# # of futures contract required

Usually in calculating the # of futures required to decrease/increase duration of a bond or bond portfolio, the DD (Dollar Duration) is assumed to be based on 1% change in interest rate. Please advise how to get the answer in following scenario (interest rate will rise 25 basis point).

Kaufman is afraid that interest rate will rise 25 basis point in the near future and would like to decrease the duration of a \$40M bond portfolio from 6.3 to 5.0 for a short period of time by using a Treasury bond futures with duration of 4.2, yield beta of 1.1 at a price of \$245,000.-(including the multiplier).

Is it that how the interest rate will change (eg.,+2%, -3%, - 25bp, …) is irrelevant ?
Anyone can clarify ?

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its not irrelevant because the magnitude of the interest rate change impacts the dollar duration of the portfolio (i.e. how extreme a change in NAV will be)

the DDport = 6.3(0.0025)(40mm) = \$630,000
DDtarget=5.0(0.0025)(40mm) = \$500,000

therefore you must shorten the DD by \$130,000 through selling futures contracts on Treasury Bonds (a cross hedge, I’m assuming the portfolio is a non treasury port since they provide a yield beta)

The DDf = 4.2(1.1)(0.01)(245,000) = 11,319

# contract = 130,000/11,319 = 11.49 ~ 12 contracts

desmoquattro

Char-Lee,

Schweser’s Q-bank is : {[(5.0-6.3) x 40M] x 1.1} / (4.2 x 245,000) = - 55.59
I am confused !

On the other hand,
DDf shall be = (4.2 x 0.01 x 245,000)/1.1 ?

Anyone else ?

I’m sorry, i made a little mistake - forgot to adjust the DDf for a 25bps move NOT the 100bps i used - and the use of the term “beta” is somewhat confusing in this case. To me it seems like schweser is confusing the two (or more likely, i’m confused).

if 1.1 was the conversion factor then
DDf = 4.2 x 0.0025 x 245,000 / 1.1 = 2338.64

and # contracts = (500,000 - 630,000) / 2338.64 = 55.59

i seem to remember an equation like this:

# contracts = (DDt-DDp)/(DDf/conversion factor)

=> # contracts = (500,000-630,000)/(2,572/1.1)= 55.59 (same result)

———————————————————————————————————–
but since they use the term beta, my original calcuations would have yielded something like 45 contracts (there is a formula in the schweser notes for the DDf calcuation)

The DDf = 4.2(1.1)(0.0025)(245,000) = 2829.75

and # contracts = (500,000 - 630,000)/ 2829.75 = 45.94

———————————————————————————————————–

i’m at work and don’t have my notes, if anyone has access to their notes perhaps they could shed some light.

desmoquattro

The formulas Char-lee has given here are correct.

AMC,

What seems to be the problem? Could you give me specifics

derswap07,

My question :
Is it that how the interest rate will change (eg.,+2%, -3%, - 25bp, …) is irrelevant ?

“interest rate will rise 25 basis point in the near future” seems irrelevant in Schweser’s solution as the result is same.

On the other hand, only yield beta of 1.1 is given here. Shall we assume that the conversion factor is 1 if it is not given ?

So what’s your comment ? And anyone else ?

AMC Wrote:
——————————————————-
> derswap07,
>
> My question :
> Is it that how the interest rate will change
> (eg.,+2%, -3%, - 25bp, …) is irrelevant ?

No. In the duration formula, this number will chnage the duration.
>
> “interest rate will rise 25 basis point in the
> near future” seems irrelevant in Schweser’s
> solution as the result is same.

I will need specific problem where this is cited.
>
> On the other hand, only yield beta of 1.1 is given
> here. Shall we assume that the conversion factor
> is 1 if it is not given ?
>

Yes.

> So what’s your comment ? And anyone else ?

derswap07 Wrote:
——————————————————-
> AMC Wrote:
> ————————————————–
> —–
> > derswap07,
> >
> > My question :
> > Is it that how the interest rate will change
> > (eg.,+2%, -3%, - 25bp, …) is irrelevant ?
>
> No. In the duration formula, this number will
> chnage the duration.
> >
> > “interest rate will rise 25 basis point in the
> > near future” seems irrelevant in Schweser’s
> > solution as the result is same.
>
> I will need specific problem where this is cited.

derswap07,
1. The problem was indicated at the beginning of this post. The question was : how many
future contracts are required ?
2. If you have Schweser’s 2009 Practice Exam Volume 2 on your hand, please refer to its
Exam 3 Q18.4.B. Again I am confused by it.

AMC,

This one is confusing.

The dollar duration of the CTD for a change in YTM of 50 bp based on the expected price at expiration is: 108,500 × 1.259 × 0.005 × 10.15 = 6,932.53.

The dollar duration of the \$25,000,000 corporate bond issue based on the expected yield to maturity at issuance with a constant spread to Treasuries is:
25,000,000 × 0.005 × 9.90 = \$1,237,500

NF = -1237500/6932/1.259 *1.05–236

derswap07,

Please also refer to Schweser’s 2009 Practice Exam Volume 1 Exam 3 Q15.1