Calculate the effective duration of a bond to a 100 basis

Question

Finance: Investment Analysis and Portfolio Management 

SHOW YOUR WORK.

You wish to hedge 90 percent of the current portfolio value with futures. The value of the portfolio is $ 50 million and tracks the S&P 500 index. The index is 1,076.32 ($250 per point) and the portfolio has a beta of 1.2. Calculate the appropriate number of contracts to realize the hedge.

 This material is presented in Chapter 21 and the Lectures. 

What would be the swap fixed rate (SFR) for a plain vanilla, two-year interest rate swap, payments every six months beginning 07/01/0x with the following assumptions/data:

Swap initiation, January 1, 200x

FRA_1,0 = 2.221%; FRA_1,1 = 2.258%; FRA_1,2 = 2.322%; FRA_1,3 = 2.388%; FRA_1,4 = 2.520%; FRA_1,5 = 2.632%; (Read the notation, FRA_1,0 as “six-month forward rate from 01/01/0x, FRA_1,1 as “six-month forward rate, six-months from 01/01/0x, FRA_1,2 as “six-month forward rate, one-year from 01/01/0x, etc..

LIBOR to remain at 2.18%.

 

Chapter 23 and the Lectures: please keep in mind that fixed side of a swap is always 30/90/180/360/360 convention for accruals; while the floating side is Actual/360. 

The futures contract quote on 5,000 bushels of soybeans traded on the CBOT, Monday, December 31, 2001 was:

Open: 423-3/4 ($4.2375/bushel)

High: 424 ($4.24/bushel)

Low: 419-1/2 ($4.1950/bushel)

Settle: 421 ($4.21/bushel)

You shorted 3 contracts at $4.22 on December 31, 2001. 

The settlement for January 2, 2002 was $4.18 (the markets were closed on New Year’s). If you had to post a $1,000 initial margin per contract upon placing the trade, what would be your trade account balance at the close of January 2, 2002?

This material is presented in Chapter 21 and the Lectures. 

Using the following data, calculate the fixed-rate payer’s first two net quarterly payments/receipts for a hypothetical interest rate swap described below.

 

Notional principal                                  $10 million

Fixed rate                                             7.0%

Days in first quarter                               91

Days in second quarter              92

Current LIBOR (LIBOR₀)              5.0%

Expected LIBOR (LIBOR₁)                      5.3%

Expected LIBOR (LIBOR₂)                      4.8%

 Chapter 23 and the Lectures: please keep in mind that fixed side of a swap is always 30/90/180/360/360 convention for accruals; while the floating side is Actual/360.  

Calculate the effective duration of a bond to a 100 basis point change in interest rates with a 6-1/4 coupon, 10-years remaining to maturity, and an asking quote of 110.7811 (decimal, not 32nds).

Please use Chapter 18 material and the Lectures. 

Calculate the effective convexity to a 100 basis point change of the bond in Question 5. 

Please use Chapter 18 material and the Lectures. 

Calculate the total percentage price change (duration and convexity) to a 65 basis point decrease in interest rates for the bond in Questions 5 and 6. 

Please use Chapter 18 material and the Lectures. 

Given the following Treasury spot rate curve, calculate the arbitrage-free value of a 6 percent coupon, 2-year Treasury note.

Period                          Years                            Spot Rate (%)

1                                  0.5                                3.0000

2                                  1.0                                3.3000

3                                  1.5                                3.5053

4                                  2.0                                3.9164

 

Please use Chapter 18 material and the Lectures. 

What is the price of a $100,000 Treasury bill with 151 days left to maturity and a discount yield of 3.75 percent? 

Please use Chapter 18 material and the Lectures. 

Using put-call parity, what market actions would you take to create a synthetic stock?

Please use Chapter 20 material and the Lectures