TRADING THE ODDS

Option Expiration and Down-Days

admin — Sat, 21 Aug 2010 07:38:52 +0000

In full compliance to historical probabilities and odds (see SPY’s Option Expiration Seasonalities), the SPY posted another down day on option expiration, on a back-to-back session to Thursday’s serious down-day (-1.74%). In addition, trading lower (than the previous session’s close) at the start of the final hour of option expiration’s session (see my Twitter Feed), (compliant to historical odds) the SPY was not able to recoup more than +0.50% of it’s intraday losses and couldn’t turn an intraday loss into a gain.

Table I below shows the SPY‘s performance (since 01/01/1990) on thoses sessions immediately following option expiration (in this event the session on Monday, August 23, 2010) assumed one went long on close …

Strat. #1: of a(ny) option expiration session,
Strat. #2: of a(ny) option expiration session when the SPY closed lower ,
Strat. #3: of a(ny) option expiration session when the SPY closed lower on a back-to-back session (two consecutive lower closes),
Strat. #4: of a(ny) option expiration session when the SPY closed lower on a back-to-back session (two consecutive lower closes), but reduced it’s losses on option expiration (a smaller loss than the one of the previous session).

All four setups were triggered on close of Friday, August 20, 2010.

There seems to be something special with those session at and/or around option expiration. Although at-any-time historical probabilities show a positive (short-term mean-reversion) tendency on a session immediately following a serious down day (e.g. SPY lost at least -1.50%) and/or following two consecutive down-days, not so on and immediately following option expiration. Long-term probabilities (winning percentage) and odds (expectancy) are (partly significantly) tilt in favor of another (a third) lower close, but at least most recent occurrences show a remarkable positive tendency.

Table II below shows the most recent twenty historical occurrences (the SPY‘s performance on a session immediately following option expiration) and their respective returns, assumed one went long on close of an option expiration session when the SPY closed lower (Strat. #2):

With respect to setup #2, the SPY closed higher on all of the most recent nine occurrences, and higher on 16 out of the last twenty occurrences, with thirteen out of those sixteen gains exceeding +0.50%.

Although long-term probabilities and odds are tilt in favor of a potential third lower close on Monday’s session, and not taking into account volume and/or market breadth data but closing prices alone, time-weigthed (most recent) probabilities and odds favour a positive outcome (a higher close) on Monday, August 23,2010.

Successful trading,
Frank

Disclaimer: No position in the securities mentioned in this post at time of writing.

Remarks: Due to their conceptual scope – and if not explicitely stated otherwise -, all models/setups/strategies do not account for slippage, fees and transaction costs, do not account for return on cash, do not use position sizing (e.g. Kelly, optimal f) – they’re always ‘all in‘ -, do not use leverage (e.g. leveraged ETFs) - but a marginable account is mandatory -, do not utilize any kind of abnormal market filter (e.g. during market phases with extremely elevated volatility) , do not use intraday buy/sell stops (end-of-day prices only), and models/setups/strategies are not ‘adaptive‘ (do not adjust to the ongoing changes in market conditions like bull and bear markets).

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SPY’s Option Expiration Seasonalities

admin — Fri, 20 Aug 2010 06:51:17 +0000

Ahead of Friday’s option expiration the SPY (S&P 500 SPDR.) posted a serious down-day, losing -1.74% on the close.

Table I below shows the SPY‘s performance (since 01/01/1990) on option expiration assumed one went long on close …

Strat. #1: of a(ny) session immediately preceding option expiration,
Strat. #2: of a(ny) session when the SPY had lost at least -1.50%,
Strat. #3: of a session when the SPY had lost at least -1.50% immediately preceding option expiration (like on Thursday, August 19, 2010).

Table II below shows all historical occurrences (the SPY‘s performance on option expiration) and their respetive returns, assumed one went long on close of a session when the SPY had lost at least -1.50% immediately preceding option expiration (Strat. #3):

From my perspective a favorable mean-reversion tendency on option expiration looks quite different (in contrast to the SPY‘s overall mean-reversion tendency after posting a down-day of that magnitude, see Strat. #2). On almost two out of every three (11 out of 17) occurrences (Strat. #3), the SPY posted another down-day on option expiration, and it is a single occurrence on 11/21/2008 (+5.39%) only which turns the compound return and profit factor into a positive number.

