# Optimal hedge rations and tailing the hedge

#### JSING5137

##### New Member
Subscriber
Hi

can someone please explain me those two topics, I Tried reading it from core but wasn't able to grasp the understanding and logic for both the topic

Thanks

#### gsarm1987

Subscriber
@JSING5137 you have a stock $100, its beta with a broad market (eg. S&P500) is 0.7, if S&P is down 2% your stock should be down 1.4%. The futures available say SP500 future (futures are standardized by size and may not be a perfect fit) may have beta 1 with that broad market. When it comes to hedging, you can either hedge the entire 100% (not so optimal in this case) or just hedge by the amount suitable per hedge ratio (we are getting there). so whenever the market moves, we need to make sure we keep that hedge ratio constant. that's tailing the hedge. if you note, when nothing moves we are optimal if we go in line with the hedge ratio, but when markets move, it may require adjusting the hedge up/down just in a race to maintain the optimal cover for the basis. this is one disadvantage that you will have to be in a constant state of worry, trying keeping the balance (requiring frequent rebalancing, it comes at the cost of trading and risk of missing the next bus after you drop out of one). Ill write one of the ways of doing it when it comes to deciding how many contracts you'd need: Value of stocks * (Target beta - Current beta)/(value of futures * future's beta) = number of future contracts you will need to enter. There are different ways of doing this, depending on the question. i'd say refer to example on page 14-15 of chapter 8, Financial Markets & products, BT notes. Also see Last edited: #### JSING5137 ##### New Member Subscriber @JSING5137 you have a stock$100, its beta with a broad market (eg. S&P500) is 0.7, if S&P is down 2% your stock should be down 1.4%. The futures available say SP500 future (futures are standardized by size and may not be a perfect fit) may have beta 1 with that broad market. When it comes to hedging, you can either hedge the entire 100% (not so optimal in this case) or just hedge by the amount suitable per hedge ratio (we are getting there). so whenever the market moves, we need to make sure we keep that hedge ratio constant. that's tailing the hedge. if you note, when nothing moves we are optimal if we go in line with the hedge ratio, but when markets move, it may require adjusting the hedge up/down just in a race to maintain the optimal cover for the basis. this is one disadvantage that you will have to be in a constant state of worry, trying keeping the balance (requiring frequent rebalancing, it comes at the cost of trading and risk of missing the next bus after you drop out of one). Ill write one of the ways of doing it when it comes to deciding how many contracts you'd need: Value of stocks * (Target beta - Current beta)/(value of futures * future's beta) = number of future contracts you will need to enter. There are different ways of doing this, depending on the question. i'd say refer to example on page 14-15 of chapter 8, Financial Markets & products, BT notes. Also see
Hi Gsarm 1987

Thanks for the explanation, I think I got the broad perspective but can you let me know what is beta ?
I just did first 7 chapters in FMP and there was no mentioning in it, I did it from core (self study). How are the video lectures, can i prepare from them ?

or can you help me out how i should prepare

#### gsarm1987

##### Member
Subscriber
@json5137 beta is the regression coefficient of performance of an asset against the border market performance. one way to write it is : Beta = Corr*StdevAssetreturns/StdevMarketreturns. beta is related as sensitivity to market factor. In anycase, the quants reading will help you understand it better. Videos are very insightful and help with keeping focus on LOS , i'd say keep regular with practicing quants questions. but again, you also need to read from notes/core. Focus on the LOS. Some readings will have to go parallel with the quants knowledge, especially when you reach the VAR topic in the other book. I'd suggest taking quants as a daily dose along with your general progress in preparation. split your day

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#### JSING5137

##### New Member
Subscriber
thanks for the insights GSarm, I was trying to complete FMP first and then tackling quants