Advanced Options Trading Strategies Part 1pages.hmc.edu/evans/e136l7.pdf · AA Alcoa HD Home Depot MO Altria ... leverage and start using identical or nearly identical trading strategies?

Here is your teacher waiting for Steve Wynn to come on down so I could explain index options to him. He never h d I th t h ill h tshowed so I guess that he will have to

download this lecture and figure it out like everyone else. He was a nice host, though. And he seems very interested in math. A lot of things going on in this large curved building behind me seemedlarge curved building behind me seemed to have a connection to math.

Advanced Options Trading StrategiesAdvanced Options Trading Strategies... ... (part 1) options basics 104 review(part 1) options basics 104 review

© 2014 Gary R. EvansRead chapter 7 and review lectures 8 and 9 from Econ 104 if you don’t remember this stuff.

So what are we to make So what are we to make of this?of this?

  WeightsINTC 0.250BAC 0.250MO 0 250

I want you to finish yours so that it gets this result we are of this?of this?

Can you understand why ...

MO 0.250JWN 0.250Sum:  1.000

DCGR Mean Var SDINTC 0.00093 0.000166 0.01288

this result ... we are not done.

1. This is a good portfolio as is ... we have a volatility that is lower than the volatility of our least volatile stock (0.0081

d 0 00897)!

BAC 0.00104 0.000216 0.01469MO 0.00086 0.000080 0.00897JWN 0.00065 0.000118 0.01088

Correlation Matrixcompared to 0.00897)!

2. Why these numbers in the covariance matrix must be really low!

INTC BAC MO JWNINTC 0.23317 0.26090 0.24442BAC 0.30034 0.35182MO 0.38890JWN y

3. What we would do if we found a number in the correlation matrix above our th h ld ( 0 4 0 5)

INTC BAC MO JWNINTC 0.0000441 0.0000301 0.0000342BAC 0.0000396 0.0000562MO 0 0000380

Covariance Matrix

threshold (say 0.4 or 0.5).

4. What we would do to raise our alpha!

MO 0.0000380JWN

6.65674E‐05  0.0081589

Weighted portfolio variance:  Weighted portfolio volatility:  

5. What we would to to get an optimal risk/yield tradeoff for these four stocks.0.000869016

0.218123077

e g ed po o o o a y

Portfolio alpha: Annualized Portfolio alpha: 

The relevance of this to the LongThe relevance of this to the Long--Term Capital story Term Capital story

Remember that professional exotic investments by Hedge Funds will select very high alpha and very high beta investments like sovereign debt, distressed debt,

h d d i i i k i i dexchange-rate dependent equity investments, emerging market equities, etc. and they know that safety is in numbers ... if the investments are uncorrelated.

They are often funding out of spreads from a carry-trade of come kind, borrowing y g p y , gat 2% and looking for alphas of 6% or 7% or higher. The borrowing gives them leverage inverse to the percentage of their equity stake (10% equity stake gives them 10 to 1 leverage). Running to a higher-yield asset at times like 2013 and 2014 i l b i i d bt th t h hi h b bilit f d f lt2014 involves buying, say, sovereign debt, that has a high probability of default.

You should understand by now that given any portfolio variance, leverage modifies the volatility proportionately L2(V). This means that a 5% loss becomes y p p y ( )a 50% loss in this scenario (ask students about the math of this).

Of those covariances go from near zero to one in a market panic, you are dead.

[Read page 188 and 149]

Standard & Poor’s Estimated Average Cumulative Standard & Poor’s Estimated Average Cumulative Default Rates for various credit ratingsDefault Rates for various credit ratingsDefault Rates for various credit ratingsDefault Rates for various credit ratings... showing their estimates of the

i d l iestimated cumulative default rate (e.g. the estimate of a CCC/C junk bond defaulting j gwithin 2 years is above 30%, within 7 years is above 45%).

Source: Standard and Poor’s Global FixedPoor s Global Fixed Income Research, “The Time Dimension of Standard & Poor’s Credit Ratings,” September 22,

Remembering actual default rate Remembering actual default rate probabilities of junkprobabilities of junk--rated debt from rated debt from Econ 104: Econ 104:

Ratings, September 22, 2101, p.3 Chart 1.

Statistical ArbitrageStatistical Arbitragegg(stat arb)(stat arb)

Statistical Arbitrage (called stat arb) is a "quant" strategy used by many of theStatistical Arbitrage (called stat arb) is a quant strategy used by many of the largest hedge funds, like Citadel. Generally stat arb involves building an equity portfolio of mixed long and short positions in stocks.

i ll h h d f d i k h f li k lTypically the hedge fund strives to make the portfolio "market neutral," meaning that performance does not depend upon a rising or falling market.

