Trading the Odds

A statistical approach to profit in the US equity markets, trading the markets like professional card counters are playing Blackjack or expert poker players are playing Poker.

Trading the RSI(2) from 1950 to 2009

A few days ago Michael Stokes at MarketSci made an excellent post concerning RSI(2) readings, the changing frequency of extreme readings, its (the RSI’s) quality of forecast and efficiency of trading short-term mean-reversion in the markets over the course of time since 1950 (Extreme RSI(2) Readings Becoming Less Common, and he already covered the topic here and here), and based on his findings and conclusions -for exemplary purposes- I set up a static trading strategy (static means no adjustments of RSI time frame and break points) for the time frame since 1993 (SPY, see Trading the RSI as a Static Strategy) which would not only have been profitable over the course of time but would have been outperformed the index as well (and on top of that with a lesser maximum month-end drawdown).

But what would Michael’s finding that extreme RSI(2) readings currently become less common than in the past mean percentage-wise concerning a potential RSI(2) strategy ?

I conducted the same analysis for the time frames from 1950 until 1970, 1970 until 1990 and 1990 until 2009 for the S&P 500 with a 2-day RSI as I did for the static trading strategy with an RSI (2.5) for the SPY, meaning I determined the distribution of gains and losses on those sessions (the first and second day thereafter) immediately following a session when the S&P 500 RSI(2) closed between a lower and upper break point in order to evaluate an ideal exit point for a potential RSI(2) strategy (where the sum of all gains minus the sum of all profits = expectancy turns from positive to negative, which means -on average- the maximum possible gain on the upside would have been achieved).

For the three different time frames from 1950 to 1970, 1970 to 1990 and 1990 to 2009 , the following tables Table I to Table III show the respective distribution of profits and losses for the S&P 500 and the RSI(2) over the course of the then following 2 sessions, broken down by different ranges (potential upper breaking points) for the RSI (2), assumed one would’ve bought the S&P 500 on close of every session when the RSI (2) closed anywhere between the lower and the upper break point (no overlapping trades allowed). Please take a special look at the third last row (‘Profitability’).

Table I (1950 – 1970)

survey-20090424-rsi-1950-1970-1

Regarding the time frame from 1950 until 1970

  • all RSI(2) readings above 70 led -over the course of the then following two sessions- on total to profitable trades if one would have bought the S&P 500 on close of a session with an RSI(2) reading between the lower and upper break point,
  • all RSI(2) readings above 70 show positive win/loss ratio, profitability and profit factor significantly above the at-any-time profit factor for the time frame from 1950 until 1970, and
  • there were significantly more extreme RSI(2) readings between 90 and 100 than between 70 and 90 combined (the sum off all occurrences between 70 and 90),
  • and RSI(2) readings between 90 and 100 show the highest profitability of all RSI(2) ranges.

So any RSI(2) strategy build upon a potential short on any RSI(2) reading above 90 would have been a clear receipt for disaster, and the upper break point would had to been set close to 100 in order to achieve maximum gains on the upside.

____________________________________

Table II (1970 – 1990)

survey-20090424-rsi-1970-1990-1

Regarding the time frame from 1970 until 1990

  • all RSI(2) readings above 70 led -over the course of the then following two sessions- on total to profitable trades if one would have bought the S&P 500 on close of a session with an RSI(2) reading between the lower and upper break point,
  • all RSI(2) readings above 70 show positive win/loss ratio, profitability and a profit factor either slightly, partly significantly above the at-any-time profit factor for the time frame from 1970 until 1990, and
  • the amount of extreme RSI(2) readings between 90 and 100 approximately equals the total amount of RSI(2) readings between 70 and 90 combined (the sum off all occurrences between 70 and 90),
  • and RSI(2) readings between 80 and 90 show the highest profitability of all RSI(2) ranges.

So any RSI(2) strategy build upon a potential short on any RSI(2) reading above 90 would have been still a clear receipt for disaster, and the upper break point would had to been set close to 90 in order to achieve maximum gains on the upside.

But profitability and total amount of extreme RSI(2) were less extreme than the respective figures concerning the time frame from 1950 until 1970.

