Lecture 6

Question 1

Interest rate sensitivity - stylized facts

Answer 1

1. Bond prices and yields are inversely related
2. An increase in a bond’s yield to maturity results in a smaller price change
   than a decrease of equal magnitude
3. Long-term bonds tend to be more price sensitive than short-term bonds
4. As maturity increases, price sensitivity increases at a decreasing rate
5. Interest rate risk is inversely related to the bondʼs coupon rate
6. Price sensitivity is inversely related to the yield to maturity at which the
   bond is selling

Question 2

Duration

Answer 2

A measure of the effective
maturity of a bond

It is shorter than maturity for all
bonds, and is equal to maturity
for zero coupon bonds

Duration tells investors of the length of time, in years, that it will take a bunch of cash flows to repave investor the price he or she paid for the bond.
Duration also tells investors how much of bonds price might change when interest rates change —> how much risk of a face with interest rate changes

The price of a bond with a duration of five will increase or decrease by 5% when interest rates move by 1%

Question 3

What determines the duration of a bond

Answer 3

• The duration of a zero-coupon bond equals its time to maturity
• Holdingmaturity constant, a bond’s duration is higher when the coupon rate is lower
• Holding the coupon rate constant, a bond’s duration generally increases with its time to maturity
• Holding other factors constant, the duration of a coupon bond is higher when the bond’s yield to maturity is lower
• The duration of a level (non-growing) perpetuity is equal to:
D= (1 + y) / y

Question 4

Bond convexity

Answer 4

Bonds with greater curvature gain more in price when yields fall than they lose when yields rise

Question 5

Mortgage-backed Securities (MBS)

Answer 5

MBS are based on a portfolio of callable amortizing loans

Homeowners do not refinance as soon as rates drop, so implicit call price is not a firm ceiling on MBS value

Question 6

Immunization / Durationmatching

Answer 6

• In a portfolio, the interest rate exposure of assets and liabilities are matched
• Match the duration of the assets and liabilities
• Price risk and reinvestment rate risk exactly cancel out
• As a result, value of assets will track the value of liabilitieswhether rates rise or fall

Passive strategy

Question 7

Active management of interest rate risk

Answer 7

• Interest rate forecasting– anticipate movements across the fixed income market
• Identification of relative mispricing within the fixed-income market.
• Swapping strategies
1. Substitution swap
2. Intermarket spread swap
3. Rate anticipation swap
4. Pure yield pickup swap
5. Tax swap

• Select a particular holding period and predict the yield curve at the end of period

Question 8

Difference Forward - Future

Answer 8

• Standardized contracts create liquidity
• Marked to market
• Exchange mitigates counterparty (credit) risk

futures trader cannot walk away from the contract if it is not profitable.

At the time the contract is entered into (inception), no money changes hands, only at the final settlement.

Question 9

Margin & Marking to market

Answer 9

Marking to market - each day the profits or losses from the new futures price are paid over or subtracted from the account

• InitialMargin - funds or interest-earning securities deposited to provide capital to absorb losses
• Maintenance margin – level at which the accountmust be replenished or position reduced
• Margin call - when the maintenance margin is reached, broker will ask for additional margin funds
• Convergence of price - as maturity approaches the spot and futures price converge

Question 10

Explain Index Arbitrage

Answer 10

Exploiting mispricing between underlying stocks and the futures index contract
• Futures price too high - short the future and buy the underlying stocks
• Futures price too low - long the future and short sell the underlying stocks

• Transactions costs are often too large
• Trades cannot be done simultaneously
• Other traders may act first

Question 11

Swaps

Answer 11

Swaps are multi-period extensions of forward contracts.

• Dealer enters a swap with Company A —> Pays fixed rate and receives LIBOR
• Dealer enters another swap with Company B —> Pays LIBOR and receives a fixed rate
• When two swaps are combined, dealer’s position is effectively neutral on interest rates.