04 Valuation and Risk Models

VRM 1: Measures of Financial Risk

What the mean-variance framework says about risk and return Investing trades one thing against another, since accepting more uncertainty is what buys a higher average outcome. The mean-variance framew

VRM 2: Calculating and Applying VaR

Linear and non-linear portfolios: definitions and examples A portfolio is linear when its value responds in strict proportion to the market variables underneath it. Hold 100 shares priced at USD 50 ap

VRM 3: Measuring and Monitoring Volatility

How asset return distributions deviate from the normal distribution A volatility that never moved would be easy to pin down. Feed a long run of past returns into the usual standard deviation formula,

VRM 4: External and Internal Credit Ratings

What a credit rating measures and why credit rating agencies exist A credit rating is a compressed answer to one question: how likely is it that a borrower fails to pay what it owes? Everything else a

VRM 5: Country Risk

What country risk is and why investors and lenders measure it A company with plants, customers or subsidiaries abroad picks up exposures that have nothing to do with the quality of its products and ev

VRM 6: Measuring Credit Risk

Economic capital vs regulatory capital: what each one covers Losses have to land somewhere, and in a bank they land on equity capital first. A bank carrying equity capital of USD 5 billion that suffer

VRM 7: Operational Risk

What operational risk is and how the Basel Committee defines it Financial institutions have had to take operational risk far more seriously over the past twenty years, and part of what makes the subje

VRM 8: Stress Testing

Why stress testing is used as a risk management tool Stress testing asks a blunt question about a financial institution. If something extreme but believable happened, would the firm still be standing?

VRM 9: Pricing Conventions, Discounting, and Arbitrage

What a discount factor is and how to calculate present and future values A discount factor ties a certain payment arriving on a future date to what it is worth today. If a security’s price says

VRM 10: Interest Rates

How compounding frequency changes the value of a bond Discount factors alone are enough to value any Treasury instrument, and observed Treasury prices can be used to imply the discount factors behind

VRM 11: Bond Yields and Return Calculations

Gross realized return and net realized return on a bond A bond’s realized return sets the value of the initial investment against what it is worth at the end of the holding period. What matters

VRM 12: Applying Duration, Convexity, and DV01

What a one-factor interest rate model is and which interest rate factors it uses DV01, duration and convexity are one-factor risk measures. Behind all three sits one assumption: a single source of ran

VRM 13: Modeling Non-Parallel Term Structure Shifts and Hedging

Why DV01 and duration miss non-parallel term structure shifts DV01, duration and convexity all assume that every rate on the curve moves by the same amount at the same moment. Real term structures twi

VRM 14: Binomial Trees

How a no-arbitrage argument prices an option on a one-step binomial tree Derivatives are priced by a no-arbitrage argument, which simply means the price is pinned down by the requirement that nobody c

VRM 15: The Black-Scholes-Merton Model

What the Black-Scholes-Merton model prices and where it came from Two papers published in 1973 changed how the market thinks about options. Fischer Black and Myron Scholes wrote one, reaching the pric

VRM 16: Option Sensitivity Measures: The Greeks

What the Greek letters measure and the position behind them A derivatives desk does not avoid risk. It takes risk deliberately and then measures what it has taken, and the Greek letters are those meas