____________________________________

Table III (1990 – 2009)

survey-20090424-rsi-1990-2009-1

Regarding the time frame from 1990 until 2009

  • only RSI(2) readings between 75 and 80 led -over the course of the then following two sessions- on total to profitable trades if one would have bought the S&P 500 on close of a session with an RSI(2) reading between the lower and upper break point,
  • only RSI(2) readings below 80 show positive win/loss ratios and a profit factor close to the at-any-time profit factor for the time frame from 1900 until 2009, and
  • the amount of extreme RSI(2) readings between 90 and 100 approximately equals half of the total amount of RSI(2) readings between 70 and 90 combined (the sum off all occurrences between 70 and 90).

So any RSI(2) strategy build upon a potential short on any RSI(2) reading above 90 could have been profitable for the first time since 1950, and the upper break point would had to been set somewhere between 70 and 80 in order to achieve maximum gains on the upside

So I completely agree with Michaels bottom line (cit.) ‘the markets are becoming more contrarian in the short-term. That means the market tends not to move in a single direction for as long, which means that the market tends to register less extreme readings on short-term indicators such as this one.

Successful trading,

Frank

P.s.: WordPress recently implemented a Twitter widget, so I’ll regularly make some intraday updates as well using Twitter (as I already did during the last couple of session, but unfortunately there seems to be a connectivity issue between WordPress and Twitter; hope that will be solved soon). If you’re interested in, please have a look at the blog during the trading session as well or subscribe directly to Twitter.

Filed under: Studies/Survey, Trading Strategies

Trading the RSI as a Static Strategy

A few days ago Michael Stokes at MarketSci made an excellent post concerning RSI(2) readings, the changing frequency of extreme readings, its (the RSI’s) quality of forecast and efficiency of trading short-term mean-reversion in the markets over the course of time since 1950 (Extreme RSI(2) Readings Becoming Less Common, and he already covered the topic here and here).

Although I completely agree to his findings and conclusions which could be summarized as (cit.) ‘I don’t think this says anything about the effectiveness of strategies based on indicators such as RSI(2), but it does say that they might trigger a bit less over time.‘ and (cit.) ‘But I would be hesitant to trade the RSI(2) in the simple form I’ve described here as a static strategy.‘, I was incited by Bill Luby’s comments on Michael’s post concerning the usage of deviating break points (e.g. 95/5 and 98/2 instead of 90/10) and/or different moving averages (e.g. RSI (3) and RSI (4) instead of RSI (2)).

The RSI Relative Strenght Index was developed by J. Welles Wilder and introduced in 1978. The RSI (x days) oscillates between 0 and 100 and compares the magnitude of an assets (e.g. stock or index) recent gains to the magnitude of its recent losses, with low readings indicating oversold and high readings indicating overbought conditions.

My objective was to check if and to what extend the Relative Strength Index (not taking into account any additional indicator and/or condition, so in its pure form) could be utilized for a mechanical (and static) trading strategy, with investigations focused on the following questions:

  • could an RSI based strategy stand the test of time without any adjustments (e.g. break points) and/or adaptions to the then current market conditions (e.g. bull/bear markets),
  • its profitability year by year, in the long run, and its capability to deliver positive returns in bull and bear markets likewise,
  • its capability to outperform the SPY as a tradable proxy for the S&P 500,
  • the possibility to reduce the time in market in comparison to a buy and hold approach (which is always in the market) in order to reduce the risk of being hit by a potential ‘black swan’ event.

As an additional restriction I took into account and allowed for long trades only (the addition of potential short sales will probably be addressed in a future post), and no adjustements  (e.g. break points) are allowed for. No leverage is taken (no position sizing, money management and/or stops except the break points), but the strategy is always ‘all in’ (compounded returns, means any potential profits are always reinvested on the next trade in order to be comparable to a ‘buy and hold’ approach which is evenly always ‘all in’, assumed that no money is taken out). Due to the fact that this is a proof of concept/survey only, performance figures do not account for commissions, fees and slippage.

First of all I figured out that with respect to all the conditions listed above, it is not the 2-day or 3-day or 4-day RSI but the 2.5-day RSI which met those requirements best. Sounds surprisingly, but with respect to the computation of the RSI is makes no difference using 2.5 as a moving average instead of 2/3/4/… /x (even numbers for the number of sessions).

