Thanks to the Magician, I solved most of the questions.
One remains outstanding - see under 1.
How were the coupon (benchmark yield) of 187.500 and 275.000 calculated?
Adding Credit Duration under a Static Credit Curve
A Sydney-based investor notes the following available option-free bonds for an A rated Australian issuer:
The 5-year, 10-year, and 15-year Australian government bonds have YTMs and coupons of 0.50%, 0.75%, and 1.10%, respectively, and both corporate and government bonds have a semiannual coupon. As an active manager who expects stable benchmark yields and credit spreads over the next six months, the investor decides to overweight (by AUD50,000,000 in face value) the issuerās 15-year versus 10-year bond for that period. Calculate the return to the investor of the roll-down strategy in AUD and estimate the returns attributable to benchmark yield versus credit spread changes.
Solution:
To estimate credit curve roll-down returns, we must solve for the first two return components from Coupon income +/ā Roll-down return and separate the impact of benchmark yield versus credit spread changes.
1 Solve for the respective 5-year, 10-year, and 15-year bond credit spreads. Yield spread and G-spread are reasonable approximations because the bonds are option-free, with maturities closely aligned to par government securities.
5-year spread: 0.50% (= 1.00% ā 0.50%)
10-year spread: 0.50% (= 1.25% ā 0.75%)
15-year spread: 0.85% (= 1.95% ā 1.10%)
2 Solve for 6-month expected returns of the 10-year versus 15-year bond:
a Incremental coupon income = $162,500 (= (2.00% ā 1.35%)/2 Ć $50 million)
How were the coupon (benchmark yield) of 187.500 and 275.000 calculated?
Divide incremental coupon into benchmark and credit spread components:
Income due to benchmark yields: $87,500 = $275,000 ā $187,500
Income due to credit spreads: $75,000 = $225,000 ā $150,000
b Price appreciation is determined by the bondās price today and in six monthsā time based on unchanged benchmark rates. In six months, the 10-year and 15-year positions will be 9.5-year and 14.5-year bonds, respectively, at a yield and yield spread point along the curve. Estimate all-in YTMs and yield spreads using interpolation to arrive at the following results:
Calculate price appreciation using the difference between current bond prices and those in six months using the Excel PV function (= āPV(rate, nper, pmt, FV, type)) where ārateā is the interest rate per period (0.01225/2), ānperā is the number of periods (19), āpmtā is the periodic coupon (1.35/2), āFVā is future value (100), and ātypeā (0) involves payments made at the end of each period.
10-year: Initial price: 100.937
Price in six months: 101.118 (= āPV (0.01225/2, 19, 1.35/2, 100, 0))
Price appreciation: $89,660 (= (101.118 ā 100.937)/100.937 Ć $50 million)
Because the yield spread curve is flat at 0.50%, the full $89,660 price change in the 10-year is benchmark yield curve roll down.
15-year: Initial price: 100.648
Price in six months: 101.517 (= āPV (0.0188/2, 29, 1, 100, 0))
Price appreciation: $431,700 (= (101.517 ā 100.648)/100.648 Ć $50 million)
Because the 0.07% decline in YTM is estimated to be equally attributable to benchmark yield and yield spread changes, each is assumed equal to $215,850.
3 Incremental income due to price appreciation is therefore $342,040 (=$431,700 ā $89,660), of which $215,850 is attributable to credit spread changes. In total, the incremental roll-down strategy generates $504,540 (=$342,040 + 162,500), of which $290,850 (= $215,850 + $75,000) is estimated to be due to credit spread curve roll down.