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Fin6116 Fixed Income Securities

A. A complete hedge uses only one instrument to offset all interest rate risk across all maturities — it’s impractical because no single instrument can perfectly match all cash flows.

B. A complete hedge neutralizes risk at every individual maturity point by using a separate hedging instrument for each — it’s impractical due to high transaction costs, complexity, and overkill (many risks cancel out).

C. A complete hedge assumes parallel yield curve shifts and uses duration matching — it fails when rates move non-parallelly, making it unreliable.

D. A complete hedge requires holding zero-coupon bonds for every maturity — it’s impossible because not all maturities have liquid bonds.

2. Why do practitioners prefer PCA or factor model hedging (like Nelson-Siegel) over hedging each maturity individually?

A. Because PCA identifies only two factors — level and slope — making hedging simpler than managing dozens of maturities.

B. Because over 90% of yield curve movements are captured by just three factors (level, slope, curvature), so hedging these three with 3–4 instruments is sufficient, cheaper, and more realistic than hedging every maturity.

C. Because PCA eliminates cross-hedge risk entirely by using only government bonds.

D. Because factor models assume all bonds have the same convexity, simplifying the math.

A. A loan secured by the borrower’s primary residence, with the highest priority in case of default.

B. A loan that is fully amortizing with a fixed interest rate for the entire term.

C. A junior loan on the same property, paid only after the first lien is satisfied — higher risk and higher interest rate.

D. A government-backed loan for low-income borrowers, guaranteed by Ginnie Mae.

A. Its value decreases because prepayments reduce the total interest received.

B. Its value increases because borrowers refinance, returning principal earlier than ex pected.

C. Its value remains unchanged because PO strips are not sensitive to prepayments.

D. Its value decreases due to increased credit risk from higher default rates.

A. OAS assumes a fixed prepayment speed (e.g., 100 PSA) forever, making it simpler to calculate.

B. OAS accounts for path dependency, interest rate volatility, and the embedded pre payment option.

C. OAS is always higher than static spread, indicating a better return for investors.

D. OAS ignores borrower behavior and focuses only on historical cash flows.

6. Which of the following best describes the convexity of a typical MBS compared to a standard bond?

A. MBS has positive convexity — price rises faster than it falls when yields change.

B. MBS can have negative convexity — price gains are capped when rates fall (due to prepayments), and losses are amplified when rates rise.

C. MBS has zero convexity — price is unaffected by changes in interest rates.

D. MBS has convexity identical to Treasury bonds — stable and predictable price be havior.

(1) What are the duration and convexity of each bond?

(2) What are the duration and convexity of the portfolio?

(3) Show that the duration and convexity are both additive.

(1) What is the quantity ϕ of the hedging instrument that the investor has to sell?

(2) We suppose that the yield curve increases instantaneously in parallel by 0.1%. What happens if the bond portfolio has not been hedged? And if it has been hedged?

(3) Same question as the previous one when the yield curve increases instantaneously in parallel by 2%.

Q4. Assume a 2-year Euro-note, with a $100,000 face value, a coupon rate of 10%. If today’s YTM is 10.5% and assume term structure is flat. Coupon frequency and compounding frequency are assumed to be annual.

(1) What is the Macaulay duration and the convexity of this bond?

(2) What is the exact price change in dollars if interest rates increase by 10 basis points (a uniform shift)?

(3) Use the duration model to calculate the approximate price change in dollars if interest rates increase by 10 basis points.

Q5.Hedging with the Extended Nelson-Siegel (Svensson) Model

β0 = 0.05, β1 = −0.02, β2 = 0.01, β3 = −0.005, τ1 = 2.0, τ2 = 5.0

You wish to hedge this portfolio against changes in the four parameters β0, β1, β2, β3 using four hedging instruments H1, H2, H3, H4, whose dollar sensitivities (per unit) are given below:

Compute Rc(0, θi) for each maturity first, then compute each Dk. Show your work.

Q6. Cash Flow Analysis of RMBS

• Current Balance: $400,000,000

• WAC (Weighted-Average Coupon): 8.125% per year

• Pass-Through Rate: 7.5% per year (investor’s net coupon)

• WAM at Issuance: 334 months (average remaining term of loans in the pool)

• Prepayment Assumption: 100 PSA

You are to construct a 5-month cash flow projection table for Months 1 through 5, using the 100 PSA prepayment assumption. For each month (t = 1 to 5), calculate and fill in the following columns:

(2) Complete the 5-row table above. All values should be calculated to the nearest dollar. Round SMM to 6 decimal places.

You are valuing a pass-through MBS with the following characteristics:

• Current Market Price: $98.50 per $100 of face value

• Current MBS Balance: $400,000,000

• WAC (Weighted-Average Coupon): 8.125% per year

• Pass-Through Rate: 7.5% per year (investor’s net coupon)

• WAM at Issuance: 334 months (average remaining term of loans in the pool)

• Prepayment Assumption: 100 PSA

• Treasury Yield (for comparison): 4.2% (10-year)

(2) You are told that a more sophisticated valuation using Monte Carlo Simulation yields the following:

• Option-Adjusted Spread (OAS): 120 basis points (1.20%)

• Static Spread (from Part 1): 180 basis points (1.80%)

(b) Explain what the Option Cost represents in the context of MBS valuation. Why does it exist?

(c) Why is the OAS considered a more realistic measure of value than the Static Spread? (Hint: mThink about prepayment risk and path dependency.)

(d) If interest rates were to fall sharply next year, how would you expect the actual return on this MBS to compare to the Static Cash Flow Yield? Why?