## Jul 14, 2010

### 8 Simple Rules For Measuring Risk

Below I describe fast and easy heuristics that relate the price of ATM straddle to expected volatility, range, high, low, and maximum drawdown. These formulas may be useful to traders to quickly reassess their trading positions after a jump in price/volatility, or provide alternative view for a fair value of an option based on traders’ opinion on expected range, for example calculated from support / resistance levels.

To derive the formulas I assume the price follows arithmetic Brownian motion with no drift, and zero interest rate. These assumptions or course are not realistic, but quite workable for short-dated options, or for small volatility. The advantage of making such assumptions is great simplification of formulas. Heuristics work well for stocks and currencies, where there is no mean reversion in price, but would not work for interest rates, or VIX index.

1. Expected price volatility ≈ 1.25 * ATM straddle
2. Expected price range = 2 * ATM straddle
3. Expected high = current underlying price + ATM straddle
4. Expected low = current underlying price - ATM straddle
5. Expected maximum draw-down ≈ 1.6 * ATM straddle
6. All the formulas are linear in underlying price
7. All the formulas are linear in return volatility
8. All the formulas are linear in √T

Example: IWM closed today at 63.98. Strike-64 straddle expiring on 21-Aug-2010 closed at 5.21 using mid-market prices. The expiration is in 27 trading days.

1. Expected volatility (until expiration) is \$6.5. This can be translated into implied by 6.5 / 64 * √252/27 = 31% ( which is about 0.5 points away from implied that I see in my software ) . Daily volatility is of course 6.5 / 64 / √27 = 2%.

2. Expected price range, that is expected high - low is \$10.42. Daily expected range is 10.42 / √27 = \$2

3. Expected high (resistance) is 63.98 + 5.21 = \$69.19
4. Expected low (support) is 63.98 - 5.21 = \$58.77
5. Expected MDD is 1.6 * 5.21 = \$8.34

Over the next month I'll keep an eye on how these implied measures compare to realized, and will write an update after Aug expiration. Hedge your deltas!