FRM 2008 Practice PII question 7 - pfol insurance using index futures

[hsuwang]

Hello David,

so if we lose on the long call and gain on the short shares, then shouldn't the answer be "zero effect" due to the hedge?

I'm a bit confused with the "constant rebalancing" delta-neutral hedging, if as above, long call and short share will give us a hedge when stock prices move (small move), then why is it necessary to constantly re-hedge? That is, if the stock prices do not move too much, then re-hedging doesn't seem to help much?

Thanks!

 

[hsuwang]

I'm sorry but I think I might be answering my own question here,

is it due to the curvature that is causing the long call to lose "less" and the short share to gain "more"? and that's why you said the answer should be a.net profit?

so with buy low, sell high, does it mean besides the gain from positive position gamma (curvature), we're also profiting from buying low and selling high (constant re-hedging)? it looks like a double profit.

 

[David Harper CFA FRM]

Hi Jack,

Re: so if we lose on the long call and gain on the short shares, then shouldn’t the answer be “zero effect” due to the hedge?
Yes, for small moves in a short period of time.
This is essence of the "linear approximation" that is also true for bond duration (or duration hedge), and any of the 1st derivative greeks (vega), and the marginal VaR: the slope of the tangent line is the delta, but the actual line is curved, so the hedge (if left unbalanced) is not good beyond small/ moves

Re: why is it necessary to constantly re-hedge: because of transaction costs, you are right, to a point. The re-balancing is required simply because the delta changes (i.e., we are delta hedged but not gamma hedged). If transaction costs > benefits, you are right, but the essence of the delta hedge...
(Hull.s illustrated here: http://www.bionicturtle.com/premium/spreadsheet/4.b.5_dynamic_delta_hedge/)
...whenever the delta changes

David

 

[David Harper CFA FRM]

Re: is it due to the curvature that is causing the long call to lose “less” and the short share to gain “more”? and that’s why you said the answer should be a.net profit?
Yes, exactly!

Re: so with buy low, sell high, does it mean besides the gain from positive position gamma (curvature), we’re also profiting from buying low and selling high (constant re-hedging)? it looks like a double profit.
Yes, double due to static (option has gamma, share does not; i.e., option has curve, share is straight line) plus dynamic (buy low/sell high) *if* we are reblancing, right? (dynamic rebalancing is a 2nd optional step) that's why i say there are two things here: static & dynamic. Erog, i agree with your "double profit" take...is this a free lunch? no, because we paid the option premium! that's why, at the essence of the long call position is the long gamma: the option premium is based on the implied volatility ... if the realized volatlity = implied premium, our realized profit will = our premium. If realized volatlity > implied, our profit is greater.

...also, we might consider this position a gamma versus theta: our worst case scenario is no volatility (the other side of the trade is "long" theta, in a way) because the call option automatically loses value via time decay. no volatility means we lose the option premium (that was priced based on implied volatiilty) but realized vol < implied vol.

David

 

[hsuwang]

I see.. Thank you for the clarification!

 

[rahul.goyl]

Hi All,

@Ajsa delta-neutral hedge using Only Options, however in the Question we are using Synthitic Hedging using No. of Future Contract * put delta (Negative)

a. Buy an amount of index futures equivalent to the change in the call delta x original portfolio value.
c. Buy an amount of index futures equivalent to the change in the put delta x original portfolio value.

Choice a. would be wrong bcause (Look at the below e.g, I have changed the delta to Positive (Long Call) from my earlier post.

So if you are long 100 share of MS call delta is say Positive (0.60)
Then simply sell 100*+0.60/250 * Index value (i.e 5)
+60/1250
+ 0.048
That means buy 0.048 S&P Future 500 index. (This will make you Long future (a.Buy), which will not hedge your portfolio.
C is obviously wrong choice, you can-not Buy index futures, given under portfolio insurance you are long the underlying.

David examples are excellent, which helps clearing confusion between Portfolio Hedging & Portfolio Insurance.

Regards,
Rahul