Beta and Volatility of Underlying
Right, so I was attending this zero-day interview for this analytics firm, when I was asked "Given a stock and an index - everything else being equal - a call option will be higher priced on which underlying?
I answered that an index is generally less volatile, thus I would expect it to be cheaper compared to a stock.
The interviewer asked me, what if the underlying stock has a beta of less than one (or if it is negative)? Will my answer change. I panicked and said then maybe it is possible that the Call option on underlying could be higher.
Could the community help me out on this.
P.S. I cracked the interview and got the job. But I am still unsure of what the answer to this question is!!
ceteris paribus a higher beta implies a higher volatility. Hence, the put call premium increases as beta increases.
I'll do my best here and then let a charter holder tear me a new one:
I would have asked them to clarify "everything else being equal" - obviously option pricing is driven by a host of factors (risk-free rate, time to exp., implied volatility, etc..), but consider the underlying actual value. For example, an at the money call option on an index in a scenario with identical factors will always be higher (in explicit monetary terms), than an ATM option on a stock due to what minimum price fluctuations will represent in terms of actual value, even if we're talking about Berkshire Class A ( ...and unless the index only contains ONE stock...which would be a pretty shitty index)
Once again, index option should be higher based on explicit monetary value...but now we've changed the "everything being equal" part of the equation. Theoretically, it seems possible, depending on the index and what the other underlying is, but now you're comparing apples to oranges
If the Var(Index)=SUM(r-u)^2 Where R = return of market and u=average return Then the Var(Stock) = SUM(Br-Bu)^2= B^2 SUM (r-u)^2. If Beta is 1 than it must have a lower variance
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