Presented by Lawrence G. McMillan · Presented by Lawrence G. McMillan ... Therefore, buy 600...
Transcript of Presented by Lawrence G. McMillan · Presented by Lawrence G. McMillan ... Therefore, buy 600...
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Risk Management
Presented byLawrence G. McMillan“The Option Strategist”Continuing Webinar Series
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McMillan Analysis Corp.A Derivatives Firm
Recommendations (newsletters)
Money Management
Option Educationincluding Mentoring
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Today’s TopicsPosition Sizing
The Concept Of Expected Return
Stops and Partial Profits
Using Greeks to Manage Risk
Portfolio Protection
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Determining Trade Size
• Fixed Percent of Assets
• The Kelly System
• Optimal f
• Probability of Ruin
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What NOT To Do…• Double up to catch up
• Martingale:
–1 –2 –4 –8 –16 +32 = +1
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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
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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 winand decreases when you lose
Example: Account size = $100,000You plan to risk 5 points on a stock trade
Therefore, buy 600 shares of stock (3% risk)
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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)
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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!
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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 losep = probability of winning
If result is negative, don’t bet
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Applying Kelly: Sports BettingIn 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
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Kelly: Sports ExampleAmount 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
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Kelly: More Complex SituationsApplying (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%
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The Probability Of RuinDefine “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!
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The Probability Of RuinDefine “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
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More on the Probability of RuinKelly 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
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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
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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.
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The Concept of Expected Return
A logical way to analyze, compare, enter and exit
strategies
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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.
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Expected Return ExampleA 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%
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Calculating The Expected Profit
Now, add in the profit picture of the strategy:
Stock Price Prob Profit Expected Profit< 50 45% -$300 -$13552 8% -$100 -$ 854 7% +$100 +$ 756 6% +$300 +$ 1858 4% +$500 +$ 20>60 30% +$700 +$210
Total: 100% +$112
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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
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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
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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
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Trading Decisions Based on Expected ReturnIn 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!
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Expected Return onThe Strategy Zone
and Option Work BenchOur statistics on The Strategy
Zone include expected return for
• Calendar spreads
• Covered Call Writes
• Naked Put Sales
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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
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Applying KellyIn 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
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EXAMPLE:CEPH Calendar
$75,000 account
CEPH: 44.60Buy Aug 45 call Sell May 45 call
for 1.20 DBe = 17.2%
(not annualized)
Kelly Method:pwin = (1+e)/(2+e) = 54%
pwin - ploss = 8%So, risk 8%, or $6,000
=> 50 spreads
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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)
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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. Bernstein-----------------------------------------------
The Handbook of Portfolio Mathematics: Formulas for Optimal Allocation & Leverage
by Ralph Vince
Recommended Reading
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Risk ManagementOnce the Trade Has Been Made
Stops
Partial Profits
Rolling
Portfolio Greeks
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Speculative PositionsWhy hedge?
1) Lock in some gains2) Reduce risk
Any time you adjust or hedge a speculative position, you harm your potential profits.
Most harmful: partial profits
Modestly harmful: rolling
As a result, hedging should not be overdone.
I don’t like: selling out-of-moneys against long options,hedging calls with puts and vice versa, or other
methods of converting long option to another strategy.
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Trailing StopsType of Stops20-day SMA10% EMAChandelierParabolic
Closing stops recommended
Should be applied to all
unhedged trades
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Profit-taking Methods1) Partial Profit:
Sell a portion (quarter or a third) of your position
Or 2) Roll the position:
Sell the options you own (when they are fairly deep in-the-money)
And buy a strike that is near-the-money
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Profit-Taking:Allows you to book some gains
“I feel I should be doing something”
ATK:
17 points as shown
43 points if no partial profits had
been taken
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Partial Profits: Completely eliminates any further gains from the
portion that you sold
Everyone worries about a gain turning into a loss
Works best if stock (or market) is not trending
A huge mistake in a trending situation
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Rolling (Up)Is moderately harmful.
WHY?
Your position: Long 10 XYZ Jan 50 calls
with XYZ = 60
Roll:
Buy 10 XYZ Jan 60 callsSell 10 XYZ Jan 50 calls
This is a bear spread, but you are bullish!
But at least you retain your upside quantity
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Speculative Summary• In a trending market, the best gains come from merely holding until your trailing stop is elected.
• Hedging/Adjusting in trending markets is harmful
• It behooves you to know if the underlying is prone to trending or not. Many commodities and
commodity-related stocks trend.