Option expiration – from a statistical and historical perspective - seems to be a session where generally a long trade is a trade against the odds: although the percentage of winning trades is slightly positive (51.85%), the distribution of returns (a ranking of a setup’s returns in comparison to at-any-time returns) undercuts the at-any-time median return of a buy-and-hold approach, and only 6.58% of the SPY‘s returns on option expiration fall into the top tenth of the SPY‘s at-any-time top tenth (best) returns (disproportionally small), while 10.70% fall into the bottom tenth of the SPY‘s at-any-time bottom tenth (worst) returns, slightly above-average.

Successful trading,
Frank

Disclaimer: No position in the securities mentioned in this post at time of writing.

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XLE vs. XLU on August 17, 2010

admin — Tue, 17 Aug 2010 11:09:20 +0000

On a Twitter update on Monday, August 16 (see the Twitter Feed box on the right), I alluded to a favorable pairs trading (buying) opportunity in XLE (Energy Select Sector SPDR) vs. XLU (Utilities Select Sector SPDR), meaning long XLE and selling short XLU in equal money amounts, targeting a higher close the next day (out-performance of the XLE in comparison to the XLU on close – or during the session – of Tuesday, August 17). The opportunity might still arise at or shortly after the open on Tuesday’s session.

Below you’ll find the reason why.

Table I below shows the performance metrics (since 01/01/2002) for a pairs trade XLE (Energy Select Sector SPDR) vs. XLU (Utilities Select Sector SPDR), assumed one would’ve bought the pair (is equivalent to buying the first and selling short the second ETF in equal money amounts (number of shares in each ETF = 100% net asset value / share price)) on close of a session when

Strat. #1: XLE closed lower on five consecutive sessions,
Strat. #2: the pairs’s (the ratio of the ETF’s closing prices) Bollinger Bands %B with 4-days EMA and 1 standard deviation closed below -0.70 ,
Strat. #3: XLE closed lower on five consecutive sessions and under-performed the XLU on those five consecutive sessions as well,
Strat. #4: XLE closed lower on five consecutive sessions , and the 4-day CCI (Commodity Channel Index) of the pair (the ratio of the ETF’s closing prices) closed below -100.

XLE vs. XLU (Benchmark) represents a buy-and-hold approach (assumed one would always be long the XLE and short the XLU in equal money amounts).

Especially setup #3 and #4 offer excellent odds (probabilities of a winning trade greater than 75%, and a superior median winning trade of gt. +1.20% in comparison to a median losing trade of -0.36%). The only shortcoming is the fact that the number of occurrences (especially with respect to setups #3 and #4) is way too small to read anything statistically significant into it, but nonetheless worth mentioning.

Successful trading,
Frank

Disclaimer: Long XLE and short XLU at time of writing.

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Pairs Trading Part II – SPY vs. RTH

admin — Mon, 16 Aug 2010 14:32:45 +0000

One of the most interesting findings dealt with in a previous posting (Pairs Trading (ETFs) was the RTHs (Retail HOLDR.) salient feature of being a favorable candidate for a potential mean-reversion strategy in conjunction with a major market or sector ETF. With respect to the primarily method used for cointegration (the augmented Dickey-Fuller test), the RTH showed a probability better than 90% of being cointegrated with the IWM (Russel 2000) and the SMH (Semiconductor HOLDR.), and missed being cointegrated with SPY and QQQQ by a hairbreadth only (two price series are called cointegrated if the pair has a consistent mean and standard deviation, both prices series never indefinitely wandering off in opposite directions and never drifting farther and farther away from its mean without eventually returning to the initial ratio or mean).

But the RTH doesn’t seem to be a favorable candidate for a longer-term (the half-life – the expected time to revert half of its deviation from the mean – is regualary measured in weeks or month) pairs trading strategy only, but may provide favorable short-term mean-reversion opportunities as well (market timing).

Table I below shows the performance metrics (since 06/01/2001 due to the RTH‘s inception in May 2001) for different pairs in conjunction with the RTH and – for demonstration puposes – different pairs of major market ETFs (SPY, QQQQ and IWM) and sector ETFs (XLY – Consumer Discretionary – and XLP – Consumer Staples -) based on an exemplary mean-reversion strategy, assumed one would’ve bought the pair (is equivalent to buying the first and selling short the second ETF in equal money amounts (number of shares in each ETF = 100% net asset value / share price)) on close of a session when the 4-day EMA (Exponential Moving Average) of the pair (the ratio of the closing prices) is less than the 4-day EMA of the ratio of closing prices for yesterday, and vice versa (selling short the first and buying the second ETF in equal money amounts in the event of a rising 4-day EMA of the ratio of closing prices).

