Risk Management Applications of Swaps

Question 1

Duration of a pay-fixed receive-floating swap

Answer 1

= duration of a floating-rate bond - duration of a fixed-rate bond with equivalent cash flows

Question 2

Duration of a fixed-rate bond

Answer 2

Approximately 75% of the maturity

Question 3

Duration of a floating-rate bond

Answer 3

• Approximately equal to the time remaining until the next coupon payment
• Example: Time between payments is approximately 0.25 for a bond with quarterly payments → The average duration is approximately 0.125

Question 4

Swaption

Answer 4

• An option giving the right to enter into a swap
• Payer swaption (put) - enter as the fixed rate payer
• Receiver swaption (call) - enter as the fixed rate receiver

Question 5

Swaption versus options on bonds

Answer 5

• A receiver swaption is analogous to a call option on a bond
• A payer swaption is analogous to an put option on a bond

Question 6

• To synthetically add a call feature to a bond (call feature held by the issuer)
• To synthetically remove a call feature on a bond (call feature previously held by the issuer)

Answer 6

• Purchase a receiver swaption
• Sell a receiver swaption

Question 7

• To synthetically add a put feature to a bond (put feature held by the bondholder)
• To synthetically remove a put feature on a bond (put feature previously held by the bondholder)

Answer 7

• Sell a payer swaption
• Purchase a payer swaption

Question 8

The notional principal of a swap necessary to change the duration of a bond portfolio worth B from MDUR_B to a target duration MDUR_T

Answer 8

Question 10

Converting foreign cash flows into domestic currency

Answer 10

• Foreign notional amount = foreign currency cash flows / (foreign currency swap rate / n)
• Domestic notional amount = foreign notional amount * current fx rate
• Domestic currency cash flows = domestic notional amount * (domestic currency swap rate / n)

Question 11

Delta hedge at expiration

Answer 11

At expiration, at-the-money call options move very rapidly to a delta of 1 or 0. At this point, the gamma is the highest and it is very difficult to maintain a delta-hedged position

Question 12

• Economic exposure
• Transaction exposure
• Translation exposure

Answer 12

• Arises when overseas sales of a manufacturer decline in the face of a stronger or weaker currency
• Arises when overseas sales denominated in a foreign currency must be converted to the domestic currency
• Arises when the financial statements of an overseas subsidiary must be converted to the domestic currency

Question 13

Annualized VaR

Answer 13

Question 14

Effective rate on a loan with a collar

Answer 14

Loan balance × (Actual days in period/360) × [Libor_t-1 + Spread – max(0, Libor_t–1 – Cap rate) + max(0, Floor rate – Libor_t–1)]

Question 15

Swap rate quotation

Answer 15

The quote is the rate that the swap pays or receives

• Ex. If the swap rate is 4.9% in the US and 5.3% in the UK, it is possible to enter a swap that pays 4.9% on the USD notional and and receives 5.3% on the GBP notional.

Question 16

Credit risk of swaps as a function of their maturity

Answer 16

• Credit risk is highest for interest rate swaps near the middle of their life because as the swap ages, the counterparties’ credit worthiness may have changed. As the swap nears its maturity and the number of remaining settlement payments decreases, credit risk decreases.
• Credit risk is highest for currency swaps between the middle of their life and their maturity due to the exchange of principal on the maturity date.

Question 17

Determining the fixed interest rate on a swap

Answer 17

The fixed interest rate on a swap is the rate that makes the present value of the fixed and floating payments equal