R19.P1.T3.Hull-Chapter 6- Calculation of Hedge Ratio

[gargi.adhikari]

In reference to R19.P1.T3.Hull-Chapter 6, Topic: Calculation of Hedge Ratio:-
How do we arrive at the Contract Price Fc= 98,000 ?
What does the phrase "Each Contract Delivers $100,000 " with a current price of 98 mean ?

 

[Deepak Chitnis]

Hi @gargi.adhikari, as I understand it means your getting PV $98 for each $100. You can calculate this as 100000/100*98=98000. Hope that helps.
Thank you

 

[bpdulog]

T-bond multiplier is 100,000 meaning the quoted price*100,000 is the actual amount per contract. This is similar to the S&P 500 futures 250 multiplier. Example: If S&P futures are trading at 1,000 each contract is for $250,000.

 

[gargi.adhikari]

@Deepak Chitnis @bpdulog Thanks! So can we always assume $100 as the FV for T-Bonds...?

 

[bpdulog]

@Deepak Chitnis @bpdulog Thanks! So can we always assume $100 as the FV for T-Bonds...?

I think the way it's quoted is a % of face value, here is the quote for the 5 year T-n0te: http://www.cmegroup.com/trading/interest-rates/us-treasury/5-year-us-treasury-note.html

 

[bpdulog]

Also, check this out: https://www.cmegroup.com/trading/interest-rates/files/us-treasury-futures-and-options-fact-card.pdf

It seems like the 2 year is based on a $200,000 notional as opposed to $100,000 but for the exam we are assuming $100,000?

 

[David Harper CFA FRM]

HI @gargi.adhikari

FRM tends to expect you to know that the contract size of a US Treasury Bond is face value of $100,000, thank you @bpdulog for the fact card! (Keep in mind that US Treasury bonds also use an act/act day count, versus 30/360 for corporate bonds)

Hull Chapter 2: "The correct size for a contract clearly depends on the likely user. Whereas the value of what is delivered under a futures contract on an agricultural product might be $10,000 to $20,000, it is much higher for some financial futures. For example, under the Treasury bond futures contract traded by the CME Group, instruments with a face value of $100,000 are delivered. ...
Price Quotations of US Treasury Bonds [this refers to the underlying bond]: Treasury bond prices in the United States are quoted in dollars and thirty-seconds of a dollar. The quoted price is for a bond with a face value of $100. Thus, a quote of 90-05 or 90 5/32 indicates that the quoted price for a bond with a face value of $100,000 is $90,156.25." -- Hull, John C (2014-02-19). Options, Futures, and Other Derivatives (9th Edition) (Page 27)

to be honest, I did not even realize that the 2-year and 3-year Treasury Note Futures have a contract size of $200,000. Thanks!

 

[gargi.adhikari]

@David Harper CFA FRM Thanks much as always for sharing your invaluable insights . Every time I learn something new from you I am good on the standardization of the Contract Sizes. However, that being said though, whenever, they say 98$ ( or 'X'- amount of Dollars) as the current price, would it be safe to assume 98 $ for each 100$....and then calculate the Fc based on that..?

 

[David Harper CFA FRM]

Hi @gargi.adhikari Thank you for your kind word!

Yes, you are exactly correct; it's actually a little tricky. If you take a look at the US Treasury Bond Futures Contract Specs (http://www.cmegroup.com/trading/int...us-treasury-bond_contract_specifications.html) you'll notice Price Quotation: "Points ($1,000) and 1/32 of a point. For example, 134-16 represents 134 16/32. Par is on the basis of 100 points."

The contract specifies that a point is equal to $1,000 and par is on the basis of 100 points. So, Par = 100.00 (ie, 100 00/32) which is 100 points such that the contract price at par is 100 * $1,000 per point = $100,000 is the contract price at par. The contract size of the futures contract is $100,000 but "the quoted price is for a bond with a face value of $100." This means that the quoted price is multiplied by $100,000/$100 -->
Contract Price = Quoted Price/100*$100,000 = Quoted price * $1,000;
e.g., if quoted price is $98.00, then contract price is 98 * 100,000/100 = 98 * $1,000 = $98,000.

btw, its similar to DV01 (and KRO1) which are also quoted "per $100 face value" which always creates confusion. You will see something like, "DV01 of $0.05" but it's actually "DVO1 of $0.05 per $100 face value" so, in Tuckman explains, if the face value of the bond is $100,000 and the DV01 is $0.05, then the price increase implied by a one basis point decline in the rate is given by $0.05 * $100,000/100, not 0.05 * 100,000 as you might expect.

I hope that's helpful!

 

[gargi.adhikari]

@David Harper CFA FRM as usual I learnt so much from the above ! Thank You !