wilmott.com

How is the Sharpe Ratio related to Option Hedging?I mean if you want to achieve a certain Sharpe Ratio, you would need to sell the option at a certain price. Obviously we would want as high a Sharpe Ratio as possible.

Instantaneously, a derivative is just a levered portfolio of the underlying. Since the Sharpe ratio is unaffected by leverage, the derivative should have the same Sharpe ratio as the underlying at every instant in time. That does not mean, however, that it has the same Sharpe ratio over a finite period of time. Moreover, if the option price differs from its theoretical value, the Sharpe ratio can be different instantaneously as well.It is not necessarily true that you want the highest possible Sharpe ratio. That is true only if the portfolio represents your entire wealth and the underlying return is Lognormal.

Say i am hedging an option that i have written... with transaction costs therefore incomplete markets. So the theoretical BS price willl be lower thann the price of my hedging portfolio. i have computed that i need to sell the option at a certain price to achieve a particular sharpe ratio. wat would be the importance of this in measuring the mean variance tradeoff of option hedging.Kevin Seah

QuoteOriginally posted by: skwengSay i am hedging an option that i have written... with transaction costs therefore incomplete markets. So the theoretical BS price willl be lower thann the price of my hedging portfolio. i have computed that i need to sell the option at a certain price to achieve a particular sharpe ratio. wat would be the importance of this in measuring the mean variance tradeoff of option hedging.Kevin SeahNot very important. Assuming you mean to do this as a business, most of your risk should diversify away. The Sharpe ratio might make sense if you were hedging only one position, or perhaps if you were hedging a position so large that total capital limits became important.Also, you don't say what model you are using. If you use Black-Scholes, for example, then you will ignore the crucial vega risk.A better measure would look at your overall hedging portfolio and strategy to try to measure the risk of that.

Basically what i did was that, i was analysing the total hedging error for the the Toft strategy. Which minimises the expected transaction costs. However what i do is slightly different, instead of looking at the error and the transaction cost separately. I combined them by saying that the function taht i want to minimise is E[ (V_t+1-H_t+1)^2]where V_t+1= (1+r)V_t + Delta_t*Stock_t*Excess Return - k*Stock_t+1*|delta_t+1- delta_t|So basically V_t+1 will be smaller the more frequent the rebalancing, therefore the price of the hedging portfolio will increase. I was going to analyse the optimal hedging interval and also the mean variance tradeoff of the option hedging. But I'm not sure what does it mean by the mean variance tradeoff. How is it related to the Sharpe Ratio? I derived a formula for the Sharpe Ratio and it has both the mean and also the variance terms.

The Sharpe ratio does indeed measure the ratio of standard deviation to excess return. It can be used to set an optimum rebalancing strategy if you hedge only one option. You would maximize the Sharpe ratio then either increase or decrease the option position in order to get your desired level of risk. This would have higher expected return than simply setting the rebalancing strategy to the appropriate risk level.However, the problem, as I mentioned before, is that most people are concerned about the risk of doing this regularly, not just once. They are concerned about what portion of the risk is systematic, rather than how much total risk there is on each position.

Surely, most of you already read it. To me, it is an incredible good article (as most of Sharpe´s are), "The Sharpe Ratio" by William Sharpe:http://www.stanford.edu/~wfsharpe/art/sr/sr.htm