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Risk Management Risk Management Presented by Lawrence G. McMillan “The Option Strategist” Continuing Webinar Series www.optionstrategist.com 1-800-724-1817 [email protected] McMillan Analysis Corp. A Derivatives Firm Recommendations (newsletters) Money Management Option Education including Mentoring www.optionstrategist.com/mentoring www.optionstrategist.com 1-800-724-1817 [email protected] Special offers on most of our newsletters, software, and educational products Visit: www.optionstrategist.com/webinar www.optionstrategist.com 1-800-724-1817 [email protected] Today’s Topics Position Sizing The Concept Of Expected Return Stops and Partial Profits Using Greeks to Manage Risk Portfolio Protection www.optionstrategist.com 1-800-724-1817 [email protected] Determining Trade Size • Fixed Percent of Assets • The Kelly System • Optimal f • Probability of Ruin www.optionstrategist.com 1-800-724-1817 [email protected] What NOT To Do… • Double up to catch up • Martingale: –1 –2 –4 –8 –16 +32 = +1 www.optionstrategist.com 1-800-724-1817 [email protected] A Better Approach… • Increase size as you profit • Fibonacci-style: 10, 15, 25, 40, 65, 105, 170, 275, … 7 wins, 1 loss: +$155 vs +$60 Return to initial size ($10) when you lose www.optionstrategist.com 1-800-724-1817 [email protected] How Many Options Should I Buy? Fixed Percentage Risk Management Risk a fixed percent of your account on each trade (3%, e.g.) Automatically increases when you win and decreases when you lose Example: Account size = $100,000 You plan to risk 5 points on a stock trade Therefore, buy 600 shares of stock (3% risk) www.optionstrategist.com 1-800-724-1817 [email protected] How Many Options Should I Buy? You could figure your risk = premium, but that’s unrealistic. Option costs 10 points ($1000) So buy 3, if your account size is $100,000 (3% risk) www.optionstrategist.com 1-800-724-1817 [email protected] How Many Options Should I Buy? Using the model to estimate risk. Oct 100 call costs 10 today ($1000). What would it be worth if XYZ fell to 95 in a week? Black-Scholes model says: In 1 week, if XYZ = 95, Oct 100 call = 7 Therefore, risk = 3 points ($300) so you can buy 10 calls, not 3! www.optionstrategist.com 1-800-724-1817 [email protected] Another Approach: The Kelly Criterion J. L. Kelly, Bell Labs, 1954 Original Formula: Amount to bet = (W + L) * p – L Where W = amount you could win L = amount you could lose p = probability of winning If result is negative, don’t bet www.optionstrategist.com 1-800-724-1817 [email protected] Applying Kelly: Sports Betting In sports betting L = 1.1 * W (you lay $110 to win $100) Amount to bet = (W + 1.1W) * p – 1.1W = W *( 2.1p – 1.1) Will be negative if p <= .52 Assume W = 1 (your risk bankroll) Amount to bet = 2.1p – 1.1 www.optionstrategist.com 1-800-724-1817 [email protected] Kelly: Sports Example Amount to bet = 2.1p – 1.1 Example, assume p = 60% (i.e., you can predict sports winners with 60% accuracy*) Then amount to bet = 2.1 * .60 – 1.1 = .16 which means risk 16% of your bankroll on the next bet. *: if you can do that, you don’t need this seminar www.optionstrategist.com 1-800-724-1817 [email protected] Kelly: More Complex Situations Applying (W + L) * p – L Where p = probability of a winning trade PDR System: avg win $2359; avg loss $1952 And p = 56.7% So L = .83W Amount to bet = (1.83p – 0.83) Amount to risk = 21% www.optionstrategist.com 1-800-724-1817 [email protected] The Probability Of Ruin Define “ruin:” down 80%? If you risk 50% of your capital, and lose it all on each trade, then: One loss: 50% left Two losses: 25% left Three losses: 12.5% left = ruined! www.optionstrategist.com 1-800-724-1817 [email protected] The Probability Of Ruin Define “ruin:” down 80%? How many losses in a row would ruin you? (1 – r)n = 0.2, where r = % of assets you risk on each trade If r = 3%, n = 52 If r = 50%, n = 2.3 www.optionstrategist.com 1-800-724-1817 [email protected] More on the Probability of Ruin Kelly is designed to optimize your results, not protect your capital! Professional blackjack players rejected Kelly because the probability of their bankroll shrinking to any percentage was that percentage itself. 