Because the return margins on these enormous portfolios are usually pretty g p y p ythin, stat arb portfolios are usually hugely leveraged (maybe 100 to 1) by cheap borrowed money (e.g. carry trade or commercial paper).

Stat Arb also uses delta hedging (theoretically) so we will come back toStat Arb also uses delta hedging (theoretically) so we will come back to discuss this in the future.

Stat Arb (cont.)Stat Arb (cont.)Obviously an old example

AA Alcoa HD Home Depot MO Altria

Dow Jones Industrial Averages 30 components

( )( )

AA Alcoa HD Home Depot MO AltriaAIG AIG HON Honeywell MRK MerckAXP American Express HPQ Hewlett Packard MSFT MicrosoftBA Boeing IBM IBM PFE PfizerC Citicorp INTC Intel PG Procter GambleCAT Caterpillar JNJ Johnson & Johnson T AT&TDD Du Pont JPM JP Morgan Chase UTX United TechnolgiesDIS Disney KO Coca Cola VZ VerizonGE General Electric MCD McDonalds WMT Wal MartGM General Motors MMM 3M XOM Exxon MobileGM General Motors MMM 3M XOM Exxon Mobile

Suppose we take a market basket of stocks, like the index above (but not restricted to indexes ... this is an example), and suppose we are bullish on the index, but not every stock in the index. We therefore decide to go long in most stocks but short some of them (shown in red in the example above, based upon l t 2007 k t ) B t i h t titi ? Thi i h t t b b i ithlate 2007 markets). But in what quantities? This is where stat arb begins, with a portfolio of longs and shorts, like any hedge fund. But stat arb also aspires to be market neutral.

Stat Arb Market NeutralityStat Arb Market NeutralityStat Arb Market NeutralityStat Arb Market NeutralityStatistical Arbitrage builds an equity portfolio of longs and shorts (see previous slide) but stat arb also typically aspires to be "market neutral." This

h id ll h f li ' f i i d b i h imeans that ideally the portfolio's performance is not improved by either a rise or decline in the overall index (or portfolio). In the previous example, this portfolio, if correctly weighted to be "market neutral," would be insensitive to a rise or fall in the DJIA [Your teacher once asked a stab arb deskto a rise or fall in the DJIA. [Your teacher once asked a stab arb desk supervisor, a Mudder, whether he thought the market was going to rise or fall in emerging months. His answer was, "Who cares?"].

How do they achieve market neutrality? On the risk side, they use some very complicated algorithms to assess portfolio risk to make the portfolio risk neutral. We will learn that approach in a few weeks when we cover advanced

l tilitvolatility.

What therefore is the basis of profitability? Generally, you have to be more or less right about the longs and the shorts. In a rising market, the longs have to rise more than the shorts. In a falling market, the shorts have to fall more than the longs.

Stat Arb Problems??Stat Arb Problems??Stat arb has been seen in recent years as the coolest of the quant strategies, but in

the fall of 2007, in the midst of the sub-prime meltdown, that some stat arbh d f d h d b l i hi h d dhedge funds had been losing money, something they were not supposed to do.

At issue (teacher's comments):

1. They are heavily leveraged.y y g

2. Their borrowing source is (was) a troubled market.

3. Some bullish bias may have been built into some of these funds.

4. "Quantagion?"

Financial Contagion or "Quantagion"Financial Contagion or "Quantagion"g Q gg Q g(a dangerous new phenomenon?)(a dangerous new phenomenon?)

[Not required, but recommended, for class]: see "What Happened to the Quants in August 2007?" by Amir E. Khandani and Andrew W. Lo, September 20, 2007 draft available on http://www2.hmc.edu/~evans/khandanilo.pdf l i ibl il bllater versions possibly available on http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1015987.

What happens when large hedge funds use huge amounts of leverage and start using identical or nearly identical trading strategies?

First, profit ranges must narrow, which may require even more leverage.

Margin calls, credit drying up, etc., may force severe correlated liquidation.

Our recent HPQ strangleOur recent HPQ strangleName: Date:

Gary R. EvansFebruary 26, 2014

I compare this to the historical daily

Stock Symbol: HPQ Interest rate:

Stock Price: 29.640 0.010

Strangle Implied Daily Volatility Calculator volatility (HDV) of HPQ for 2 years, one year, 90 day and 30 day, using a model like the one we developed in HW1CALL PUT

Month: Mar MarStrike: 30.00 29.00

Expiration: 3/22/14 3/22/14Price: 1.130 1.110

HW1.

