Relative Value Methods

Welcome to Relative Value Methods!

Welcome to one of the most exciting parts of the CAIA Level II curriculum! If you’ve ever gone shopping and realized that a 2-liter bottle of soda is cheaper than a 1-liter bottle, you’ve already practiced relative value analysis. In this chapter, we’ll move away from asking "Is this stock going up?" and start asking "Is this asset cheap compared to its neighbor?" This shift in perspective is what makes hedge funds and alternative investors so successful. Don't worry if the math looks a bit scary at first—we’ll break it down step-by-step!

1. The Core Concept: What is Relative Value?

In traditional investing, we often look at absolute value (e.g., "I think Apple is worth \$200"). In Relative Value (RV), we look at the relationship between two or more securities. We are looking for mispricings between related assets.

The "Neighbor" Analogy: Imagine two identical houses on the same street. House A sells for \$500,000, and House B sells for \$450,000. You don't need to know if the housing market is going up or down to know that House B is a better deal relative to House A. You might buy House B and "short" (bet against) House A, expecting the prices to eventually meet in the middle.

Key Terms to Know:

\nConvergence: The process of two prices coming back together as the mispricing disappears.
\nDivergence: When the gap between two prices gets wider (this is usually when RV traders lose money!).
\nMean Reversion: The mathematical assumption that prices or spreads will eventually return to their historical average.\n

Key Takeaway:

Relative value isn't about picking winners; it’s about picking discrepancies. We profit when the relationship between two assets returns to "normal."

2. Pairs Trading: The Foundation of RV

Pairs trading is the simplest form of relative value. You find two stocks that usually move together (like Coca-Cola and Pepsi) and trade the "spread" between them.

How to do it (Step-by-Step):

\n1. Identify a Pair: Find two assets with high historical correlation.
\n2. Calculate the Spread: This is the price difference. Let \( S = P_A - (w \times P_B) \), where \( w \) is the hedge ratio.
\n3. Wait for a Deviation: If Stock A becomes much more expensive than Stock B, the spread "widens."
\n4. Execute the Trade: Sell (short) the expensive one and buy the cheap one.
\n5. Exit: Close the positions when the spread returns to its historical mean.\n

Quick Review: Why do we short one and buy the other? Because we want to be market neutral. If the whole stock market crashes, our long position loses money, but our short position makes money, cancelling out the market risk!

Did you know? Pairs trading was pioneered by teams at Morgan Stanley in the 1980s using early mainframe computers to spot these tiny price gaps.

3. Relative Value in Fixed Income

Fixed income (bonds) is where relative value methods really shine because bonds have mathematical relationships based on interest rates and time.

The Yield Curve and "Carry"

Investors often look at the Yield Curve (the graph of interest rates for different maturities). Two major concepts here are:

\nCarry: This is the "free" income you get just for holding the position (e.g., the interest you earn minus the cost of borrowing).
\nRoll-Down: As time passes, a 10-year bond becomes a 9-year bond. If the yield curve is upward sloping, the bond's yield drops as it gets closer to maturity, which means its price goes up!\n

Butterfly Trades

This is a classic CAIA concept. A butterfly trade involves three different maturities on the yield curve (the "wings" and the "body").

Example: You might buy 2-year and 30-year bonds (the wings) and sell 10-year bonds (the body). You are betting on the curvature of the yield curve rather than whether interest rates are going up or down.

Key Takeaway:

Fixed income RV focuses on spreads (like the difference between Corporate bonds and Treasury bonds) and the shape of the yield curve.

4. Convertible Bond Arbitrage

A convertible bond is a corporate bond that can be changed into shares of stock. It’s like a regular bond with a "call option" attached. Relative value players look for "cheap" options hidden inside these bonds.

The Strategy:

Traders usually buy the convertible bond and short the underlying stock. This is called Delta Hedging.

Why do this?
\nIf the stock price goes up, the bond gains value (because of the conversion option).
\nIf the stock price goes down, the short position makes money.
\nThe goal is to set the sizes so that you make money from volatility regardless of which way the stock moves!

Common Pitfall to Avoid:

Don't forget Credit Risk! If the company goes bankrupt, both the stock and the bond could crash together, and your "hedge" won't save you. This is why RV traders must monitor the creditworthiness of the issuer.

5. Volatility Arbitrage

Volatility can be traded just like a stock. Relative value traders look at the difference between two types of volatility:

\n1. Implied Volatility (IV): What the market predicts will happen (priced into options).
\n2. Realized Volatility (RV): What actually happens in the market.\n

The Trade: If you think the market is overestimating future craziness (IV is higher than what you think RV will be), you "sell" volatility. This is often done using variance swaps or straddles.

Memory Aid: Think of Implied Volatility as the Insurance Premium. If people are scared, premiums go up. If you think the "weather" will actually be calm, you sell the insurance and pocket the premium.

6. Modeling and Mathematics in RV

To find these values, we use models. The curriculum focuses on how we measure the richness or cheapness of a security.

The Z-Score

This is a vital tool for RV traders. It tells us how many "standard deviations" a spread is away from its average.

\( Z = \frac{Spread_{current} - Spread_{average}}{Standard Deviation} \)

\n- A high positive Z-score means the spread is much wider than usual (maybe sell the spread).
\n- A low negative Z-score means the spread is much tighter than usual (maybe buy the spread).\n

Regression Analysis

We use regression to find the "hedge ratio." If Stock A moves \$2 every time Stock B moves \$1, your hedge ratio (beta) is 2.0. You would short \$2 of Stock A for every \$1 you buy of Stock B.

Quick Review Box:

- Goal: Profit from mean reversion of spreads.
- Risk: "Gap risk" or the spread never coming back together.
- Tools: Correlation, Cointegration, Z-scores, and Delta hedging.

Summary: Putting it All Together

Relative Value methods are the "detective work" of the finance world. Instead of betting on the direction of the wind (the market), you are betting that two things that belong together will eventually stay together. Whether it's through pairs trading, yield curve plays, or volatility arbitrage, the goal is always the same: find a relationship that is "out of whack" and wait for it to fix itself.

Final Tip: When studying for the exam, remember that RV strategies are generally low beta (they don't move with the S&P 500) but can suffer during "liquidity shocks" when everyone tries to exit the same trades at once. Good luck, you've got this!