Here is the link to the stats in a more ‘readable’, original size: Statistics 1

While – with respect to the specific setup defined – the SPY vs. QQQQ, the SPY vs. IWM, the XLY vs. XLP and the SPY itself (buy and hold) as a benchmark virtually went nowhere (or even closed in the red) over the course of the last 9 years – especially after accounting for fees and transaction costs -, the RTH as a pairs trading component in conjunction with the SPY, the QQQQ, the IWM and the SMH not only easily out-performed a (S&P 500) buy-and-hold approach by a wide margin (and almost year by year as well, see ‘Periodic Returns‘ in the stats above), but comes up with a smoother equity curve as well, meaning there are much less dramatic departures from a gradually/geometrically increasing trendline (R-squared, maximum drawdown, maximum sessions in drawdown) in comparison to a SPY‘s buy and hold approach.

Interestingly the SPY vs. RTH and SMH vs. RTH pairs trading strategies and a S&P 500 buy-and-hold approach do NOT differ with respect to the probability of a winning trade (the probability is almost always slightly above 50% only). The reason for the deviation in total returns is the fact that – in contrast to the SPY‘s buy and hold approach – the median winning trade (+0.51%) now equals or slightly exceeds the median losing trade (-0.50% ), significantly improving the respective expectancy (probability of winning * average gain – probability of losing * average loss).

But a SPY vs. RTH‘s pairs trading strategy has another advantage as well: Chosing a slightly different setup in order to especially exploit those reversal opportunities where the pair is (from a historical and statistical perspective) exceptionally stretched to one or the other side would be sufficient to not only surpass previous compounded returns, but to cut in half the time in market and the maximium drawdown as well. Table II below shows the performance metrics (since 06/01/2001 due to the RTH‘s inception in May 2001) for the same pairs, assumed one would’ve bought the pair (buying the first and selling short the second ETF in equal money amounts) on close of a session when the pair (the ratio of the closing prices) closed at least -0.50% below its 4-day EMA, and vice versa (selling short the first and buying the second ETF in equal money amounts in the event of a close at least +0.50% above the 4-day EMA of the ratio of closing prices).

Here is the link to the stats in a more ‘readable’, original size: Statistics 2

With respect to SPY vs. RTH (Strat. #1), time in market and maximum drawdown have been exactly cut in half (giving you the chance to earn an additional return on cash) while the geometric growth rate per trade doubled. Although the probability of a winning trade (again) only slightly improved (from 54.63% to 57.44%), it is (again) the effectiviness (doing things right instead of doing the right thing only, meaning increasing your gains when you’re right and cutting your losses when you’re wrong) of the strategy which makes for the improvement in key performance metrics.

But what about the robustness of a SPY vs. RTH pairs trading strategy ? It it works with a -0.50%/+0.50% level below/above a 4-day EMA, it should work with a -/+0.30% up to a -/+0.70% level and a 3-day and 5-day EMA as well showing some gradual – no radical - changes with respect to the key performance metrics only.

Table III below shows the performance metrics for the SPY vs. RTH pairs trading strategy, assumed one would’ve bought the pair (buying the first and selling short the second ETF in equal money amounts) on close of a session when the pair (the ratio of the closing prices) closed at least

Strat. #1: -0.30% below (long) and +0.30% above (short) its 4-day EMA,
Strat. #2:-0.40% below (long) and +0.40% above (short) its 4-day EMA,
Strat. #3:-0.50% below (long) and +0.50% above (short) its 4-day EMA,
Strat. #4:-0.60% below (long) and +0.60% above (short) its 4-day EMA,
Strat. #5:-0.70% below (long) and +0.70% above (short) its 4-day EMA.

SPY vs. RTH (Strat. #6) represents a buy-and-hold approach (assumed one would always be long the SPY and short the RTH).

