Assume that you perfectly know what is the AVERAGE real return of a stock, say 1% monthly. But you don' t know what will be the distibution of the future outcomes (you assume they are lognormal). Is it possible to capitalize this knowledge with options trading? For example: manager A don't know anything about the average future outcome, so he simply buy and hold. He gets in the long term 1% montly on average. manager B knows this and want to beat manager A in terms of risk/reward, how can he do this? For example he can sell every months a 1% OTM, but he needs an option pricing model where he can put the 1% drift to compare prices with the options market. First, do you think that manager B has any edge on manager A? Second, if manager B has a real edge, how can he take advantage of it? Thanks for any suggest, P.

I have to think about it, but I am sure that what you are asking can be done, but it is far more complex than it is evident at first. At first blush, long stock, short a 30 day call each month where the strike is slightly above the 1% return of the underlying for that month would seem to work, but options are far more complicated than this. For example, if interest rates went up, the value of the call would go up, all other things being equal. One thing to remember, options prices (IV) are valued not on the returns of the underlying, but on the expected average volatility of the underlying over the course of the options term (in a classic Black Scholes world). This is obvious since you can hedge an option with an underlying and remove all return risk of the underlying from the option (assuming some form of delta/gamma/vega/skew hedging and no transacation costs). Since this is an american style option, it further complicates things. I think this is a deep question and is really interesting. Unfortunately I don't have the time to go into it deeply I will chime in more later... nitro

Thanks nitro, I found a post on a Wilmott forum about this topic, see http://www.wilmott.com/messageview.cfm?catid=19&threadid=4296&FTVAR_MSGDBTABLE= It seems that you are right, expected value doesn't play any role in option pricing. To know the future expected value does not give us any advantage. P.

basically you are saying that if xyz is currently at 100 , price "guarantee" to be at 112+ twelve month from now , right ? Manager B have a huge edge , regardless to any(down , the more the better) price action in the next few months. Where do I sign up for this deal ?