Question

Can you please determine the current yield curve my understanding is this

100,000,000/(1+0.02615)^10

=77,248,757.92 would 7.724% be the current yield curve.

We you need to implement a hedging strategy to ensure that the fund has enough capital to meet a liability. The superannuation fund will need to pay $100 million in 5 years’ time.

(a) Use the current yield curve to determine the present value and also the modified duration of the liability.

Code Coupon Maturity Years Face Value ZCB Yield

GSBG25

3.25%

5.00

100

2.615%

I look forward to hearing from you.

Answer 1

Price of the bond is the present value of outstanding coupon payments and the maturity amount. For calculating the present value, yield of ZCB is used. Since the bond offers higher coupon rate than the ZCB yield, it will be priced at more than face value at the beginning of year 1.

Current Yield is the annual coupon payment divided by the price of the bond.

Current Yield Curve is the graphical representation of changes in current yield over the life of the bond.

In the given case, the price of the bond is calculated as follows:

Year	Payments (Million $)	Present Value Factor	Present Value (Miilion $)	Year*PV
1	3.25	0.975	3.17	3.17
2	3.25	0.950	3.09	6.18
3	3.25	0.925	3.01	9.03
4	3.25	0.902	2.93	11.72
5	103.25	0.879	90.75	453.75
		4.631	102.94	483.85

Present Value of the bond liability at the beginning = 102.94 $ million

Modified Duration = (483.85/102.94)/1.02615 = 4.58 years

Price at the beginning of year 1 is the present value of payments outstanding from Year 1 to 5,

Price at the beginning of year 2 is the present value of payments outstanding from Year 2 to 5

Price at the beginning of year 3 is the present value of payments outstanding from Year 3 to 5

Price at the beginning of year 4 is the present value of payments outstanding from Year 4 to 5

Price at the beginning of year 5 is the present value of payments outstanding at the end of year 5

Current yield = Coupon Payment/Price of the bond

Thus price at the beginning of years is as follows,

Year Price Coupon Current Yield

1 102.94 3.25 3.16%
2 99.77 3.25 3.26%
3 96.69 3.25 3.36%
4 93.68 3.25 3.47%
5 90.75 3.25 3.58%

The Current Yield Curve will look as follows:

X Axis: Years

Y Axis: Current Yield

Note: Present Value Factors are calculated as