced into loan spreads/provisions
• Economic capital is driven by Unexpected Loss

Value-creating rule: RAROC > Cost of Equity (WACC) → the business unit creates shareholder value.

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Portfolio Performance Metrics

Metric	Formula	Perspective
Sharpe Ratio	(R_p − R_f) / σ_p	Excess return per unit of total risk
Treynor Ratio	(R_p − R_f) / β	Excess return per unit of systematic risk
Jensen’s Alpha	R_p − CAPM(R_p)	Absolute excess return
Information Ratio	α / TE	Active return per unit of active risk
Sortino Ratio	(R_p − R_f) / σ_downside	Only penalizes downside volatility

Tracking Error (TE): Standard deviation of (portfolio return − benchmark return)

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FRM Exam Checklist

• Duration Gap formula: D_A − (L/A) × D_L
• RAROC: subtract EL in numerator; use economic capital (not regulatory) in denominator
• Full immunization: 3 conditions (duration, value, convexity)
• Hedge fund biases: survivorship, self-reporting, backfilling
• Re-pricing Gap: positive GAP = asset-sensitive = benefits from rising rates

Chapter 8 closes the FRM series with a comprehensive 30-question mock exam covering all topics.