If the IDV in the model to the right is substantially higher than the HDV then h i i “ i d hi h ” dPrice: 1.130 1.110

Days to maturity: 24 24DTM override: 32 32

the option is “priced high,” and not a good candidate for any kind of long position, but may be ideal for a short position like an iron condor or writing

Implied daily volatility: 0.01919 0.02146One-day time decay: 0.020 0.021

Version 3.3 August 16, 2011

p gcovered calls.

Calculate

Reading the Options ChainReading the Options ChainIBM's stock info

In the

Out of the Money

Expiration Bid/Ask St ik P iIn the Money

pdate

Bid/Ask same as stocks

Strike Prices

Source: Out of the

MoneyIn the MoneyVolume & Open Interest

Reading … Reading … (blowup from previous page)(blowup from previous page)

You can buy the IBM November 19 195 You can buy the IBM November 19 175You can buy the IBM November 19 195 Call for $1.82 (OOM), which gives you the right to buy IBM for $195 per share between now and Nov 19.

You can buy the IBM November 19 175 Put for $8.05 (ITM), which gives you the right to sell IBM for $175 per share between now and Nov 19.

Note: These examples assume purchases at Best Ask. Obviously you can submit a limit order at any price.

Source: Note the big Bid/Ask – the less the liquidity the bigger these spreads.

Potential Call Option Values(upon expiration)

$10 00

$12.00

(upon expiration)

This shows only what the option ill b h if h ld i i

$8.00

$10.00 will be worth if held to expiration, given the possible prices of IBM.

hi i h ( )

$4.00

$6.00 This is the Nov 19 (exp) IBM OOM 195 Call, purchased at $1.82 (BA) on Sep 29, when IBM was $177.62 (last)

$0.00

$2.00(last).

‐$4 00

‐$2.00This is a bet that the stock price will rise.

$4.00175 180 185 190 195 200 205

Profit/Loss Gross value

The allThe all--important pimportant premium on OTM optionsremium on OTM options

The premium for an in-the-money option converges to zero as the optionconverges to zero as the option approaches expiration.

h i f f h i b h h f i lThe premium of an out-of-the-money option can be thought of as simply the price of the option because the option has an intrinsic value of 0 at the moment.

The premium for either is a function of

1. Time to maturity (shorter is smaller) – time decay

2. The underlying stock's volatility (greater is larger)

3. The degree to which the option is in the money (more is smaller)

Issue 1: Time Issue 1: Time DecayDecay

1.40

1.60 This shows the actual projected time decay of a March 75 DIA call option, purchased for $1.51, when DIA was trading at $72.15 (implied daily

l tilit t 0 0156) l l t d i ti

1 00

1.20volatility at 0.0156), calculated using an option calculator. This assumes no change in DIA price and no change in volatility.

0.80

1.00

0.40

0.60

0.20

0.0033 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

Issue 2: The Impact of VolatilityIssue 2: The Impact of Volatilityp yp y

3 00

3.50Put Option Price CalculatorDaily Volatility

2.00

2.50

3.00Stock symbol: TLT

Put option: Oct 106Date Today: 8/25/2010

Expiration Date: 10/16/2010DTM: 52

0 50

1.00

1.50

DTM: 52

108.14106.00

Daily Volatility: 0.0117Interest Rate: 0.010

Ti 52

Stock Price: Strike Price:

0.00

0.50Time: 52

d1 Numerator: 0.02142Duration Volatility: 0.08437

N(-d1): 0.3998 N(-d2): 0.4327( )

Option Price: 2.57Option Premium: 2.57 Scenario: 20 days have passed, leaving 32, no

change in price, so the graph above shows the g p , g psensitivity to volatility alone.Note: This is mapped in TLT Volatility in

Finance>Volatility Calcs

Issue 3: DistanceIssue 3: Distance(Old slide from the glory days)

The premium on an option is determined by the three components

Spread10/9/08

DIA at 91 55listed on the last slide, (1) the volatility of the stock and the market in general, (2) spread from the strike

i ( h h i h )

Strike Ask Premium75 17.10 0.5580 12.25 0.70

DIA Nov Call AskDIA at 91.55 Closer is

greater

price (whether in the money or out), and, (3) especially for out-of-the-money options, the time before the option expires

Time

90 4.45 2.90

Moreoption expires.

