FRM Part 1 - Book 4 - Valuation and Risk Models (Part 2/2)

After completing this reading, you should be able to:

• Define discount factor and use a discount function to compute present and future values.

• Define the “law of one price,” explain it using an arbitrage argument, and describe how it can be applied to bond pricing.

• Identify arbitrage opportunities for fixed income securities with certain cash flows.

• Identify the components of a US Treasury coupon bond, and compare and contrast the structure to Treasury STRIPS, including the difference between P-STRIPS and C-STRIPS.

• Construct a replicating portfolio using multiple fixed income securities to match the cash flows of a given fixed-income security.

• Differentiate between “clean” and “dirty” bond pricing and explain the implications of accrued interest with respect to bond pricing.

• Describe the common day-count conventions used in bond pricing.

After completing this reading, you should be able to:

• Calculate and interpret the impact of different compounding frequencies on a bond’s value.

• Define spot rate and compute spot rates given discount factors.

• Interpret the forward rate and compute forward rates given spot rates.

• Define the par rate and describe the equation for the par rate of a bond.

• Interpret the relationship between spot, forward, and par rates.

• Assess the impact of maturity on the price of a bond and the returns generated by bonds.

• Define the “flattening” and “steepening” of rate curves and describe a trade to reflect expectations that a curve will flatten or steepen.

• Describe a swap transaction and explain how a swap market defines par rates.

• Describe overnight indexed swap (OIS) and distinguish OIS rates from LIBOR swap rates.

After completing this reading, you should be able to:

• Distinguish between gross, and net realized returns and calculate the realized return for a bond over a holding period, including reinvestments.

• Define and interpret the spread of a bond and explain how to derive a spread from a bond price and a term structure of rates.

• Define, interpret, and apply a bond’s yield-to-maturity (YTM) to bond pricing.

• Compute a bond’s YTM, given a bond structure and price.

• Calculate the price of an annuity and perpetuity.

• Explain the relationship between spot rates and YTM.

• Define the coupon effect and explain the relationship between the coupon rate, YTM, and bond prices.

• Explain the decomposition of P&L for a bond into separate factors, including carry roll-down, rate change, and spread change effects.

• Explain the following four common assumptions in carry roll-down scenarios: realized forwards, unchanged term structure, consistent yields and realized expectations of short-term rates; and calculate carry roll down under these assumptions.

After completing this reading you should be able to:

• Describe an interest rate factor and identify common examples of interest rate factors.

• Define and compute the DV01 of a fixed income security given a change in yield and the resulting change in price.

• Calculate the face amount of bonds required to hedge an option position given the DV01 of each.

• Define, compute, and interpret the effective duration of a fixed income security given a change in yield and the resulting change in price.

• Compare and contrast DV01 and effective duration as measures of price sensitivity.

• Define, compute, and interpret the convexity of a fixed income security given a change in yield and the resulting change in price.

• Explain the process of calculating the effective duration and convexity of a portfolio of fixed income securities.

• Explain the impact of negative convexity on the hedging of fixed income securities.

• Construct a barbell portfolio to match the cost and duration of a given bullet investment, and explain the advantages and disadvantages of bullet versus barbell portfolios.

After completing this reading you should be able to:

• Describe and assess the major weakness attributable to single-factor approaches when hedging portfolios or implementing asset liability techniques.

• Define key rate exposures and know the characteristics of key rate exposure factors including partial ‘01s and forward-bucket ‘01s.

• Describe key-rate shift analysis.

• Define, calculate, and interpret key rate ‘01 and key rate duration.

• Describe the key rate exposure technique in multi-factor hedging applications; summarize its advantages and disadvantages.

• Calculate the key rate exposures for a given security, and compute the appropriate hedging positions given a specific key rate exposure profile.

• Relate key rates, partial ‘01s and forward-bucket ‘01s, and calculate the forward-bucket ‘01 for a shift in rates in one or more buckets.

• Construct an appropriate hedge for a position across its entire range of forward-bucket exposures.

• Apply key rate and multi-factor analysis to estimating portfolio volatility.

After completing this reading you should be able to:

• Calculate the value of an American and a European call or put option using a one-step and two-step binomial model.

• Describe how volatility is captured in the binomial model.

• Describe how the value calculated using a binomial model converges as time periods are added.

• Define and calculate delta of a stock option.

• Explain how the binomial model can be altered to price options on: stocks with dividends, stock indices, currencies, and futures.

After completing this reading you should be able to:

• Explain the lognormal property of stock prices, the distribution of rates of return, and the calculation of expected return.

• Compute the realized return and historical volatility of a stock.

• Describe the assumptions underlying the Black-Scholes-Merton option pricing model.

• Compute the value of a European option using the Black-Scholes-Merton model on a non-dividend-paying stock.

• Define implied volatilities and describe how to compute implied volatilities from market prices of options using the Black-Scholes-Merton model.

• Explain how dividends affect the decision to exercise early for American call and put options.

• Compute the value of a European option using the Black-Scholes-Merton model on a dividend-paying stock.

• Describe warrants, calculate the value of a warrant, and calculate the dilution cost of the warrant to existing shareholders.

After completing this reading you should be able to:

• Describe and assess the risks associated with naked and covered option positions.

• Describe the use of a stop loss hedging strategy, including its advantages and disadvantages and explain how this strategy can generate naked and covered option positions.

• Describe delta hedging for an option, forward, and futures contracts.

• Compute the delta of an option.

• Describe the dynamic aspects of delta hedging and distinguish between dynamic hedging and hedge-and-forget strategy.

• Define and calculate the delta of a portfolio.

• Define and describe theta, gamma, vega and rho for option positions and calculate the gamma and vega for a portfolio.

• Explain how to implement and maintain a delta-neutral and a gamma-neutral position.

• Describe the relationship between delta, theta, gamma, and vega.

• Describe how portfolio insurance can be created through option instruments and stock index futures.