Aclaration on (III.2.50)

Discussion of Pricing, hedging and Trading Financial Instruments
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damaran
Posts: 2
Joined: Sun Jun 22, 2014 12:56 pm

Aclaration on (III.2.50)

Postby damaran » Wed Jun 25, 2014 10:55 pm

Hi Carol,

First of all Congratulations for the book I'm really enjoying it and my apologies for any possible language mistake.
I have to questions relating to the section of futures and forwards:

1)
I've worked the math In expression (III.2.9) [rf(t,T) ~ rs(t) - r(t,T) + y(t,T)] but I get [rf(t,T) ~ rs(t) + r(t,T) - y(t,T)] which I find more consitent with the theoretical forward price. F(t,T)=S(t)*exp(r(t,T)-y(r(t,T))). I mean, if the discount rate increase the theoretical futures value increase, if the dividend yield increase the theoretical futures value decrease. What I am missing?

2)
I have problems with expresion (III.2.50) relating to the decomposition of the basis risk in a hedged stock portfolio.
I have consulted the changes for the second reprinting and this equation was then modified. I find that the previous expression is more sensible.
The decomposition of the three components of the basis risk now and before is as follow:

NOW
- An exposure -NB to the spot index (we have the same exposure as without hedge with opposite sign)
- An exposure N(1+B) to the discount rate of the same maturity as the future. (the discount rate is far more than the nominal forward position NB, the nominal stock position is added as discount rate exposure )
- An exposure -NB to the dividend yield

BEFORE
- An exposure N(1-B) to the spot index (the exposure is reduced with the hedge)
- An exposure NB to the discount rate of the same maturity as the future (the nominal forward position is NB ).
- An exposure -NB to the dividend yield

The arguments by which I find more sensible the previous expression are:
*If we are hedging the original stock portfolio shorting futures contracts the resulting stock exposure should be reduced.
*The discount rate exposure is introduced when we add short futures positions to the original portfolio, therefore the resulting discount rate exposure should be equal
to the nominal futures position


Surely I'm loosing something, I would appreciate your help

Thanks in advance

damaran
Posts: 2
Joined: Sun Jun 22, 2014 12:56 pm

Re: Aclaration on (III.2.50)

Postby damaran » Wed Jun 25, 2014 11:18 pm

Forget the first question, I found my mistake.


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