50% chance of losing 50% 20% chance of losing 80% 10% chance of losing 90% Was too much risk for them www.optionstrategist.com 1-800-724-1817 [email protected] Kelly for Traders • Our investment is not equal to our risk • Our win amount is not fixed, either • We don’t make sequential investments • Not all of our trades have equal probabilities of profit (unless we only trade one system) Reference: Google papers by Edward Thorp www.optionstrategist.com 1-800-724-1817 [email protected] Optimal f f = Kelly formula According to Ralph Vince, in a complex trading system, the f that provides the maximum return on our money can only be determined by iteration. We cannot average our wins and losses from trading and obtain the true optimal f using the Kelly formula. Your Bet unit = (System’s Largest loss) / f The full concept of understanding Optimal f requires reading the book. www.optionstrategist.com 1-800-724-1817 [email protected] The Concept of Expected Return A logical way to analyze, compare, enter and exit strategies www.optionstrategist.com 1-800-724-1817 [email protected] What is Expected Return? The return one could expect to make on a position over a large number of trials. Assumes the distribution of possible stock prices can be defined; also assumes implied volatilities of an unexpired option can be estimated as well. Highly dependent on volatility estimate. www.optionstrategist.com 1-800-724-1817 [email protected] Expected Return Example A Call Bull Spread XYZ: 52 Oct 50 call: 7 Oct 60 call: 4 Assume the stock must be at one of the following prices: Stock Price Probability < 50 45% 52 8% 54 7% 56 6% 58 4% >60 30% Total: 100% www.optionstrategist.com 1-800-724-1817 [email protected] Calculating The Expected Profit Now, add in the profit picture of the strategy: Stock Price Prob Profit Expected Profit < 50 45% -$300 -$135 52 8% -$100 -$ 8 54 7% +$100 +$ 7 56 6% +$300 +$ 18 58 4% +$500 +$ 20 >60 30% +$700 +$210 Total: 100% +$112 www.optionstrategist.com 1-800-724-1817 [email protected] How Will This Spread Do? • Expected Return = $112 / $300 = 37.3% • Annualized Exp Return = 37.3% x 4 = 112% • But the only point you actually would make $112 is if stock is at 54.12 at expiration. • Chance of that is < 0.005 • In any one case, you could make as much as $700 or lose as much as $300 www.optionstrategist.com 1-800-724-1817 [email protected] What is Expected Return NOT? • It is not a black box, “magic” formula • It is not a guarantee of profits • It is not a shortcut to the diligence needed to trade options profitably www.optionstrategist.com 1-800-724-1817 [email protected] What Does It Mean? • On average, if you invest in positions with high expected return, you should approach that return eventually • The “Casino Analogy” • Erroneous Assumptions - Distribution not lognormal - Bad volatility estimate - Event Risk www.optionstrategist.com 1-800-724-1817 [email protected] Trading Decisions Based on Expected Return In the bull spread example, Suppose XYZ moves from 52 to 55 quickly And you have a profit of $120. That’s your expected profit. Should you take it? If you do, your annualized return increases! www.optionstrategist.com 1-800-724-1817 [email protected] Expected Return on The Strategy Zone and Option Work Bench Our statistics on The Strategy Zone include expected return for • Calendar spreads • Covered Call Writes • Naked Put Sales www.optionstrategist.com 1-800-724-1817 [email protected] Position Sizing Using Expected Return • Kelly is useful because it optimizes results while increasing our trading size when winning and reducing it when losing • It is a rational way of investing in a consistent manner, placing the most money on the most likely profitable trades • We have expected return as a guide • We can also often determine the probability of winning or losing on a trade • In complex situations, Kelly effectively reduces to: Amount of account to risk = pwin –ploss www.optionstrategist.com 1-800-724-1817 [email protected] Applying Kelly In some cases, we can compute pwin and ploss but that might not relate well to expected return (naked writing, for example) Better to use expected return, e pwin = (1 + e) / (2 + e) Ploss = 1- pwin www.optionstrategist.com 1-800-724-1817 [email protected] EXAMPLE: CEPH Calendar $75,000 account CEPH: 44.60 Buy Aug 45 call Sell May 45 call for 1.20 DB e = 17.2% (not annualized) Kelly Method: pwin = (1+e)/(2+e) = 54% pwin -ploss = 8% So, risk 8%, or $6,000 => 50 spreads www.optionstrategist.com 1-800-724-1817 [email protected] Portfolio Considerations Can’t just use the Kelly or Optimal f number for each position: What if Kelly says “invest 12%,” but you have more than 8 positions you want to establish? Two approaches: 1) Use Kelly on remaining equity in account, or 2) Rebalance all positions (daily) www.optionstrategist.com 1-800-724-1817 [email protected] Recommended Reading Fortune’s Formula “The Untold Story of the Scientific Betting System that Beat The Casinos and Wall Street” By William Poundstone ----------------------------------------------- Against The Gods “The Remarkable Story of Risk” By Peter L.
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