The next step was to evaluate the ideal lower and upper break points. From my perspective the optimal approach would be to determine the distribution of gains and losses (for the SPY) over the course of the then following first two days after a trade would have been entered at the lower break point, broken down by different RSI (2.5) ranges, and respectively at the upper break point in order to ride any upmove to its ideal extent (and before any potential profit would turn into a loss). For the time frame since 01/03/1993, the following tables (Table I for the upper break point,and Table II for the lower break point) show the respective distribution of profits and losses for the SPY over the course of the then following 2 session, broken down by different ranges for the SPY’ RSI (2.5), assumed one would’ve bought the SPY on close of every session when the RSI (2.5) closed anywhere between the lower and the upper break point (no overlapping trades allowed).

In order to maximize profits, the ideal exit is located between 67.5 and 72.5. That would present the ideal upper break point because any exit above (too late) or below (too early) would have reduced any already achieved or have missed any potential further gains due to the fact that the market’s tendency to reverse course significantly increased with an RSI (2.5) above 70. The same principle applies to the lower break point. The highest profitability (sum of all gains minus the sum of all losses, not the profit factor or anything else because the ‘opportunity factor’ plays a decisive role) would have been achieved with a lower break point of 18 (+179.06% during the then following two days if one woud have bought the SPY on close of every day when the RSI (2.5) closed below 18).

Strategy: Buy the SPX on close of a session when the RSI (2.5) closes below the lower break point (18); close the trade on close of a session when the RSI (2.5) closes above the upper break point (70).

(please note that trade performance figures were assigned to the date -and therefore regarded as achieved and realized- when the ‘buy’ was triggered, not on the date the trade was closed; that doesn’t make a difference concerning the total gains/lossed achieved, but due to the deviating distribution of gains/losses -not their total- the equity curve would look a bit different)

Table I

survey-20090423-rsi-22

Table II

survey-20090423-rsi-32

Table III shows the respective equity curve. Some additional stats:

  • Maximum month-end drawdown: -11.22%
  • % month positive: 74%
  • Month outperformance SPY: 52.85%
  • Time in market: 31.50%

survey-20090423-rsi-11

So I completely agree with Michaels bottom line (cit.) ‘I do think RSI(2) has wings in today’s market. … But I would be hesitant to trade the RSI(2) in the simple form I’ve described here as a static strategy.‘, but not mainly concerning the point that it wouldn’t make sense to trade the RSI (2.5) as a static strategy (which would have been considerably profitable, less risky than a ‘buy and hold’ approach and would have almost always outperformed the SPY, but with hindsight only because we determined the ideal break points in 2009 and not in 1993) but in particular with respect to the fact that it will probably be possible to build a strategy around the RSI (2.5) in combination with one or more other indicator/conditions like Michael does in his State of the Market report which would be superior to any static RSI strategy alone.

Successful trading,

Frank

P.s.: WordPress recently implemented a Twitter widget, so I’ll regularly make some intraday updates as well using Twitter (as I already did during the last couple of session, but unfortunately there seems to be a connectivity issue between WordPress and Twitter; hope that will be solved soon). If you’re interested in, please have a look at the blog during the trading session as well or subscribe directly to Twitter.

Filed under: Studies/Survey, Trading Strategies

The Market Shows it Pays to be a Contrarian

The Market Shows it Pays to be a Contrarian

There are some often cited adages amongst investing commentators and traders, e.g. “Don’t try to catch a falling knife”, “The trend is your friend.”, “Nobody rings a bell at the market bottom.”, “Buy on strength” and “Sell into weakness” (the trend following approach), among others. But due to the fact that I’m one of those contrarians who see opportunity where others fear “disaster” (and vice versa), and being a ‘scientific sceptic’ (who regularly questions the reliability of those adages) I’m always eager to check if and to what extend those adages might prove true in the current (and past) investment cycle, and how to capitalize on any observations made during my investigations. To make a long story short: The current investment cycle  requires to -at least- question some adages and/or shows opportunity to add some fresh adages to the already long list.

