FRM一级模考

FRM一级模拟题

1 . A trader executes a $420 million 5-year pay fixed swap (duration 4.433) with one client and a $385 million l0 year receive fixed swap' (duration 7.581) with another client shortly afterwards. Assuming that the 5-year rate is 4.15 % and l0-year rate is 5.38 % and that all contracts are transacted at par, how can the trader hedge his net delta position?

A. Buy 4,227 Eurodollar contracts

B. Sell 4,227 Eurodollar contracts

C. Buy 7,185 Eurodollar contracts

D. Sell 7,1 85 Eurodollar contracts .

Answer! B

Step l. First swap is equivalent to a short position in a bond with similar coupon characteristics and maturity offset by along position in a floating-rate note.

its DVOI = $420 millionx4.433 x O.OOOI = $186,186

Step 2 . Second swap is equivalent to a long position in a bond with similar coupon characteristic's and maturity offset by a short position in a floating-rate note.

its DVOI = $385 million x 7.581 x 0.0001 = $291,868.5.

Step 3. Net DVOI of ( first swap+ second swap) =-186186+291868.5=$105682.5

Step 4. The optimal number is Nss = -(DssS S)/ (DssF F )=-105682.5/25=4227 (Note that the DVBP of the futures is about 0.25 x $1, 000, 000 x 0.0l% = $25.) '

2 . Two banks enter into a l-year plain vanilla interest-rate swap with the following terms:

Notional principal is $500,0'00,000.

The fixed component of the swap is 7%, which is the current market rate.

The floating component of the swap is LIBOR + 200bps.

If the current risk-free rate is 4%, the value for this swap at inception is closes to:

A. $500,000,000

B. $8,750,000

C. $35,000,000

D. $0

Answer: D

The initial value of a swap is always zero. As interest rates move and payments take place, the value of the swap will change for both parties.

3 . A financial institution has entered into a plain vanilla currency swap with one of its customers. The period left on the swap is two years with the institution paying 4.5% on USD120 million and receiving 2% on JPY3,500 million annually. The current exchange rate is 120 JPY/USD, and the flat term structure in both countries generates a 3 % rate in the U.S. and a 0.5% rate in Japan. The current value of this swap to the institution is closest to:

A. $93,300,000 '

B. -$118,090,000

C. -$93,300,000

D. $118,090,000

Answer: C

Step I. The institution is paying USD and receiving JPY so the value of this swap 'will equal the current exchange rate times the value of the JPY portion minus the value of the USD portion.

Step 2.The JPY portion of this swap = 70e(-o.o05) + 3570e(-o.o05 x 2) = JPY3,604,1 3 0,000. .

Step 3.The USD portion of the swap = 5.4e(-0.03) + 125.4e(-0.03 x 2) = USD123,340,000.

Step4.The value to the institution - [JPY3604.13/(JPY120/USD)] - USD123.34 =

-USD93,300,000.

424.You have entered into a currency swap in which you receive 4% per annum in yen and pay 6% per annum in dollars once a year. The principals in the two currencies are 1000 million yen and l0 million dollar. The swap will last for another two years, and the current exchange rate is 115 yen for l dollar. Suppose that the annualized spot rates (with continuous compounding) are given as in the table below, what is the value of the swap to you in million dollars?

5 . gamma industries inc issues an inverse floater with a face value of USD 50-000.,000 that pays

a semiannual coupon of 11.50% minus LIBRO, gamma industries intends to execute an arbitrage strategy and earn a profit by selling the notes. Using the proceeds to purchase a bond with a fixed semiannual coupon rate of 6.75% a year and then hedge the risk by entering into an appropriate swap. Gamma industries receives a quote from a swap dealer with a fixed rate of 5.75% and a

floating rate of LIBOR. What would be the most appropriate type of swap of Gamma industries, Inc., to enter into to hedge its risk?

A. Pay-fixed, receive-fixed swap

B. Pay-floating, receive-fixed swap

C. Pay-fixed, receive-floating swap

D. The risk cannot be hedged with a swap .

Answer: B

A. Incorrect.

The com pany has a floating outflow of (11.50% - LIBOR) and a fixed inflow of

(6.75%)(USD 50,000,000). The swap suggested has two fixed legs which is not an appropriate

structure for an interest rate swap which should have a fixed leg and a variable leg.

B. Correct.

The company has a floating outflow of (11 .50% - LIBOR) and a fixed inflow of

(6.75%)(USD 50,000 ,000.On the outflow, -LIBOR is the same as an inflow Pay-floating,

Receive-fix. Gamma Industries is exposed to interest rate fluctuations of LIBOR. Therefore, the appropriate swap would be. a pay-floating, receive-fixed. swap.

C. Incorrect.

The company has a floating outflow of (1 1.50%- LIBOR) and a fixed inflow of (6.75%)(USD 50,000,000). On the outflow, -LIBOR is the same as an inflow Pay-floating, Receive-fix.

Gamma Industries is exposed to interest rate fluctuations of LIBOR. Therefore, the appropriate swap should pay-floating (not fix) and receive fixed (not floating).

D. Incorrect.

This risk can indeed be hedged by entering into a swap as the company has both fixed and variable rate cash flows arising from the arbitrage transaction described. .