Futures VS Forward and more

[USTC]

Questions 1.

As I understand, forward and futures contracts are treated almost the same way except for those mentioned specifically to differentiate them from each other. But on Page 231-232 (Volume 2) of the All 10 manual, the Delta of forward and future contracts are totally different. Anybody can give me a hint?


Question 2.

When calculating the taxes for the capital gain and the interest income. Is the following true?

1. If the bond is not sold, no matter it is a coupon bond or zero-coupon bond, no matter whether the YTM changes or not, there is no capital gain. So there is no tax charged against capital gain.

2. If there YTM stays unchanged, there is no capital gain.

Question 3. (kinda of related to Question 2.)

Page 167 of All 10 manual (Volume 1), in the end of the page, it says that the imputed interest is $3.97. Is this the total amount will be taxed for interest or only part of the interest to be taxed? I am thinking it this way:
The total interest to be taxed should be 549.69*8%=$43.9752. In the $43.9752, $40 is coupon income, and the $3.9752 is due to the fact that the bond was originally sold at discount.

Thanks for any discussion.
:exams:

[bg23516]

For your question 2 (and a bit of 3):
Taxes are paid on original issue discount bonds. The IRS imputes taxable interest income on these bonds equal to the built-in price increase (calculated at the original yield-to-maturity) during the year, regardless of whether a sale occurs.

If the bond is sold, a capital gain/loss is recognized equal to the difference between the value at the original YTM and at the sale value.

[frank_exams]

Questions 1.

As I understand, forward and futures contracts are treated almost the same way except for those mentioned specifically to differentiate them from each other. But on Page 231-232 (Volume 2) of the All 10 manual, the Delta of forward and future contracts are totally different. Anybody can give me a hint?

On p.231, 1.0 is the delta of the value of a forward contract (obtained by taking the derivative of S - Ke^{-rt} with respect to S). On p.232, e^{rt} is the delta of the futures price, not the delta of the value of a futures contract. The delta of the value of a futures contract would be 1.

It's probably easier to disassociate the math. If you own either a future or forward contract, the value of the contract should move in tandem with value of the underlying asset.

When calculating the taxes for the capital gain and the interest income. Is the following true?

1. If the bond is not sold, no matter it is a coupon bond or zero-coupon bond, no matter whether the YTM changes or not, there is no capital gain. So there is no tax charged against capital gain.

2. If there YTM stays unchanged, there is no capital gain.


1. is definitely true and I'm 99.9% sure 2. is true, but I'm too lazy to work out the details right now. I'm halfway through Goldfarb and I'm a little woozy.

Page 167 of All 10 manual (Volume 2), in the end of the page, it says that the imputed interest is $3.97. Is this the total amount will be taxed for interest or only part of the interest to be taxed? I am thinking it this way:
The total interest to be taxed should be 549.69*8%=$43.9752. In the $43.9752, $40 is coupon income, and the $3.9752 is due to the fact that the bond was originally sold at discount.


That's the total amount of interest you'll be taxed on in that year. The calculation looks good to me.

Frank

[USTC]

For your question 2 (and a bit of 3):
Taxes are paid on original issue discount bonds. The IRS imputes taxable interest income on these bonds equal to the built-in price increase (calculated at the original yield-to-maturity) during the year, regardless of whether a sale occurs.

If the bond is sold, a capital gain/loss is recognized equal to the difference between the value at the original YTM and at the sale value.

If the YTM doesn't change, the difference between the value at the original YTM and at the sale value should equal to zero. So it means my understanding is correct, right?

Thank both of you.

Good luck.

[ramanujan]

On p.231, 1.0 is the delta of the value of a forward contract (obtained by taking the derivative of S - Ke^{-rt} with respect to S). On p.232, e^{rt} is the delta of the futures price, not the delta of the value of a futures contract. The delta of the value of a futures contract would be 1.

It's probably easier to disassociate the math. If you own either a future or forward contract, the value of the contract should move in tandem with value of the underlying asset.

Frank

The difference between futures and forwards is that a futures contract is marked to market .

If you are long a forward contract, the value of the contract changes by the same amount as the underlying stock. Same is true for a future, but since it is marked to market, you have to pay (or recieve) the difference right now. This payment grows to exp(rt) dollars for evey dollar paid at maturity. Therefore, the delta of a future contract is exp(rt).

Also remember that the maturity here is not the maturity of the future but of the option that that you are trying to hedge because that is the time you would sell the contract as you don't need to hedge anymore.

Agree with rest of Frank's answers.

[frank_exams]

A simple Google search verifies that this is correct. Most likely Hull agrees, although I won't have access to the book until Tuesday. However, I still can't wrap my head around it, maybe I could get some help.

For any change in the underlying stock, you could always trade your forward contract OTC and realize the gain/loss (again under the common assumptions regarding spreads and transaction costs). In both cases (forward or future), the gain/loss is directly tied to the underlying, the timing of the gain/loss is the same, so the delta should be the same.

This may be one of those things I put in a shoebox on a dusty shelf in my brain until the exam is over...

Frank

[bg23516]

If the YTM doesn't change, the difference between the value at the original YTM and at the sale value should equal to zero. So it means my understanding is correct, right?

Thank both of you.

Good luck.

Right.