Due to the recently often discussed short-term mean-reversion character of the markets, and in order to check if there is a way to increase the quality of forecast for the respective next session’s outcome (probabilities for a higher/lower open, higher high, lower low and/or higher/lower close), I took a deeper dive into the (trend following) “Buy on strength” and “Sell into weakness” adages.

For the time frame since 10/01/2007 (approximately the beginning of the current bear market), I checked for the SPY‘s outcome of the respective next session after the following setups had been triggered:

  • at-any-time: Buy on close on every session regardless of any setup (no questions asked), sell on close the next session
  • Survey I: SPY posted a higher high above the previous session’s high (as a proxy for intraday strength)
  • Survey II: SPY posted a lower low below the previous session’s low (as a proxy for intraday weakness)
  • Survey III: SPY DID NOT post a higher high above the previous session’s high (limited upside potential, as a proxy for some intraday weakness)
  • Survey IV: SPY DID NOT post a lower low below the previous session’s low (limited downside potential, as a proxy for some intraday strength)

The following table shows -over the course of all 382 sessions since 10/01/2007- the SPY‘ behavior and the respective performance on those sessions immediately following the session when the respective setup was triggered. Odds (potential payout and expectancy, NOT the true chances that the event will occur) significantly above or significantly below their respective at-any-time odds (in this case +/-20.00%, but this percentage is up to everyone’s decision what may be regarded as ’significant above’ or ‘below’) are marked by a green (for a probable bullish or favorable outcome) and red (for a probable bearish or unfavorable outcome) background color. This should make it possible to catch on a glimpse if (any), where (e.g. EOD end-of-day change compared to the previous session’s close, or C-O close minus open for intraday strength/weakness) and to what extent (compared to historical odds) the respective setup out- or underperformed the market and if any tradable edge is provided.

survey-20090408-12

(click on image to enlarge)

First impressions:

  1. Survey (Setup) I -SPY posted a higher high than the previous session’s high- provides an unfavorable setup (concerning a bullish bias) due to the fact that the average profit on winning trades (+0.61%) is lower, and the average loss on loosing trades (-0.91%) is higher than the respective averaged at-any-time profits (+0,75%) and losses (-0,88%). In addition the profit factor of 0.66 (+104.85%/158,19%) is far worse than the even worse (because lower than 1) at-any-time profit factor of 0.85 (+285%/336,58%).
  2. Survey (Setup) II -SPY posted a lower low than the previous session’s low- seems to provide a highly favorable setup (concerning a bullish bias) due to the fact that the average profit on winning trades (+0.90%) is higher, and the average loss on loosing trades (-0.78%) lower than the respective averaged at-any-time profits (+0,75%) and losses (-0,88%). In addition the profit factor of 1.15 (+185.99%/161,30%) is significantly higher than the respective at-any-time profit factor of 0.85 (+285%/336,58%). Concerning a potential mechanical trading system -buy the SPY on open, sell on close on a session following those sessions on which setup II had been triggered-  survey II would outperform a respective at-any-time trading system as well, means on average the market closed above it’s open more often and to a greater extent after setup II had been triggered than on an at-any-time session.
  3. Survey (Setup) III -SPY DID NOT post a higher high than the previous session’s high- seems to provide a neutral setup in comparison to the respective at-any-time performance figures because it did neither out- nor underperform the market to any significant extent.
  4. Survey (Setup) IV -SPY DID NOT post a lower low than the previous session’s low- seems to provide a highly unfavorable setup (concerning a bullish bias) -to say the least- due to the fact that the average profit on winning trades (+0.57%) is significantly lower, and the average loss on loosing trades (-0.99%) higher than the respective averaged at-any-time profits (+0,75%) and losses (-0,88%). In addition the profit factor of 0.57 (+99.17%/173,94%) is far worse than the even worse (because lower than 1) at-any-time profit factor of 0.85 (+285%/336,58%). The same applies accordingly concerning intraday trades following a potential mechanical trading system -buy the SPY on open, sell on close on those sessions following those sessions on which setup IV had been triggered-.

But how to capitalize on those observations ? A logical next step would be to simply capitalize on favorable and unfavorable (from a bullish perspective) setups by taking long trades only (on close of the day when the respective setup was triggered) concerning setup II -SPY posted a lower low than the previous session’s low-, and going short (in order to turn an unfavorable bullish setup into a favorable bearish setup) on close of those session when setup I -SPY posted a higher high than the previous session’s high- OR setup IV -SPY DID NOT post a lower low than the previous session’s low- were triggered.

