Question 1:
On Friday May 19. 2017, a typical treasury bond quote is given in the form.
|
Issue
|
Bid
|
Ask
|
Ask Yield
|
|
3 7/8, 5/15/2018
|
102:19+
|
102:20
|
|
|
|
|
|
|
(a) Determine the clean bid and ask prices
(b) If you purchased the bond on May 19, 2017 at the bid price, determine the bid dirty price. Please state explicitly the day the last coupon payment was ode and the date of the next payment.
(Remember that in the Treasury market actualiactual is used for determining the accrued. Payment can only be made on a business day. )
(c) Determine the ask dirty price.
(d) Determine the ask yield.
Question 2:
A typical Treasury bill quote is of the form
|
Issue
|
Bid
|
Ask
|
Ask Yield
|
|
8/17/2017
|
0.893
|
0.892
|
|
|
|
|
|
|
Today's date is Friday May 19, 2017 and sentiment is Monday May 22, 2017.
(a) Determine the dollar bid price.
(b) Determine the dollar ask price.
(c) Determine the ask bond equivalent yield.
Question 3:
You are given information about the one year spot interest rates, assuming annual compounding.
|
Year
|
1
|
2
|
3
|
4
|
|
Spot rates (%)
|
1.161
|
1.2.80
|
1.476
|
1.03
|
|
One year forward rates
|
|
|
|
|
One year forward rates
Determine the forward rates.
Question 4:
A trader, after viewina the pricing information given in the Table below, thinks that a 5-year bond is overpriced and expects the price to decrease very soon. At present the term structure is flat. To make a profit, she decides to short 10,000 of the 5-year bonds. However, given the interest risk, the trader needs to design a hedging strategy by trading some other bonds. There are two other bonds available in the mallet
|
Man city
(Years)
|
Coupon rate
(%)
|
YT NI
(%)
|
Bond price
($)
|
Modified
Duration
|
|
5
3
6
|
1.2
1.2
1.2
|
1.2
1.2
1.2
|
100
100
100
|
4.83888
2.93799
5.77241
|
The trader uses a butterfly strategy to hedge agaiust interest risk. Based on the above infonnaticra, determine the quantities of each bond to be traded in this strategy_ Examine the sensitivity of the hedged portfolio for parallel shifts in the term structure of +/- 50 basis points.
Question 5:
You own a treasury bond with 2 years left to maturity, a coupon of 1 7.18% face value of 100 and a price of 100:5. The next coupon is in six month time.
(a) Determine the 3i.eld to maturity.
(b) Calculate the modified duration of the bond.
Please provide an explanation of the logic used to derive the results.
Question 6:
A 60 year old woman is comiclerina the purchase of an annuity that pays $1,000 every months for the rest of her life. Assume that the term structure of semi-annual compounded spot rates is flat at 0.95% lithe annuity costs $500,000, how long mug the woman expect to live in order to break-even?
Question 7:
After the trade in question in Question 3 is placed, the term structure moves upwards in response to moves by the Federal Reserve and is described by
| Maturity |
Discount Rates |
| 0.5 |
1.25 |
| 1 |
1.3 |
| 1.5 |
1.37 |
| 2 |
1.44 |
| 2.5 |
1.5 |
| 3 |
1.56 |
| 3.5 |
1.64 |
| 4 |
1.72 |
| 4.5 |
1.81 |
| 5 |
1.94 |
| 5.5 |
2.02 |
| 6 |
2.13 |
where the discount rate is the zero coupon yield, expressed in percentage form assuming semiannual compounding. What is the value of the trader's position after this shift?
Querion Interest Rate swaps
| Maturity |
Zero Yield |
Price of Zero |
|
0.5
|
1.09
|
0.99458
|
|
1.0
|
131 |
0.98703
|
|
1.5
|
1.57
|
0.97681
|
|
2.0
|
1.89
|
0.96308
|
|
2.5
|
2.11
|
0.94888
|
|
3.0
|
237 |
0.93176
|
|
3.5
|
2.59
|
0.91387
|
|
4.0
|
2.81
|
0.89439
|
|
4.5
|
3.00
|
0.87459
|
|
5.0
|
121 |
0.85280
|
|
|
|
Total = 933779
|
Semi annually compounded.
We want to value a 5 year swap, assuming the floating side is reset every six months. Given the information in Table 1, please determine
(a) Determine the present value of the floating rate payments;
(b) What is the present value of the fixed rate payments, if the swap rate was unity.
(c) Determine the 5 year swap rate, assuming the floating side is reset every six months.
(d) Determine the 5 year swap rate, assuming the floating side is reset every dree months. What are the benefits and the costs?