Here is the link to the stats in a more ‘readable’, original size: Statistics 3

And last but not least, table IV below shows the performance metrics for the SPY vs. RTH pairs trading strategy, assumed one would’ve bought the pair (buying the first and selling short the second ETF in equal money amounts) on close of a session when the pair (the ratio of the closing prices) closed at least

Strat. #1:-0.50% below (long) and +0.50% above (short) its 3-day EMA,
Strat. #2:-0.50% below (long) and +0.50% above (short) its 4-day EMA,
Strat. #3:-0.50% below (long) and +0.50% above (short) its 5-day EMA.

SPY vs. RTH (Strat. #4) represents a buy-and-hold approach (assumed one would always be long the SPY and short the RTH).

Neither a slight variation in the percentage level below/above the 4-day EMA nor a variation in the duration of the EMA itself affects any of the strategy’s key performance indicators in a significant way, except – but expectedly – the so called opportunity factor (total number of sessions and time in market).

Summary: A SPY vs. RTH‘s pairs trading strategy, assumed one would’ve bought the pair (buying the SPY and selling short the RTH in equal money amounts) on close of a session when the pair (the ratio of the closing prices) closed at least -0.50% below its 4-day EMA, and vice versa (selling short the SPY and buying the RTH in equal money amounts in the event of a close at least +0.50% above the 4-day EMA of the ratio of closing prices), historically provided a (consistently) profitable market timing strategy (a median annual return of +15.65%), (consistently, in 8 out of the last 9 years) out-performing a S&P 500 buy-and-hold approach, with a smooth equity curve (R-squared, maximum drawdowns on a week/month/year end basis, maximum time in a drawdown), meeting at least basic requirements for robustness and reliability. Unfortunately a shortcoming is the deviation in yearly returns (one standard deviation = 32.72%).

A favorable basis for some further investigations and refinements (accounting for return on cash, position sizing, and making the strategy adaptiv to changing market conditions – if necessary).

to be continued …

Successful trading,
Frank

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Disclaimer: Long SMH and short XRT at time of writing.

SMH vs. XRT on AUG. 13, 2010

admin — Fri, 13 Aug 2010 11:11:00 +0000

One of those favorable short-term reversal opportunities ( see Pairs Trading (ETFs) ) may be provided on today’s session (August 13, 2010), assumed one would’ve bought the pair SMH vs. XRT (Semiconductor HOLRDS. vs. S&P 500 Retail SPDR) on close of the last session (August 12, 2010).

During the last couple of sessions, the SMH more or less posted a waterfall decline, losing -2.44%, -2.47% and -1.81% (adjusted for dividend and cash payments) on the last three trading days, while the XRT out-performed the SMH by a wide margin.

The table below shows the respective performance metrics (since 07/01/2006 due to the XRT‘s inception in June 2006) for the pair SMH vs. XRT, assumed one would’ve bought (is equivalent to long SMH and short XRT in the right proportion, means equal money amounts (number of shares in each ETF = 100% net asset value / share price)) on close of a session when,

#1 the SMH under-performed the XRT by at least -2.25% on the close, and the 4-day CCI (Commodity Channel Index, w/ closing prices used for the ‘typical price‘) of the pair closed at -133 (lowest level possible),
#2 the SMH under-performed the XRT by at least -2.25% on the close, and under-performed XRT on the last three consecutive sessions as well,
#3 the SMH under-performed the XRT by at least -2.25% on the close, and under-performed the QQQQ by at least -1.0% on the same session,
#4 the SMH under-performed the XRT by at least -2.25% on the close (no additional condition).

It is especially interesting to note that historically there is a significantly above-average probability (and odds as well) that the SMH will turn the tables and out-perform the XRT on the then following session (like today), regularly by a wide margin. Since 07/01/2006 there were 70 occurrences where the SMH under-performed the XRT by at least -2.25%, and on 51 out of those 70 occurrences (73.63%) the SMH out-performed the XRT on the then following session (like today, August 13, 2010) for a respectable median profit (considering all 70 trades) of +0.84%.

The second table below shows all historical occurrences (since 07/01/2006) and the strategies (#4) performance on close of the then following session assumed one would’ve bought the pair on the previous close where the signal (the SMH had under-performed the XRT by at least -2.25% on the close) had been triggered.

to be continued …

Successful trading,
Frank

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Disclaimer: Long SMH and short XRT at time of writing.