# Error on Paul Wilmott Section 5.2?

I gave this a long and hard thought because Paul Wilmott is a respected quant and I don't want to criticize his book, but am I correct in concluding that this section contains lots of errors? These are my observations and the specific section is at the bottom. I'm not trying to bash him, I'm just genuinely interested to master quantitative finance but couldn't get past this section because I think the calculations are wrong.

• Could you be a little bit more specific where you think the errors are or even what you think would be correct? Thank you – vonjd May 12 '18 at 11:18
• I've attached the table of where I think he made mistakes, the corrections and the reason why. I hope you can help correct me if I'm wrong. – gaston May 12 '18 at 11:41
• Ah, ok, I didn't see that, I thought that this is a table from the book too. Thank you. – vonjd May 12 '18 at 12:48
• You are incorrect! When you sell the stock as a hedge, you need to invest the proceeds at the risk free rate for one period. – dm63 May 12 '18 at 12:56
• But that is already imputed into the future expectation of the entire portfolio. The equation already found the PV of the entire portfolio value/gain. – gaston May 12 '18 at 14:27

I finally found my error,thanks dm63 for the explanation. I had a hard time imagining the negative position value and that it implies that I also get the interest from getting cash for the short..I used a slightly different approach but got the same result.

FV when stock goes up = FV when stock goes down

1 -1Δ+100Δ(r)=1Δ+100Δ(r)

1 -1Δ=1Δ

Δ=.5

PV= FV/(1+r)

PV= (.5+50(.1/252))/(1+(.1/252))

PV= 0.5196

Thanks for all the help guys! Really appreciate it.

• That's good. As an advice for the future, next time don't be so willing to believe that someone who is well known and respected has made a mistake in something that basic. This is arrogant if you don't mind me saying. I know because I did the exact same thing you did once a long time ago. But now I've learned better. Don't get me wrong, there are books out there with gross mistakes. But those usually get overwhelmingly bad reviews, which is not the case here. Good luck. – Yian Pap May 13 '18 at 16:31
• You're right..I didn't stop redoing the calculations because I know the probability of me being correct and wilmott being wrong is very slim. I deleted my comments before so as not to mislead readers of this thread. I just have a different way of learning and understanding things but that doesn't make other people's approach incorrect. :) – gaston May 13 '18 at 16:54