 # How many contracts... (hedging questions)

Hello alll,

This should be fairly easy but I have been struggling with understanding the difference… I would appreciate a brief explanation/help!

Question: When do you put “multiplier” or “conversion factor” in denominator and when in nominator, when calculating the number of contracts necessary, and why?

Risk Management - altering bond exposure with contracts

Number of contracts = {[(target duration) - (portfolio duration)]/(futures duration)} * {(Value of portfolio)/(value of futures contract * multiplier )}

This makes sense. You need less futures contracts if they have high multiplier

Fixed Income - duration management

Number of contracts = (same ratio of durations as above) * {(Value of portfolio * CTD conversion factor )/(value of CTD)}

… I am not sure if it makes sense? Why would you have it in the nominator rather than denominator?

Thank you all for your help!

Your fixed income formula is wrong – for fixed income it is:

[[Duration of Target - Duration of Portfolio] * (Value of Portfolio) / (Duration Cheapest to Deliver * Price Cheapest to Deliver)]]*conversion factor * yield beta (if applicable)

Hope this helps – get this right, it will probably be tested.

Doppleganger… my formula is correct. There is no mathematical diffeference between what you wrote and what I wrote (I skipped the beta for the sake of keeping the formulas comparative).

Still, it doesn’t answer my question…

There is only one formula and CTD conversion factor is always 1 just like yield beta if you are not given it. Multiplier is also always in the formula and is one if not given it. If given two prices or durations defer to the CTD as that is the characteristics of what will actually be delivered. In futures contracts the short has the option and will most likely deliver the CTD

There is only one formula and CTD conversion factor is always 1 just like yield beta if you are not given it. Multiplier is also always in the formula and is one if not given it. If given two prices or durations defer to the CTD as that is the characteristics of what will actually be delivered. In futures contracts the short has the option and will most likely deliver the CTD

I appreciate your responses, although they have little to do with my question…

So let me say again:

(1) I know what the formulas are and how to make the calculations;

(2) I am interested in WHY you multiply by the CTD conversion factor, but divide by the multiplier.

Thank you for help, in case there is somebody out there who actually understands the material, as opposed to merely memorising the formulas…

multipler sits in the denominator.

CTD conversion factor (and also yield beta) sits in the numerator.

The multiplier is about how much “beta” is in the future contract, because it’s how many units of stock index you’re buying. If the multiplier is larger, you obviously need fewer contracts, so it would have to go in the denominator.