CAIA Level II: Relative Value Methods — Study Guide

CAIA Level II: Relative Value Methods — Study Guide

What Is It?

1. What is this topic? Relative value methods identify mispriced assets by comparing them to similar securities or theoretical models, often using spreads, ratios, or statistical arbitrage.
2. How is it tested, applied, or used? Tested via spread calculations, model interpretation, and arbitrage strategy questions. Used in hedge funds, proprietary trading, and risk arbitrage to exploit pricing inefficiencies.

Why Does the Exam Ask This?

CAIA tests this to assess: - Ability to identify mispricing using quantitative and qualitative comparisons. - Judgment in selecting appropriate benchmarks (e.g., peers, historical norms, models). - Risk awareness in arbitrage strategies (e.g., basis risk, liquidity constraints). - Compliance logic—ensuring trades align with fund mandates and regulatory limits.

What Do I Need to Know First?

1. Yield spreads (nominal, Z-spread, OAS).
2. Statistical arbitrage basics (mean reversion, pairs trading).
3. Fixed income valuation (duration, convexity, credit risk).
4. Hedge fund strategies (market-neutral, event-driven).
5. Regression analysis (beta, residuals, R-squared).

Topic Snapshot

Relative value methods sit at the intersection of quantitative finance and hedge fund strategies in CAIA Level II. They matter because: - Exploit inefficiencies without directional market exposure. - Require precise model selection (e.g., yield curve, credit spreads, volatility surfaces). - Critical for risk management—mispricing can signal liquidity traps or structural shifts.

Exam / Job / Audit Weighting

• Frequency: High (5–10% of Level II exam).
• Difficulty Rating: Intermediate.
• Question Type:
• Exam: Spread calculations, model interpretation, scenario-based arbitrage.
• Job: Trade idea generation, risk monitoring, backtesting.
• Audit: Validity of pricing models, compliance with leverage limits.

Difficulty Level

Intermediate (requires comfort with spreads, models, and risk constraints).

Must-Know Rules, Formulas, Standards, or Principles

1. Spread Decomposition:
2. Z-spread = Nominal spread – Option cost (for callable bonds).
3. OAS (Option-Adjusted Spread) = Z-spread – Option value (in bps).
4. Pairs Trading Rule:
5. Entry: When spread > 2σ from mean.
6. Exit: When spread reverts to mean or hits stop-loss.
7. Arbitrage Bounds:
8. No-arbitrage principle: If A ≈ B, then P(A) ≈ P(B) (adjusted for risk).
9. Violation: P(A) > P(B) + transaction costs → short A, long B.

Misconceptions

1. "Relative value = risk-free." → Ignores basis risk, liquidity risk, and model risk.
2. "All spreads are mean-reverting." → Some spreads (e.g., credit) can trend due to structural changes.
3. "Pairs trading works in all markets." → Fails in regime shifts (e.g., 2008, 2020).
4. "OAS is always positive." → Can be negative for bonds with embedded options (e.g., callable bonds in low-rate environments).
5. "Higher spread = better value." → May reflect higher risk (e.g., liquidity premium, default risk).

Common Mistakes

1. Ignoring transaction costs → Overestimating arbitrage profits.
2. Using wrong benchmark (e.g., comparing a BBB bond to a Treasury instead of a BBB index).
3. Overfitting models → Backtesting on limited data without out-of-sample validation.
4. Misinterpreting OAS → Confusing it with Z-spread for bonds with options.
5. Neglecting liquidity → Assuming all spreads can be arbitraged equally.

The Common Trap

Assuming spreads are stationary. - Why it’s tempting: Historical data often shows mean reversion, but structural breaks (e.g., 2008, COVID) can make spreads non-stationary. - How to avoid: Test for regime shifts (e.g., Chow test, CUSUM) before assuming mean reversion.

Terms to Remember

1. Z-spread: Constant spread added to the spot rate curve to match bond price.
2. OAS: Spread adjusted for embedded options (e.g., callable bonds).
3. Basis risk: Risk that hedging instrument doesn’t perfectly offset the asset.
4. Pairs trading: Long/short strategy based on relative mispricing between two correlated assets.
5. Arbitrage bounds: Theoretical limits preventing risk-free profits.

