Fixed Income Questions (Bonds Calculations)<\/p>\n
STARTING A NEW PAGE FOR EACH OF THE 5 MAIN QUESTIONS<\/p>\n
MARKING THE QUESTION NUMBER CLEARLY<\/p>\n
Clearly mark which is your final answer for example by writing “ANSWER:” and by underlining the numerical answer you provide for example\u00a0100.00<\/p>\n
Question 1 Portfolio<\/p>\n
There are three parts in this question. Please answer all of them.\u00a0<\/p>\n
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.<\/p>\n
Part (a).\u00a0Assume 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)<\/p>\n
Part (b).\u00a0Your 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\u00a0 to construct a portfolio as described in Table 2.\u00a0<\/p>\n
Table 1<\/p>\n
Aus. Government bonds<\/p>\n
classification<\/p>\n
Modified duration<\/p>\n
Convexity measure<\/p>\n
A<\/p>\n
Short-term<\/p>\n
1<\/p>\n
1.8<\/p>\n
B<\/p>\n
Medium-term<\/p>\n
8<\/p>\n
63<\/p>\n
C<\/p>\n
Long-term<\/p>\n
15<\/p>\n
200<\/p>\n
\u00a0<\/p>\n
Table 2<\/p>\n
Portfolio<\/p>\n
Strategy<\/p>\n
1<\/p>\n
Invest $10m in Bond A and $10m in Bond C<\/p>\n
2<\/p>\n
Invest $20m in Bond B<\/p>\n
Calculate the\u00a0expected price change\u00a0of the two portfolios in Table 2 if the yield curve changes according to your expectation. Which of the portfolio strategies\u00a0 will you follow to best capitalise on your view? (1 Mark)<\/p>\n
Part (c).\u00a0Assume you are tracking the performance of the Bloomberg Australian Treasury Bond Index. \u00a0Previously you used a pure replication strategy, but have now shifted to one of the simpler portfolios in part (b) above.<\/p>\n
Provide a written argument for\u00a0whether your decision in part b) will increase or decrease the forward-looking tracking error of your portfolio. Word limit 300 words. (3 Marks)<\/p>\n
\u00a0<\/p>\n
\u00a0<\/p>\n
Question 2 Yield curve, forward rate, bond pricing<\/p>\n
There are three parts in this question, you are expected to answer all of them.\u00a0<\/p>\n
You observe the spot rate curve as in Table 3.\u00a0Assume all the interest rates are annual effective and all the bonds pay annual coupons.<\/p>\n
Table 3<\/p>\n
year<\/p>\n
1<\/p>\n
2<\/p>\n
3<\/p>\n
4<\/p>\n
5<\/p>\n
6<\/p>\n
7<\/p>\n
8<\/p>\n
9<\/p>\n
Spot rate<\/p>\n
4.4%<\/p>\n
4.8%<\/p>\n
5.2%<\/p>\n
?<\/p>\n
5.86%<\/p>\n
6.2%<\/p>\n
6.8%<\/p>\n
7.04%<\/p>\n
7.8%<\/p>\n
Part (a). If a 4-year 8% government bond is current selling at 109, calculate the missing 4-year spot rate. (1 marks)<\/p>\n
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)<\/p>\n
Part (c).\u00a0You 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)<\/p>\n
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.\u00a0<\/p>\n
Table 4<\/p>\n
Index<\/p>\n
S&P rating<\/p>\n
Yield (p.a.)<\/p>\n
Treasury Bond<\/p>\n
AAA<\/p>\n
5.7%<\/p>\n
Semi-Government\u00a0<\/p>\n
AA<\/p>\n
5.98%<\/p>\n
Composite<\/p>\n
BBB<\/p>\n
7.24%<\/p>\n
Financials<\/p>\n
BBB<\/p>\n
7.16%<\/p>\n
Industrials<\/p>\n
BBB<\/p>\n
7.30%<\/p>\n
\u00a0<\/p>\n
\u00a0<\/p>\n
Question 3 MBS<\/p>\n
There are two parts in this question, you are expected to answer all of them.\u00a0<\/p>\n
Part (a).\u00a0Complete the following table assuming a prepayment rate of 200 PSA. (3 marks)<\/p>\n
