# Why do we have to calculate target BPV while Hedging Interest Rate Risk with Futures

I do not get clarity on why BPV has to be calculated when we try to find the Hedging Ratio with futures for the portfolio.

BPV Hedge Ratio = (( BPV target - BPV Portfolio ) / BPV Futures ) * Conversion Factor

I am missing the key here.

I worked out directly with the market Values instead of BPV’s and the Hedge Ratio is off by approx 20 pcs for Practice Problem 3 from the Reading Swaps, Forwards and Futures.

looking forward for help on the BPV concept for Hedging with Futures on FI.

It is just a simplified way of getting to the answers.
We are trying to balance the effect of a BP move.
We think what is the BP movment in portfolio we have now
What is the BP movement we want (target)
What is the difference?
Whis has to be covered by futures

It is just really a re-arrangement of the formula
The duration of a portfolio = Weighted value of the durations of the elements in it.

Can you should your calculations on why you think it is wrong.

Hey Mikey thanks for clarifying why calculating BPV is needed and the concept of hedging the movement of portfolio value based on changes in rates.

Didn’t get the last remark.
“Can you should your calculations on why you think it is wrong.”
What do you mean here.

BPV= money duration * 0.0001
= modified duration * market value * 0.0001

In the formula of the hedge ratio the modified duration of target, portfolio and futures are not same. Thus, you can’t use market value instead of BPV.

As for why we should use BPV rather than market value that is because the sensitivity of market value of portfolio and futures to the change of interest rate not same.

That is not correct. The BPV is used as a convient way of doing the caculations, As we are trying to get a target or hedge duration. The BPV is just a scalar of the duration.
You are using market valuues as your forumula describes
BPV= modified duration * market value* 0.0001

BPV is just a scala of market value x modied duration.

I am finding it hard to do the proof on this web entry but the Hedge Ratio formula is just a re-arrangement of the Portfolio duration = weighted average of elements in it.

We basically have
Current portfolio size x current duration + Hedge portfolio size x hedge duration = Current portfolio size x target duration
or
Hedge portfolio size x hedge duration = Current portfolio size x current duration - Current portfolio size x target duration
The BPV hedging formula dies this but uses BPV instead of “portfoliio size x duration”
In then adjusts for the fact we have a future and a CTD bond

The BPV is better as we don’t have to worry about the scalar factors for the future (it is based on \$100,000 par but quoted on \$100 par and it easy to be out be a factor of 10) the BPV of the future encorporates all this.

When I did the calculations on the above question using BPV and market values I get the same answer.

so the hedging formula we have is based on this.

We know “A” how much we have currently invested
We know TD x (A +B) = this is the target duration x current value of the portfolio

We are just re-arrrang

MikeyF, Many thanks.
Worked out the problem again with Market values.
I was making a calculation mistake.
I got the same answer with BPV and Market Values.

“Current portfolio size x current duration + Hedge portfolio size x hedge duration = Current portfolio size x target duration”

The equation you suggested clarifies the point.

Yes, I agree. Maybe I didn’t describe it clearly.

I mean that just using market value to instead of BPV is unreasonable due to the modified duration.

I thought dealdone had divided the modified duration of the numerator and denominator in the BPV Hedge Ratio Formula , so the market values were left and then there’s an approx 20 pcs deviation in results .