Question

You want to protect $100 million in bond investments against rising rates and plan to use 10-year treasury futures.

Do you go long or short futures?       

Current rates are 3%.

If rates go up to 4%, what is your gain or loss on the contract?

You plan to buy a 10-year corporate bond in one month. Current yields for corporate bonds are 4% when treasury rates are 3%. You want to protect against rates falling.

Do you go long or short treasury futures?

Treasury rates fall 50 bps.

How much do you gain or lose on the futures contract?

What happens if corporate bond spreads fall 50 bps over the same time period?

Treasury yield protected to 3%, but spread is 50 so net is?

Answer 1

1) In a scenario that interest rates will rise, the price of the bond will go down. In order to protect the bond investment, one will need to form a strategy that will allow him to profit from the fall in bond/treasury prices. Shorting a future is a strategy to benefit from falling prices of the underlying asset. hence, in this case one will need to go short on futures. This way, there will be loss on the bond value if interest rates rise, but there will be gain on hte short position as treasury value will fall.

2) If the current rates are 3% and they go upto 4%, then the value of the treasury falls and hence there will be a gain in the shorting of the future. The amount of gain will be as follows:

the $ 100 million treasury gives a 3% coupon every year for 10 years - ie $ 3 million every year and $ 100 million on 10th year.

Now, with 4% coupon every year, the price fall will be such that the new price will have a 4% IRR for $ 3 million every year and $ 100 million on 10th year ie the NPV of the above cash flows will have to be discounted with a 4% discount rate

Particulars	Yr 1	Yr 2	Yr 3	Yr 4	Yr 5	Yr 6	Yr 7	Yr 8	Yr 9	Yr 10
Cash flows (USD million)	3	3	3	3	3	3	3	3	3	103
Discounting factor @ 4%	0.96	0.92	0.89	0.85	0.82	0.79	0.75	0.73	0.70	0.67
Present Value (USD million)	2.88	2.77	2.67	2.56	2.47	2.37	2.28	2.19	2.11	69.58
Sum (USD Million)	91.88

Hence, gain in future is USD 100 million - USD 91.88 million ie USD 8.12 million  

3) If you want to protect against rates falling, then you need to go long on future. If rates fall, then the price of the bond/treasury will rise and hence you need to go long on future as that will give you a profit if the price of the underlying asset - treasury in this case, goes up.

4) If the current rates are 3% and they go down to 2.5%, then the value of the treasury will go up and hence there will be a gain in the long future. The amount of gain will be as follows:

the $ 100 million bond gives a 3% coupon every year for 10 years - ie $ 3 million every year and $ 100 million on 10th year.

Now, with 2.5% coupon every year, the price fall will be such that the new price will have a 2.5% IRR for $ 3 million every year and $ 100 million on 10th year ie the NPV of the above cash flows will have to be discounted with a 2.5% discount rate

Particulars	Yr 1	Yr 2	Yr 3	Yr 4	Yr 5	Yr 6	Yr 7	Yr 8	Yr 9	Yr 10
Cash flows (USD million)	3	3	3	3	3	3	3	3	3	103
Discounting factor @ 2.5%	0.98	0.95	0.93	0.91	0.88	0.86	0.84	0.82	0.80	0.78
Present Value (USD million)	2.93	2.86	2.78	2.72	2.65	2.58	2.52	2.46	2.40	80.46
Sum (USD Million)	104.37

Hence, gain in future is USD 104.37 million - USD 100 million ie USD 4.37 million