# Hedging predicted volatility

Q. If you predict the volatility of the stock is 10% a year from now and current price is X dollar, how do you hedge the risk?

Im not sure why I am finding this so hard. How do we use options (probably) to sell 10% a year volatility?

• Are you trying to hedge a 10% move in the stock or are you trying to trade a 10% move in the implied volatility of its options? IOW, are you looking for a way to limit your risk on an existing or potential equity position? – Bob Baerker Sep 15 '20 at 22:25
• @BobBaerker hedge 10% volatility in the stock, i saw it in a bank quant interview question, so im guessing its not looking for a speculative answer – Trajan Sep 16 '20 at 11:22

So as an example, SPY 1 Yr at-the-money (spot=strike=340) calls are trading at 28.72, which implies a volatility of 22.65%. The delta of these options are 0.53. If you believed that 22.65% is too high (realized volatility would be lower than this over the next year), you would sell these calls, and buy 0.53 shares of stock for every option you sold. Since exchange traded options are for 100 shares, you would sell 1 contract for 2872, and buy 53 shares of SPY. On an unleveraged basis, you would need 340*53 = 18,020 to purchase the shares, and you will receive $2872 for the call you sold. Your margin requirements with your broker will determine how much capital you will need to post to maintain your position (you may be required to post additional margin if the position works against you). You will need to rebalance this hedge periodically to maintain delta neutrality or to eliminate your exposure to the direction of the stock movement. How frequently you hedge will depend on your risk appetite and your costs of trading. If you are correct, you will extract profits from the implied volatility being greater than realized volatility over the year (less the hedging costs). You will be exposed to vega in the price of the option (currently 133.62) meaning the contract will go up by 133.62 for a 1% increase in the implied volatility. As you are short the option, this will work against you if implied volatility increases, and work for you if implied volatility decreases. Bear in mind, you will be competing with the dealers who can hedge much more efficiently. • How would you size it though? – Trajan Sep 15 '20 at 17:31 • If there is something you are trying to hedge, then you would size it such that your hedged options moves opposite to the asset you are trying to hedge by the same magnitude. Anything less than a full hedge or an outright view on implied vs realized vol will depend on your risk appetite and capital. – AlRacoon Sep 15 '20 at 17:34 • Which is how??? – Trajan Sep 15 '20 at 18:12 • This is hard to answer without a specific example. Is there a position you are trying to hedge? What is that position? – AlRacoon Sep 15 '20 at 18:52 • What about$1000 of a US stock? – Trajan Sep 15 '20 at 19:21