It is possible to segregate these three in theory and empirically and the ability

Oct 2 37DIA 94 Call Ask

DIA at 91.559-Oct-08

More distant is greater

to do so is essential for advanced options trades.

Advice: Design and use your own Advice: Design and use your own

Oct 2.37Nov 5.10Dec 5.90Mar 7.60g yg y

models!!models!!Note: Premiums were unusually high in Oct 08 because of volatility in the markets.

Strategy 1: Leveraging Long with a IWM Strategy 1: Leveraging Long with a IWM DeepDeep--inin--thethe--Money (DITM) rolling callMoney (DITM) rolling call

Econ 104 strategiesDeepDeep inin thethe Money (DITM) rolling call Money (DITM) rolling call

The IWM ETF tracks the Russell 2000 and trades at 10%.

Buy this one

The call option that you buy must have adequate open interest (at least a few hundred contracts).

Source: TD Ameritrade Option Chains, Oct. 6, 2011

Complex Strategy 2: StranglesComplex Strategy 2: Strangles

You can buy the IBM November 19 195 You can buy the IBM November 19 175You can buy the IBM November 19 195 Call for $1.82 (OOM), which gives you the right to buy IBM for $195 per share between now and Nov 19.

You can buy the IBM November 19 175 Put for $8.05 (ITM), which gives you the right to sell IBM for $175 per share between now and Nov 19.

D b th f th l t l t ? If

Source:

Do you remember these from the last lecture? If we do both it is a strangle!

Performance and Profitability of the StranglePerformance and Profitability of the Strangle

$15 00

$20.00

y gy gNote: This graph is somewhat misleading. It show the profit and value of the position on the expiration date only if the option is held to expiration. It shows nothing about the possible value of an

$10.00

$15.00

P fi

held to expiration. It shows nothing about the possible value of an option between now and the expiration date.

$5.00

ProfitProfit

‐$5.00

$0.00

LossClearly you are

‐$10.00

y yplaying volatility here. This example is a little asymmetric.

‐$15.00150 155 160 165 170 175 180 185 190 195 200 205 210 215 220

We did this in Econ 136 in 2007.

Complex Strategy 3: Goldcorp GG Hedged Complex Strategy 3: Goldcorp GG Hedged Covered Call (Collar)Covered Call (Collar)

• When you write an OTM call and buy an OTM put (for insurance) this is called a Collar.Collar.( )

• Goldcorp is $21.50• Nov 22.50 call option is $1.25p $• Nov 17.50 put option is $0.25• Buy the stockBuy the stock• Write the call• Buy the put (for insurance)Buy the put (for insurance)

Complex Strategy 4:Complex Strategy 4:Writing covered calls ....Writing covered calls ....gg

This above is a covered call I wrote specifically for this class last year. I bought AeroVironment (AVAV) last Spring for an Econ 136 experiment for around 26. I should have sold it when it popped above 35 but didn’t. So I wrote this call for us to track until November 22.

Because of high volatility this was expensive for the buyer. I pocket $1.50 per share and would actually prefer that this be exercised, allowing

t l k t $4 i ($1 41 h d I b ht th t k th ittme to also pocket a $4 cap gain ($1.41 had I bought the stock then written the call). The $2.91 gain if executed is more than 10% absolute – not bad for 50 days. If it doesn’t execute I will just write another call.

Note: This option was exercised.

Strategy 6: The Iron CondorStrategy 6: The Iron CondorTh i b t This is a cash-positive bet

1.50

2.00 The primary bet was writing a strangle consisting of a 132 call for $1.25 and a 128 put f $1 64 h DIA

This is a cash positive bet on low (and lower) volatility. You are net cash positive and want to stay that way

0.50

1.00for $1.64 when DIA was at $130.36.

that way.

-0.50

0.00

1 50

-1.00

Lower floor provided Upper floor provided

-2.00

-1.50 by 124 Long Put, which cost $0.80.

by 135 Long Call, which cost $0.35.

Possible Prices of DIA on May 19, 2012 -2.50

122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137

y

Strategy 7: Butterfly Strategy 7: Butterfly spreads (call)spreads (call)gy ygy y p ( )p ( )Betting on no or little price movement: (1) Buy one ITM call, (2) buy one OTM call, (3) write two ATM calls. This is done normally for near-term expiration dates. y p

SPY: 187.44

W: 2 187 forW: 2 187 for 2.02

B: 1 184 for 4.21

B: 1 191 for 0 390.39.