Step-by-Step Process

1. Identify the Asset Pair

• Select two highly correlated assets (e.g., two oil stocks, on-the-run vs. off-the-run Treasuries).
• Check correlation (>0.8) and cointegration (Engle-Granger test).

2. Calculate the Spread

• Fixed income: Use yield spread (YTM_A – YTM_B) or Z-spread.
• Equities: Use price ratio (P_A / P_B) or log returns.
• Derivatives: Use implied volatility spread (IV_A – IV_B).

3. Test for Mean Reversion

• Run ADF test (Augmented Dickey-Fuller) on the spread.
• If p-value < 0.05, spread is mean-reverting.

4. Set Entry/Exit Rules

• Entry: Spread > 2σ from mean (or 95% confidence interval).
• Exit: Spread reverts to mean or hits stop-loss (e.g., 3σ).

5. Size the Trade

• Dollar-neutral: Equal dollar amounts long/short.
• Beta-neutral: Adjust weights to offset market exposure.

6. Monitor Risks

• Basis risk: Check if hedge instrument diverges.
• Liquidity risk: Ensure exit is possible at target spread.
• Regime risk: Watch for structural breaks (e.g., Fed policy shifts).

Exam Answer Builder

1-Mark Question (MCQ)

What it tests: Definition of OAS. Example: Which of the following best describes the Option-Adjusted Spread (OAS)? A) The spread added to the Treasury yield to match a bond’s price. B) The spread adjusted for embedded options, reflecting the bond’s credit risk. C) The difference between a bond’s YTM and the risk-free rate. D) The spread between two bonds with the same maturity but different coupons.

Correct Answer: B Key Tip: OAS excludes optionality—it’s the spread after adjusting for embedded options.

3-Mark Question (Calculation)

What it tests: Z-spread vs. OAS. Example: A callable bond has a Z-spread of 200 bps and an option cost of 50 bps. What is its OAS? Answer: OAS = Z-spread – Option cost = 200 bps – 50 bps = 150 bps. Key Tip: OAS is always ≤ Z-spread for callable bonds.

5-Mark Question (Scenario-Based)

What it tests: Arbitrage strategy design. Example: Stock A and Stock B have historically traded at a price ratio of 1.2. Currently, A trades at $60 and B at $45. The ratio is now 1.33. Describe a relative value trade, including entry/exit rules and risks. Answer Frame: 1. Trade: Long Stock B, short Stock A (ratio > historical mean). 2. Entry: Ratio > 1.25 (2σ from mean). 3. Exit: Ratio reverts to 1.2 or hits 1.4 (stop-loss). 4. Risks:
- Basis risk: Stocks may decouple (e.g., earnings surprise).
- Liquidity risk: Shorting Stock A may be costly.
- Regime risk: Structural change (e.g., sector rotation). Key Tip: Always quantify the spread (e.g., ratio, yield difference) and set stop-losses.

Case Study (10-Mark Question)

What it tests: Model selection and risk management. Example: A hedge fund uses a pairs trading strategy on two semiconductor stocks (AMD and NVDA). The spread (AMD – NVDA) has a mean of 0.5 and σ = 0.1. Currently, AMD is $150 and NVDA is $200 (spread = –0.25). 1. Should the fund enter a trade? If so, what position? 2. What risks should the fund monitor? 3. How would you adjust the strategy if NVDA announces a stock split?

Answer Frame: 1. Trade: Yes. Spread (–0.25) < mean (0.5) – 2σ (0.3) = 0.1. Short NVDA, long AMD. 2. Risks:
- Basis risk: AMD/NVDA correlation may break (e.g., supply chain issues).
- Liquidity risk: NVDA is highly liquid; AMD may have wider bid-ask.
- Event risk: Earnings, regulatory changes. 3. Adjustment for stock split:
- Recalculate spread post-split (e.g., NVDA at $100 → new spread = 150 – 100 = 50).
- Rebalance weights to maintain dollar neutrality. Key Tip: Always re-test assumptions after corporate actions (splits, dividends).