• Stocks that depend on fundamentals for propulsion generally are not trending stocks.
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Adjusting Hedged PositionsYou should always have a stop whether you are
Speculator
Naked Option Seller
Maybe even in a limited risk spread
So it is not mandatory to adjust; you could just sit back and let the stops take care of things
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Hedged StrategiesWhether or not to adjust a hedged position, really
depends on the strategy and your attitude.
For example: Long Straddle
Long XYZ July 50 straddle @ $5
Later, XYZ = 55.
“Scalper” would sell some stock, looking to buy it back on a pullback.
“Trender” would sell the puts, and use a trailing stop on the long calls.
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Simple Adjustment to Hedged Strategies
Adjust stop as time passes to protect unrealized profits:
Assume you Sold XYZ Straddle for 12
Now XYZ is near strike and straddle is selling for 6
Stop yourself out if either side goes 6 points in-the-money
Similar to trailing stop.
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Simple Adjustment to Hedged StrategiesOr if relationship of profit to stock price is difficult to
discern, then adjust your stop in dollars
Assume you have July-April 60 calendar spread
It is marking up $200 with XYZ near 60,
But there is more to be made if XYZ stays near 60.
Stop yourself out if your profit drops to $150, say.
Similar to trailing stop.
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Position GreeksCalculate the Deltas (Gammas, Thetas, etc.) for all
options in a position and add them together.
XYZ: 45 Price Delta Gamma
Long 5 XYZ July 50c 0.95 +26 4.9Long 5 XYZ July 50p 5.90 -74 4.9Short 3 XYZ July 40p 0.72 -19 4.1
Delta: (+5x+26) + (+5x-74) + (-3x-19) = -183 (ESP)Gamma: 5x4.9 +5x4.9 – 3x4.1 = +36.7
Long gamma means you want stock to accelerate;Short delta means you have a downside bias;Hedge: buy ~200 common => now neutral
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To Scalp or Not?Whether or not to adjust a hedged position, really
depends on the strategy.
If you are a “gamma scalper” or “delta neutral trader,” then you would adjust when others might not.
In a long gamma position, all adjustments are for the purpose of taking profits;
In a short gamma position, all adjustments are for the purpose of preventing losses
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Gamma Determines Attitude
Position Gamma: Long Short
Adjustment Whipsaws Good Bad
Straight-line/gap Move Good Bad
Dull market Bad Good
Stop needed No Yes
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Neutralizing Several GreeksYou can always neutralize 2 or 3 of the Greeks, moving
exposure to the area you desire.
Example: you want to establish a call ratio spread, but you would like to neutralize your market risk and leave
only the volatility risk.
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2 Equations in 2 UnknownsPosition Delta Gamma Theta Vega IV
XYZ Jul 50c 45 4.7 -1.9 9.6 35%XYZ Jul 55c 29 3.5 -1.9 8.4 40%
To Neutralize Gamma (delta comes later) , while making $100 per point drop in Vega:
4.7x + 3.5y = 09.6x + 8.4y = -100
Rounding, x = 60; y = -80 (y / x = 1.33)
Delta = 60x45 – 80x29 = 380; so short ~400 shares
Theta = +38 (you make $38 per day in time decay)
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Staying NeutralLater, XYZ = 52
Position Delta Gamma Theta Vega IV
L 60 XYZ Jul 50c 64 4.9 -2.4 8.1 35%S 80 XYZ Jul 55c 41 4.5 -2.8 8.4 40%S 400 XYZPosition Greeks: 160 -66 80 -186
To Neutralize Gamma and Delta:Buy 15 July 55c: increases Gamma by 15 x 4.5 = 67.5Increases Delta by 41x15 = 615, so short ~800 more XYZ
Leaves Theta +38; Vega –60 (to get back to –100, mult by 1.67)
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Portfolio GreeksCan’t just add all position greeks together
Because different stocks have different volatilities
For example,
Long 200 deltas in RIMM
+ Long 400 deltas in VZ
Does not make long 600 deltas
Rather you must reduce all deltas to a common factor (EFP), such as SPX or QQQ.
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Equivalent “Market” PositionAssume “market volatility” = 15% ($SPX, say)
ESP Price Volatility Adj.Factor Adj. Dlrs
L 800 RIMM 35.5 45% 3.0 $85,200
L 2000 VZ 35.5 15% 1.0 $71,000
$156,200
So this portfolio is long $156,200 as “market equivalent”
So, if SPY = 128, then to fully hedge the risk (delta) of this portfolio, you would sell $156,200 / 128 = 1220 SPY
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What Is Portfolio Protection?
