Jacob Bower is a bond strategist who would like to begin using fixed-income derivatives in his strategies. Bower has a firm understanding of the properties fixed-income securities. However, his understanding of interest rate derivatives is not nearly as strong. He decides to train himself on the valuation and sensitivity of interest rate derivatives using various interest rate scenarios. He considers the forward London Interbank Offered Rate (LIBOR) interest rate environment shown in Table 1. Using a rounded daycount (i.e., 0.25 years for each quarter) he has also computed the corresponding implied spot rates resulting from these LIBOR forward rates. These are included in Table 1. Table 1 90-Day LIBOR Forward Rates and Implied Spot Rates Period (in months) LIBOR Forward Rates Implied Spot Rates 0 × 3 5.500% 5.5000% 3 × 6 5.750% 5.6250% 6 × 9 6.000% 5.7499% 9 × 12 6.250% 5.8749% 12 × 15 7.000% 6.0997% 15 × 18 7.000% 6.2496% Bower has also estimated the LIBOR forward rate volatilities to be 20%. The particular fixed instruments that Bower would like to examine are shown in Table 2. He also wants to analyze the strategy shown in Table 3. Table 2 Interest Rate Instruments Dollar Amount of Floating Rate Bond $42,000,000 Floating Rate Bond paying LIBOR + 0.25% Time to Maturity (years) 8 Cap Strike Rate 7.00% Floor Strike Rate 6.00% Interest Payments quarterly Table 3 Initial Position in 90-day LIBOR Eurodollar Contracts Contract Month (from now) Strategy A (contracts) Strategy B (contracts) 3 months 300 100 6 months 0 100 9 months 0 100 Bower is a bit puzzled about how to use caps and floors. He wonders how he could benefit both from increasing and decreasing interest rates. Which of the following trades would most likely profit from this interest rate scenario? A) Sell at the money cap and at the money floor. B) Buy at the money cap and sell at the money floor. C) Buy at the money cap and at the money floor. D) Sell at the money cap and buy at the money floor. -------------------------------------------------------------------------------- Bower shorts the floating rate bond given in Table 2. Which of the following will best reduce Bower’s interest rate risk? A) Buying an interest rate floor. B) Shorting Eurodollar futures. C) Shorting an interest rate cap. D) Shorting an interest rate floor. -------------------------------------------------------------------------------- Bower has studied swaps extensively. However, he is not sure which of the following is the swap fixed rate for a one-year interest rate swap based on 90-day LIBOR with quarterly payments. Using the information in Table 1 and the formula below, what is the most appropriate swap fixed rate for this swap? A) 5.65%. B) 5.75%. C) 6.77%. D) 6.01%. -------------------------------------------------------------------------------- Bower would like to perform some sensitivity analysis on a one year collar to changes in LIBOR. Specifically, he wonders how the price of a collar (buying a cap and selling a floor) is affected by an increase in the LIBOR forward rate volatility. Using the information in Tables 1 and 2 which of the following is most accurate? The price of the collar will: A) increase. B) stay the same. C) decrease. D) increase or decrease. -------------------------------------------------------------------------------- Bower computes the implied volatility of a one year caplet on the 90-day LIBOR forward rates to be 18.5%. Using the given information what does this mean for the caplet’s market price relative to its theoretical price? The caplet’s market price is: A) overvalued. B) correctly valued. C) undervalued or overvalued. D) undervalued. -------------------------------------------------------------------------------- For this question only, assume Bower expects the currently positively sloped LIBOR curve to shift upward in a parallel manner. Using a plain vanilla interest rate swap, which of the following will allow Bower to best take advantage of his expectations? Purchase a: A) pay fixed interest rate swap. B) receive fixed interest rate swap. C) fixed rate bond and enter into a receive fixed swap. D) floating rate bond and enter into a receive fixed swap.
- C 2. B? 3. B 4. B? 5. A 6. A
C B B C D A
C B B A A A
C D B A D A
cfaboston28 Wrote: ------------------------------------------------------- > C > B > B > C > D > A These are the real answers!!!
Why is the second to last answer D? If the market price assumes 20% volatility and the theoretical price assumes 18.%5 volatility, wouldn’t the market price be overvalued? Increased volatility = increase in value?
- The correct answer was C) Buy at the money cap and at the money floor. This is a straddle on interest rates. The cap provides a positive payoff when interest rates rise and the floor provides a positive payoff when interest rates fall. 2) Your answer: B was correct! If he adds a short position in Eurodollar futures to the existing liability in the correct amount, he is able to lock in a specific interest rate. A short Eurodollar position will increase in value if interest rates rise because the contract is quoted as a discount instrument so increases in rates reduce the futures price 3) Your answer: B was correct! The swap fixed rate is computed as follows: Z90-day = 1 1 + (0.055 × 90 / 360) = 0.98644 Z180-day = 1 1 + (0.05625 × 180 / 360) = 0.97264 Z270-day = 1 1 + (0.057499 × 270 / 360) = 0.95866 Z360-day = 1 1 + (0.058749 × 360 / 360) = 0.94451 The quarterly fixed rate on the swap = 1 − 0.94451 0.98644 + 0.97264 + 0.95866 + 0.94451 = 0.05549 / 3.86225 = 0.01437 = 1.437% The fixed rate on the swap in annual terms is: 1.437% × 360 / 90 = 5.75% 4) The price of the floor will increase more than the price of the cap since the floor is closer to being at the money than the cap. Therefore, the floor price is more sensitive to volatility changes in the LIBOR forward rate. Since the price of the collar is equal to the price of the cap minus the price of the floor, the net effect is a price decrease for the collar. 5)Volatility and option prices are always positively related. Therefore, since the option implied volatility is lower than the estimated volatility, this implies that the caplet is undervalued relative to its theoretical value. 6) Since the interest rates are expected to rise for all maturities, one can benefit from this rise by receiving a floating rate (LIBOR) and borrowing at a fixed rate (i.e. a pay fixed swap).
4 and 5 make sense. Thanks for posting this vignette.