Question of the hedge ratio for futures contracts.

[FRMStrawberry]

In the manual David preparted for markets and products part, on P27,
1. when Beta is 1.2, N*=32, it says that need to short 32 futures contracts.
2. Beta becomes Beta* and increases from 1.2 to 2, the optimal number of contracts is N=21.33, then long poistion on 21.33 futures contracts.
I couldn't understand why in 1., the positin is short, while in 2., the position is long.
I think that both of them should be in long position as both of N* and N are have "+" sign.
Please help me understand this.

Thanks.

 

[jeff-1984]

I was gonna ask the same question but then I saw this topic
In the notes, it says that it depends on the sign "-" means shorting and ''+" means going long but that wasnt the case in the PQ! is there another logic here that we should follow ? I came across a question which had the word increase so i understood its about going long but sometimes there's no clue !!
Please David or anyone else, can you clarify this ?

 

[David Harper CFA FRM]

Hi FRMStraberry & Jeff,

I am following Hull. If we want to rely on the signs (+/-), we can use the general form: (target beta - current beta) * V(P)/V(F) = (B* - B)*V(P)/V(F).

• So, if we are increasing the beta from 1.2 to 2.0, it implies a LONG position because (target 2.0 - 1.2) = positive.
• On the other hand, if we are NEUTRALIZING beta (i.e., "hedging") then our target beta is zero and this implies a SHORT position because (target 0 - 1.2) = negative; i.e., to "hedge" in many cases, means to neutralize so we can use target beta = 0.
  
  (Hull actually has use-cases for each, which is even more confusing, I think ...)

Although i feel it's a little risk to rely on signs for this. I personally think it's a little more robust to compute number of contracts, then use intuition to retrieve a long or a short. I hope that helps, thanks,