Valuation of Financial Instruments
Core Concepts
Valuation covers equities, bonds, derivatives, and other instruments. For bonds, candidates must understand discounted cash flow (DCF), yield to maturity (YTM), duration (Macaulay and modified), convexity, and the relationship between price and yield. For equities, dividend discount models (Gordon growth), price/earnings (P/E), and free cash flow to equity. For derivatives, put-call parity, Black-Scholes (basic assumptions), and binomial models. Key concepts: time value of money, present value, arbitrage-free pricing, and the risk-neutral valuation principle. Traps often involve confusing YTM with coupon rate, misapplying duration for large yield changes (convexity), and ignoring the assumptions of Black-Scholes (e.g., constant volatility, no dividends). Also, the valuation of structured products by decomposing into components. Candidates should know how to calculate the price of a bond given YTM and the impact of accrued interest (clean vs dirty price). Another trap: the valuation of forward contracts and the role of cost of carry.
Worked Example / Rule of Thumb
A 5-year bond, face value 1000, coupon 5% paid annually, YTM 6%. Price = 50/(1.06) + 50/(1.06)^2 + ... + 1050/(1.06)^5 ≈ 957.88. If YTM rises to 7%, price falls to ≈ 918.00. Rule of thumb: bond prices and yields move inversely; longer duration → greater price sensitivity.
Key Points
- Bond valuation: PV of future cash flows discounted at YTM.
- Duration measures price sensitivity to yield changes; modified duration = Macaulay duration / (1 + YTM).
- Convexity adjusts duration for large yield changes.
- Equity valuation: DDM, P/E, DCF.
- Derivatives: put-call parity, Black-Scholes, binomial models.
- Clean price excludes accrued interest; dirty price includes it.