This vs That

Time-Saver Hack

Eliminate wrong OAS answers fast: - If a bond is callable, OAS < Z-spread. - If a bond is putable, OAS > Z-spread. - If no options, OAS = Z-spread.

Mini Scenarios

1. Basic

Two oil stocks, XOM and CVX, have a 5-year correlation of 0.9. XOM is $100, CVX is $90. The historical spread is $10. Today, XOM is $105, CVX is $85. What’s the trade? What to notice: Spread widened to $20 (vs. $10 mean). Trade: Long CVX, short XOM.

2. Applied

A hedge fund runs a pairs trade on Coca-Cola (KO) and Pepsi (PEP). The spread (KO – PEP) has a mean of $5 with σ = $1.5. KO is $60, PEP is $50 (spread = $10). The fund enters a trade. Two weeks later, KO is $62, PEP is $55 (spread = $7). What should the fund do? What to notice: Spread tightened from $10 to $7 (still > mean + 2σ). Action: Hold or add to position (not yet at exit threshold).

3. Tricky

A bond trader observes that a 5-year Treasury yields 3%, while a 5-year BBB corporate bond yields 5%. The Z-spread is 200 bps, but the OAS is 150 bps. What does this imply? What to notice: OAS < Z-spread → bond has embedded options (likely callable). The 50 bps difference is the option cost.

Diagnostic MCQ Bank

Easy

Question: Which of the following is a key assumption of pairs trading? A) The two assets are uncorrelated. B) The spread between the assets is mean-reverting. C) One asset is always overpriced. D) The strategy requires leverage.

Correct Answer: B Explanation: Pairs trading relies on mean reversion in the spread. Trap Option: A (uncorrelated assets would make the strategy useless).

Medium

Question: A callable bond has a Z-spread of 250 bps and an OAS of 200 bps. What is the option cost? A) 50 bps B) 200 bps C) 250 bps D) 450 bps

Correct Answer: A Explanation: Option cost = Z-spread – OAS = 250 – 200 = 50 bps. Trap Option: D (adding instead of subtracting).

Hard

Question: A hedge fund runs a pairs trade on two tech stocks with a historical spread mean of $10 and σ = $2. The current spread is $14. The fund enters a trade. After one week, the spread is $13. What is the most likely reason the fund would exit the trade? A) The spread tightened to $13. B) The spread is still > mean + 2σ ($14). C) The correlation between the stocks dropped to 0.5. D) The fund hit its stop-loss at $15.

Correct Answer: C Explanation: Correlation breakdown (0.5) violates the strategy’s core assumption. Trap Option: A (spread tightening is good; no exit yet).

Real-World Patterns

1. Hedge Funds: Use yield curve arbitrage (e.g., long 2-year, short 10-year Treasuries) to profit from curve steepening/flattening.
2. Proprietary Trading: Exploit on-the-run vs. off-the-run Treasury spreads (liquidity premium).
3. Risk Arbitrage: Compare merger target stock price vs. offer price (spread should converge post-deal).

30-Second Cheat Sheet

1. OAS = Z-spread – Option cost (for callable bonds).
2. Pairs trading entry: Spread > 2σ from mean.
3. No-arbitrage bounds: P(A) ≈ P(B) ± transaction costs.
4. Basis risk kills relative value trades.
5. Test for mean reversion (ADF test) before trading.

Related Concepts

1. Fixed Income Arbitrage (yield curve trades, mortgage-backed securities).
2. Statistical Arbitrage (cointegration, factor models).
3. Event-Driven Strategies (merger arbitrage, distressed debt).

Verified Source List

1. CAIA Association. CAIA Level II Curriculum (2025–2026).
2. Fabozzi, F. Fixed Income Analysis (CFA Institute Investment Series).
3. Lo, A. Adaptive Markets (pairs trading, statistical arbitrage).
4. Hull, J. Options, Futures, and Other Derivatives (OAS, Z-spread).
5. SEC Filings. Hedge fund 13F/13D disclosures (real-world arbitrage examples).