SurveyALL: “Buy the SPY on close of those sessions when the SPY had posted a lower low than the previous session’s low, and go short the SPY on close of those sessions when the SPY had posted a higher high than the previous session’s high OR the SPY had NOT posted a lower low than the previous session’s low; if both a long and a short signal had been triggered on the same day, take the buy signal only ; close the trade on close of the next session and enter into a new one.” (the last condition wouldn’t make sense in a real trading system, if no controversinal signal would be triggered you’d still hold on to your position) That is more or less the equivalent of  “Buy on weakness and sell on strength.” and contradicts the respective trend-following adage.

The following table shows -over the course of all 382 sessions since 10/01/2007 again- the SPY‘ behavior and the respective performance on those sessions immediately following the session when the respective setup was triggered, now including SurveyALL in the last column and reflecting the potential performance figures of a combined trading system (Survey I up to IV are unchanged).

survey-20090408-11

(click on image to enlarge)

Bottom line:

  1. A mechanical trading system following SurveyALL would have had (almost) always been in the market, there were only 2 sessions out of 382 when the setup would NOT had been triggered (05/22/2008 and 12/18/2008).
  2. The system would have yielded a return of investment (not accounting for commissions, fees and slippage; not leveraged and not compounded) of 359.93%-260,47%=+99.47% compared to an at-any-time ROI of -51.42% (a ‘buy and hold’ approach would have yielded -47.08% since 10/01/2007, means the SPY has lost -47.08% during that time frame).


survey-20090408-142

(click on image to enlarge)

Not bad for a pretty easy mechanical trading system with 197 winning trades and 184 loosing trades (but unfortunately with hindsight bias only), which from a win/loss ratio’s perspective only, would be nothing to write home about (but in this case not the probability of being right or wrong but the odds count). Up to now I haven’t calculated other important figures like max. drawdown and shape ratio.

So a new adage with respect to the current investment cycle might be: “If the market did not make a lower low today – it probably will tomorrow.” or “If the market posted a higher high today – it will probably post a lower low tomorrow.” (and therefore “Buy on strength” as well as “Sell on weakness” might not represent favorable guidelines at least for today’s markets)

But please keep in mind: These statistics are provided for informational and statistical purposes only, and there would be still a lot more work to do in order to check if this combined setup could be converted into a profitable trading system (e.g. if it would be profitable and to what extent in other times frames and markets as well).

Successful trading,

Frank

Filed under: Studies/Survey, Trading Strategies

SPY and Gap Fills

SPY and Sessions until Gap Fill

After the SPY left open an unfilled downside gap on Monday’s session (see my posting Trading the Odds on Tuesday – March 31, 2009), a reader raised the question how long it regularly takes to get a downside gap in the SPY filled (as well as in other indexes).

The following table shows those 57 sessions (see also Trading the Odds on Tuesday – March 31, 2009) since 01/03/2000 after the SPY left an unfilled downside gap and the respective number of sessions it took to get the gap closed (those session with a ‘?‘ instead of any number of days mark those sessions where the gap is still unfilled).

No. Date Gap fill
x days later
1 03/02/2009 8
2 02/17/2009 27
3 01/14/2009 9
4 01/07/2009 ?
5 12/01/2008 5
6 10/22/2008 5
7 10/06/2008 ?
8 06/26/2008 31
9 06/20/2008 ?
10 06/02/2008 3
11 02/29/2008 21
12 02/05/2008 13
13 01/04/2008 93
14 12/17/2007 4
15 09/07/2007 2
16 08/28/2007 1
17 07/10/2007 2
18 02/27/2007 28
19 09/06/2006 3
20 08/01/2006 1
21 07/13/2006 4
22 08/05/2005 2
23 01/20/2005 7
24 12/17/2004 1
25 09/22/2004 7
26 08/06/2004 2
27 07/06/2004 42
28 06/14/2004 1
29 05/10/2004 1
30 03/22/2004 3
31 11/17/2003 1
32 10/22/2003 4
33 09/22/2003 9
34 06/09/2003 1
35 02/04/2003 1
36 12/18/2002 9
37 09/12/2002 3
38 09/03/2002 5
39 08/28/2002 60
40 07/19/2002 6
41 06/21/2002 241
42 04/22/2002 431
43 03/20/2002 494
44 02/19/2002 4
45 09/17/2001 12
46 07/06/2001 5
47 06/14/2001 1.038
48 05/23/2001 1.207
49 03/12/2001 26
50 03/09/2001 35
51 02/16/2001 65
52 12/20/2000 2
53 12/15/2000 2
54 07/18/2000 24
55 05/19/2000 7
56 05/03/2000 8
57 04/14/2000 2