Net: $1.80

Exam 2 question: When would you use this strategy and what role is played by each leg??

Butterfly (Call) payoff gridButterfly (Call) payoff grid

3.00

4.00

SPY stock 187.44Mar 184 Call 4.21 Buy

SPY Butterfly 3/4/14

2.00

3.00 Mar 187 Call 2.02 Write 2XMar 191 Call 0.39 BuyNet -0.56

1.00

0.00

-2.00

-1.00

180 181 182 183 184 185 186 187 188 189 190 191 192 193

Net Gross

Butterfly (Put) payoff grid Butterfly (Put) payoff grid

4.00

5.00SPY stock 187.44Mar 184 Put 1.06 BuyMar 187 Put 2.06 Write 2X

SPY Put Butterfly 3/4/14On a butterfly, it doesn’t much matter whether you use calls or puts payoff

3.00

Mar 191 Put 4.72 BuyNet -1.66

use calls or puts, payoff format is about the same.

1.00

2.00

0.00

-2.00

-1.00

180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195Net Gross

What you must do in HW4/5What you must do in HW4/5

Analyst's Name:

STRIKE PRICE PROBABILITY CALCULATOR Time is frozen to March 4, 2014, 8:52 AM.

At that moment SPY is trading for 187.410.Analyst s Name:

 Date Today:   3/14/14

Stock Symbol:  SPYStock

g

You have bought a March 22 Call option Strike Price 190 at Best Ask for $0.63. There are 8 days to expirationStock Price:   187.410

Option Strike Price:  190Option Expiration Date:  3/22/14Option Price (Best Ask):  0.630

OptionThere are 8 days to expiration.

You are to use the one-year historical volatility from HW1 to calculate:p ( )

Days to expiration:  8

Log Growth Rate Price to Strike Price:   

Sample Mean Daily Growth Rate: 0 000000

Historical Data (1) The probability that the stock price will be higher than the strike price at expiration assuming a zero alpha andSample Mean Daily Growth Rate:  0.000000

Sample Daily Standard Deviation:   Time‐adjusted Standard Deviation:   

Probability of Stock Price Greater Calculation

expiration assuming a zero alpha, and(2) The probability that the stock price will

be higher than the strike price at your estimated alpha (which may produce the

l )than Strike Price at Expiration:  same result).

1.00

1.20

20 00

25.00 When you ask the question, “What is the prob that price will go from 100 to 105?” you are also asking “How

The NormBase file ...

0.60

0.80

10 00

15.00

20.00 to 105? , you are also asking How many standard deviations is 105 away from 100, and what is the probability of that?”

0.20

0.40

5.00

10.00

Mean to+/- 3 0.9973 0.4987+/- 2 0.9545 0.4772+/-1.5 0.8664 0.4332+/-1 0 6827 0 3413

Ranges Value-0.0400 -2 0.0228-0.0200 -1 0.15870.0000 0 0.50000 0200 1 0 8413

Cumulative Probs

0.000.00-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08

1.209.00 Value90 4837 2 0 022750

Cumulative Probs

+/ 1 0.6827 0.3413+/-0.5 0.3829 0.1915

0.0200 1 0.84130.0600 2 0.9772

We transform

0.80

1.00

5.00

6.00

7.00

8.00 90.4837 -2 0.02275095.1229 -1 0.158655

100.0000 0 0.500000105.1271 1 0.841345110 5171 2 0 977250

0 20

0.40

0.60

2.00

3.00

4.00

5.00 110.5171 2 0.977250

Probability of X greater than: 105 is 0.164581

0.00

0.20

0.00

1.00

82 85 88 91 94 97 100 103 106 109 112 115 118 121 Helpful to understand ....

Name: Date:

Strangle Implied Daily Volatility Calculator

Gary R. EvansMarch 4, 2014 ... a small segment of my Visual Basic

code.

Where we are going ... the Where we are going ... the actual strangle calculatoractual strangle calculator

Stock Symbol: HPQ Interest rate:

Stock Price: 29.640 0.010CALL PUT

Month: Mar Mar

Strangle Implied Daily Volatility Calculator

actual strangle calculator actual strangle calculator that we used two weeks that we used two weeks ago.ago.

Strike: 30.00 29.00Expiration: 3/22/14 3/22/14

Price: 1.130 1.110

Days to maturity: 18 18DTM override: 32 32

Implied daily volatility: 0.01919 0.02146One-day time decay: 0.020 0.021

Version 3.3 August 16, 2011

Calculate