Fixed Income Questions (Bonds Calculations)
STARTING A NEW PAGE FOR EACH OF THE 5 MAIN QUESTIONS
MARKING THE QUESTION NUMBER CLEARLY
Clearly mark which is your final answer for example by writing “ANSWER:” and by underlining the numerical answer you provide for example 100.00
Question 1 Portfolio
There are three parts in this question. Please answer all of them.
Suppose you are managing a $100 million Australian government bond portfolio. You believe the RBA will decrease interest rates at their next board meeting. The current spot rate curve is given in the picture below.
Part (a). Assume the pure expectation theory holds. Briefly explain whether your expectation is consistent with the rest of the market as implied by the current yield curve. (1 Mark)
Part (b). Your view is that, as a result of RBA rate cut, the yield curve will shift such that the short-term interest rate will decline by 50bps, the long-term interest rate will decrease by 10bps while the medium-term interest rate will decrease by 30bps. You are considering using the bonds in Table 1 to construct a portfolio as described in Table 2.
Table 1
Aus. Government bonds
classification
Modified duration
Convexity measure
A
Short-term
1
1.8
B
Medium-term
8
63
C
Long-term
15
200
Table 2
Portfolio
Strategy
1
Invest $10m in Bond A and $10m in Bond C
2
Invest $20m in Bond B
Calculate the expected price change of the two portfolios in Table 2 if the yield curve changes according to your expectation. Which of the portfolio strategies will you follow to best capitalise on your view? (1 Mark)
Part (c). Assume you are tracking the performance of the Bloomberg Australian Treasury Bond Index. Previously you used a pure replication strategy, but have now shifted to one of the simpler portfolios in part (b) above.
Provide a written argument for whether your decision in part b) will increase or decrease the forward-looking tracking error of your portfolio. Word limit 300 words. (3 Marks)
Question 2 Yield curve, forward rate, bond pricing
There are three parts in this question, you are expected to answer all of them.
You observe the spot rate curve as in Table 3. Assume all the interest rates are annual effective and all the bonds pay annual coupons.
Table 3
year
1
2
3
4
5
6
7
8
9
Spot rate
4.4%
4.8%
5.2%
?
5.86%
6.2%
6.8%
7.04%
7.8%
Part (a). If a 4-year 8% government bond is current selling at 109, calculate the missing 4-year spot rate. (1 marks)
Part (b). You plan to purchase a 2-year zero coupon government bond in 6 years. Calculate the expected price at the time of purchase. (1 marks)
Part (c). You plan to purchase a 3-year corporate bond with a coupon rate of 5%. The issuer is a financial services provider and has a credit rating of BBB. At the time of purchase, you observe the quotes on the yields of different bond indices as in Table 4. Calculate the price of the corporate bond. (3 marks)
Hint: Use an appropriate credit spread to adjust the spot rate curve in Table 3 then use the adjusted spot rate curve to price the bond.
Table 4
Index
S&P rating
Yield (p.a.)
Treasury Bond
AAA
5.7%
Semi-Government
AA
5.98%
Composite
BBB
7.24%
Financials
BBB
7.16%
Industrials
BBB
7.30%
Question 3 MBS
There are two parts in this question, you are expected to answer all of them.
Part (a). Complete the following table assuming a prepayment rate of 200 PSA. (3 marks)
Original balance: $200,000,000
Pass-through rate: 8%
WAM: 360 months
month
outstanding balance
SMM
mortgage payment
interest
scheduled principal repayment
Pre-payment
Total principal repayment
Cash flow
1
$200,000,000
0.033%
$1,755,143.14
$1,333,333.33
$421,809.81
$66,648.34
$488,458.15
$1,821,791.48
2
$198,178,208.52
0.067%
$1,755,143.14
$1,321,188.06
$433,955.08
$132,315.36
$566,270.45
$1,887,458.50
3
？
？
$1,755,143.14
？
$446,538.14
？
？
？
Note: you don’t have to replicated the entire table in your answer. Showing the workings and values of all missing items of Month 3 suffices.
Part (b). Suppose you own a mortgage pass-through security as described in part (a). Describe the influence of a decrease in mortgage rates on the total return of the mortgage backed security as compared to an otherwise identical plain vanilla bond. (2 marks)
Question 4 Pricing of a Swap Contract
Show how to price the following Swap Contract.
Tip use Excel to solve this question:
Market Data
Maturity
Zero-Coupon Bond Price
1/5/2022
0.990
1/11/2022
0.970
1/5/2023
0.965
1/11/2023
0.960
Swap Contract Data
Settlement Date 1 November 2021
Reset Frequency: Semi-Annual
Expiry Date 1 November 2023
Size of contract 10 million USD
Task: Calculate the appropriate price for the Swap at inception (floating and fixed rates) and show all workings. (you can add a picture of your calculated spreadsheet) (5 Marks)
Question 5 Futures
There are three parts in this question, you are expected to answer all of them.
Part (a). A 4% coupon 10-year bond with a par value 100 is selling at par and is deliverable against a futures contract that settles in 4 months. The current repo rate is 6% p.a. Assume the futures price is currently 100. Identify an arbitrage opportunity as in the above scenario and demonstrate how to implement a strategy to make profits from the arbitrage opportunity. (3 marks)
Part (b). Calculate the no-arbitrage price of the futures contract. (1 mark)
Part (c). You are working for a bank and implement an immunisation strategy by matching the duration of a bond portfolio with the duration of a liability. You notice that the portfolio duration is currently higher than that of the liability. Describe what futures position you should take in order to adjust the duration of your portfolio. (1 mark)