Summary of "Ses 6: Fixed-Income Securities III"

This lecture covers two main themes: a current overview of financial markets amid crisis conditions and foundational principles of fixed-income securities pricing, focusing on arbitrage, the law of one price, and risk measurement in bond portfolios.

Part 1: Financial Market Context and Recent Events

Market Conditions and Reactions:
- The lecture begins with a market update during a financial crisis, noting unprecedented government interventions and market volatility.
- Yield curves are analyzed, especially the short-term (3-month Treasury bills) yields dropping to near zero (3 basis points) indicating panic and a flight to liquidity.
- A week later, short-term yields rose to 41 basis points, suggesting reduced panic and less demand for short-term Treasuries.
- Long-term yields (30-year bonds) also increased, likely reflecting inflation expectations due to government bailout announcements (e.g., $700 billion bailout plan).
Psychological and Market Dynamics:
- Panic led investors to rush from risky assets to safe havens like short-term Treasuries.
- A key trigger was the "breaking the buck" event where a major money market fund (The Reserve Fund) lost value, undermining confidence in supposedly safe money market funds.
- Massive withdrawals (~$90 billion) from money market funds fueled the surge in Treasury prices and yield drops.
- The government responded by guaranteeing money market funds to restore confidence, similar to FDIC insurance on bank deposits.
Implications for Investors:
- Retail investors, not just hedge funds, drove much of the flight to safety.
- The crisis creates both risks and opportunities, including distressed asset acquisitions (e.g., Warren Buffett’s investment in Goldman Sachs).
- Market prices reflect collective expectations, fears, and greed, not always “correct” valuations but important signals for financial decision-making.

Part 2: Law of One Price and Arbitrage in Fixed Income

Law of One Price (LOOP):
- Fundamental principle: Two identical cash flows must have the same market price.
- This principle underpins pricing of all securities, including derivatives.
- Violation of LOOP creates arbitrage opportunities—riskless profits by buying the cheaper asset and selling the more expensive identical one.
- LOOP does not require supply-demand equilibrium, only that at least one market participant prefers more money to less.
Arbitrage Mechanics:
- Arbitrage involves buying and selling identical cash flows to lock in riskless profit.
- Short selling is essential for arbitrage: selling securities you do not own by borrowing them.
- Government-imposed short selling bans (e.g., on financial stocks) disrupt arbitrage and pricing relationships, weakening market efficiency temporarily.
Real-World Arbitrage:
- Arbitrage desks at financial firms actively seek such mispricings, using advanced tools and linear algebra.
- Arbitrage opportunities are fleeting due to competition and market efficiency but still exist due to transaction costs, market frictions, and bond features (e.g., callable bonds).
- The lecture references historical examples where solving simultaneous linear equations revealed mispricings, leading to large profits.

Part 3: Pricing Coupon bonds via Pure Discount Bonds

Coupon bonds can be priced as portfolios of pure discount bonds.
Pricing relationships can be expressed as systems of linear equations where:
- Known: Bond prices and coupons.
- Unknown: Yield curve (spot rates for each maturity).
If the system has no solution, it signals mispricing and potential arbitrage.

Part 4: Measuring Risk in Bond Portfolios — Duration and Convexity

Duration:
- A measure of a bond’s sensitivity to interest rate changes.
- Defined as the weighted average time until cash flows are received, weighted by present value.
- Longer Duration means higher sensitivity to yield changes.
- Modified Duration adjusts Duration by yield to estimate percentage price change per basis point change in yield.
- Duration can be calculated for individual bonds or entire portfolios.
Convexity:
- Measures the curvature or second derivative of bond price relative to yield changes.
- Accounts for how sensitivity (Duration) itself changes as yields change.
- Convexity provides a better approximation of price changes for larger interest rate movements.
- Increased volatility in interest rates generally increases bond value due to option-like characteristics of bonds.
Practical Implications:
- Duration and Convexity help investors and traders assess and manage interest rate risk.
- These measures were developed to enable fast, approximate risk assessment before modern computing.