(‘date': session where the gap was left open)

Successful trading,

Frank

Filed under: Studies/Survey, Trading Strategies

Short-term Mean-Reversion Between Implied and Realized Volatility

Short-term Mean-Reversion Between Implied and Realized Volatility

The VIX® (CBOE Volatility Index) is an index that infers 30-day (calendar days, regularly between 20 and 22 trading days) expected (implied) market (S&P 500) volatility from S&P 500 index options (usually in the first and second month, and averaging the weighted prices of puts and calls over a range of strike prices). It closed at 41.04 last Friday.

The current 21-day realized (not implied) volatility closed at 49.15(%) last Friday. Thus the delta between the markets expectation of future (30-day = 21 trading days) volatility and the just experienced realized volatility during the last 21 trading days is currently at -8.11% (means the markets expectation of future volatility is  trading (significantly) below the  just experienced realized volatility), which could be regarded as some kind of complacency in the market (which regularly doesn’t bode well concerning the market’s short-term performance).

The table shows

  • percentage wise (for those 46 session which fulfilled the conditions of w/Survey I since 01/03/2007),
  • utilizing the VIX (index data) itself and not any equity index,
  • and taking into account those sessions only after the VIX closed at least -8.00% below the then current rolling 21-day realized volatility the day before (‘w/Survey I‘)

the historical probabilities (since 01/03/2007) for a higher and lower open, the average change between close and open (close -open), the average daily True Range (Wilder True Range), the historical probabilities for a higher high and lower low (than the last session’s high/low) and a higher or lower close as well as the respective sum of all profits and losses (theoretically, and for statistical purposes only due to the fact that the VIX is not a tradable asset) going long/short on open. But due to the fact that in the 2nd table probabilities significantly above or significantly below their respective at-any-time probabilities (in this case +/-15.00%, but this percentage is up to everyone’s decision what may be regarded as ’significant above’ or ‘below’) are marked by a green (for a probable bullish outcome) and red (for a probable bearish outcome) background color, one may be able to catch on a glimpse the impact of taking into account those sessions only after the VIX closed -8.00% or less below the then current rolling 21-day realized volatility on the respective probabilities and odds.

Table I

survey-20090330-1

(click on image to enlarge)

Bottom line:

  1. On those 46 occurrences which fulfilled the conditions of w/Survey I, the VIX closed -on average- the next session not only significantly above it’s opening quotation independently if it opened higher or lower, but additionally significantly above the respective at-any-time magnitudes of change. This may be regarded as some kind of a short-term mean-reversion tendency between implied and realized volatility. On those 16 sessions with a higher open the VIX’ True Range averaged 16.00% (that would correspond to an approximately 6+ move today).
  2. Going long on open (that means theoretically ‘buying’ the VIX on open) would have yielded a high profit factor of above 4 (way above the at-any-time profit factor theoretically buying the VIX on open in the event the VIX opens higher), and going short the VIX on a lower open would have yielded a profit factor below 1 for a negative expectancy.
  3. Needless to say that on average (not to be mistaken for ‘always‘) -and due to the regularly inverse relationship between the VIX and the S&P 500- this didn’t bode well for the equity indexes (S&P 500, SPY) in the past (concerning the specific session after this setup had been triggered) …

Successful trading,

Frank

Filed under: Studies/Survey, Trading Strategies

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The information on this site is provided for statistical and informational purposes only. Nothing herein should be interpreted or regarded as personalized investment advice or to state or imply that past results are an indication of future performance. Under no circumstances does this information represent an advice or recommendation to buy, sell or hold any security.

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