Sceen cast _VAR_ 4.b

[sdoshi004]

David

Risk neutrul valuation (Irrelavance of the stock's expected return)

Question

1. If we have written the call option than we must be receiving the premium on that. Where have we factored that in our calculation?

2. I found the screencast too brief considering the importance it has in the curricullam. Further, which are the formulas, we are require to remember because it became too daunting and bogged down by looking at so many greek characters.

Sorry to ask you again and again but at some point of time, you feel very bogged down so require your morale support to get it going.

Hope you understand

Thanks

Sumit

 

[David Harper CFA FRM]

Hi Sumit,

http://learn.bionicturtle.com/images/forum/hull_4b_riskneutral.png

1. Note (under this unrealistic binomial) the portfolio's future value must be $4. If stock up to $12, then long .5 shares and short the call (strike @ 10), payoff = $4 (long 0.5 shares = $6 - $2 payoff to counterpary on short option). If stock down to $8, long 0.5 shares = $4 also (call worthless). So future value of *payoff* = $4 and present value of payoff = $3.88 (i.e., $4*EXP[-12%*0.25] =$3.88). That's the key point: because the future payoff is certain (no variability), it has no risk, the riskfree rate is the appropriate rate.

Now we know that today (time 0),
Portfolio PV = $3.88 = long 0.5 shares - short 1 call option, or
Portfolio PV = $3.88 = $5 - short 1 call option, such that
short 1 call option must = $1.12

again:
$3.88 is PV of portfolio = $5 (long 0.5 shares) - $1.88 (short 1 call option)

so that's how the option premium is factored in (or really, the point is instead: we are solving for the option premium! That is the elegance). In words, we reduce the $5 cost with the premium received.

2. To be honest, I would like to spend + 50% time on every screencast. The problem is: since we follow the AIMs (which i have not counted, but I would speculate count over 700 or 800 AIMs), I can't go much slower and still finish the schedule.

But, I think you make a great point about the formulas: I wish I had thought to end each tutorial with the sequence of key formulas (i.e., needed for calculation): I think i will start doing that with topic 5 (i.e., summarize key formulas at the end). For this topic 4, including VaR, since I really do agree with your point, I will:

* Extend the focus bag (as you know i am trying to summarize, at the end of each topic, with a focus bag, than generally uses the XLS), but I will include formulas in the focus bag
* And I will add a "formulas" section to the relevent cram session that appears toward the end of the year

Re: "Sorry to ask you again and again but at some point of time, you feel very bogged down so require your morale support to get it going."
No worries, Sumit, you are a polite and valued forum customer/guest, and I very much appreciate the bogged down feeling. Frankly, I have been teaching these contents for several years, and the Full cirriculum has me feeling bogged down

David