“The use of listed derivatives to reduce or eliminate the risk of a
general market correction”
Most investors view protection as insurance or disaster protection, rather than a complete hedge of
their entire portfolio.
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Protecting A Stock Portfolio
Buy $SPX Puts (Traditional)
Or
Buy $VIX calls (Modern)
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“Macro” Protection• Using broad-based index ($SPX or $VIX) options
• Most efficient in terms of cost and effort
• Problem: Tracking error
“Micro” Protection• Hedge each individual stock with its options
• No tracking error
• Can be extremely time-consuming
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“Macro” Protection• Using broad-based index options
• $SPX or $VIX
• Or other index that represents your stock portfolio
• Most efficient in terms of cost and effort
• Problem: Tracking error
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“Macro” StrategiesBuy Broad-Based Index Puts
Buy Index Put Spreads
Sell Index Calls
Use Index Collars
Sell Index Futures
Volatility Products
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Buy Broad-Based Index Puts • Most Popular Approach; not necessarily the best approach
• Typically buy 5% to 15% Out of Money (OOM)
• The OOM portion is the “deductible”
• With care, can keep cost down to 2% - 3% of NAV
• Disadvantage: protection not dynamic if market rallies
• Advantages: fixed cost; upside profits unencumbered
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Buy Index Put Spreads
• Buy bear spreads as a hedge
• Drawback: cap on protection
• Advantage: lowers cost of protection
• In effect, your insurance benefits only engage between the strikes of your spread – a poor approach if you actually need protection
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SellIndex Calls
Drawbacks: doesn’t provide disaster
insurance; and may limit upside profits
Advantage: sale ofa wasting asset
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Index Collars• Buy OOM puts and sell OOM calls
• Calls defray cost of the puts (sometimes completely)
• Limits both risk and reward
• Distance between strikes is hurt by high dividend and/or low volatility
• Best when using LEAPS options (can spread strikes out quite far with LEAPS):
June 2007: $SPX: 1517 Feb 2011: $SPX 1340Dec (’09) 1450 put: 107.6 Dec(’13) 1200p: 120Dec (’09) 1700 call: 118.8 Dec(’13) 1400c: 125
Nowhere nearly as attractive (vol, div, rates)
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Volatility Products
• $VIX
• Futures on $VIX
• Options on $VIX
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Hedging With Volatility ProductsSince $VIX moves opposite to $SPX,
Buy VIX futures
Or Buy VIX calls• Advantages: stock upside unencumbered; cost limited to “time value premium.”
• Disadvantages: $VIX derivatives may not track well with $VIX itself.
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$VIX Calls are a better hedge than $SPX puts
Better than buying $SPX puts: protection is dynamic
If you buy $SPX puts and market rises, your protection is virtually worthless
If you buy $VIX calls and market rises, your protection is still viable
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$VIX Hedging Is “Cheap”According to a well-known study, a portfolio consisting of 90% $SPX and 10% $VIX outperforms $SPX in both up and down markets.
Later studies suggest 20% for hedging.
So you only need to hedge 10%-20% of your portfolio’s EFP, assuming it performs “in line” with the broad market.
Buy out of the money $VIX calls, one or two months out, and keep rolling them.
Strike ~= futures price + 7
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How Many $VIX Calls To Buy?• Hedge 20% of your NAV
• Assume EFP = $100,000 on 9/16/2008• VIX Oct 30 call = 4
• You buy $20,000/(30x100) = 7 calls• Stock market down 26% ($SPX 1210 to ~900)
• NAV: -$26,000 loss• Oct $VIX Futures: +125%; $VIX +131%; Oct 30 call = 27
• 7 calls x $2300 profit = +$ 16,100 gain• You lose -$9,300 = your “deductible” (9.3%)
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$VIX Option Protective “Collar”
Buy VIX calls for protection
And Sell VIX puts to help fund the calls
Problem: Put premiums small
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SummaryRisk Management is Important:
Position Sizing
Use Trailing Stops For Speculative Positions
For simple hedged positions, use dollar stops
For complex positions, hedge with Greeks
For portfolios, hedge with $VIX
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Offers One-on-one MentoringStructured to your skill level
Conducted on the internet or in person
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