Original balance: $200,000,000<\/p>\n
Pass-through rate: 8%<\/p>\n
WAM: 360 months<\/p>\n
month<\/p>\n
outstanding balance<\/p>\n
SMM<\/p>\n
mortgage payment<\/p>\n
interest<\/p>\n
scheduled principal repayment<\/p>\n
Pre-payment<\/p>\n
Total principal repayment<\/p>\n
Cash flow<\/p>\n
1<\/p>\n
$200,000,000<\/p>\n
0.033%<\/p>\n
$1,755,143.14<\/p>\n
$1,333,333.33<\/p>\n
$421,809.81<\/p>\n
$66,648.34<\/p>\n
$488,458.15<\/p>\n
$1,821,791.48<\/p>\n
2<\/p>\n
$198,178,208.52<\/p>\n
0.067%<\/p>\n
$1,755,143.14<\/p>\n
$1,321,188.06<\/p>\n
$433,955.08<\/p>\n
$132,315.36<\/p>\n
$566,270.45<\/p>\n
$1,887,458.50<\/p>\n
3<\/p>\n
\uff1f<\/p>\n
\uff1f<\/p>\n
$1,755,143.14<\/p>\n
\uff1f<\/p>\n
$446,538.14<\/p>\n
\uff1f<\/p>\n
\uff1f<\/p>\n
\uff1f<\/p>\n
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.\u00a0<\/p>\n
Part (b). Suppose you own a mortgage pass-through security as described in part (a).\u00a0Describe\u00a0the 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)<\/p>\n
\u00a0<\/p>\n
\u00a0<\/p>\n
Question 4 Pricing of a Swap Contract<\/p>\n
Show how to price the following Swap Contract.<\/p>\n
Tip use Excel to solve this question:<\/p>\n
Market Data<\/p>\n
Maturity<\/p>\n
Zero-Coupon Bond Price<\/p>\n
1\/5\/2022<\/p>\n
0.990<\/p>\n
1\/11\/2022<\/p>\n
0.970<\/p>\n
1\/5\/2023<\/p>\n
0.965<\/p>\n
1\/11\/2023<\/p>\n
0.960<\/p>\n
Swap Contract Data<\/p>\n
Settlement Date 1 November 2021<\/p>\n
Reset Frequency: Semi-Annual<\/p>\n
Expiry Date 1 November 2023<\/p>\n
Size of contract 10 million USD<\/p>\n
\u00a0<\/p>\n
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)<\/p>\n
\u00a0<\/p>\n
\u00a0<\/p>\n
Question 5 Futures<\/p>\n
There are three parts in this question, you are expected to answer all of them.\u00a0<\/p>\n
Part (a).\u00a0A 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.\u00a0Identify an arbitrage opportunity as in the above scenario and demonstrate how to implement a strategy to make profits from the arbitrage opportunity. (3 marks)<\/p>\n
Part (b).\u00a0Calculate the no-arbitrage price of the futures contract. (1 mark)<\/p>\n
Part (c).\u00a0You 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.\u00a0Describe\u00a0what futures position you should take in order to adjust the duration of your portfolio. (1 mark)<\/p>\n","protected":false},"excerpt":{"rendered":"
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\u00a0100.00 Question 1 Portfolio There are three parts in this question. Please answer […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[10],"class_list":["post-79167","post","type-post","status-publish","format-standard","hentry","category-research-paper-writing","tag-writing"],"_links":{"self":[{"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/posts\/79167","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/comments?post=79167"}],"version-history":[{"count":0,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/posts\/79167\/revisions"}],"wp:attachment":[{"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/media?parent=79167"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/categories?post=79167"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/tags?post=79167"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}