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.

Does Sector Index Out- or Under-Performance Really Matter ?

There are a lot of adages in the market, and some are related to index out- and/or under-performance compared to other major market or sector indexes and the respective implications for the market’s outlook over the course of the next couple of sessions or weeks.

Due to the fact that especially the most recent sessions were heavily affected by such performance figures (e.g. under-performance of the $SOX Semiconductor Index versus the $NDX, under-performance of the $SPXEW S&P 500 Equal Weighted Index versus the $SPX, and under-performance of the $BKX Banking Index versus the $SPX), I wanted to check if there is eny evidence in market’s history that such under-(out-)performance could possibly provide a tradable edge over the next couple of sessions, and if any such under-(out-)performance might show a better than average quality of forecast concerning the market’s performance over the next couple of sessions.

I checked for the following indexes and setups:

  1. $SPX S&P 500 Index (capitalization weighted) versus the $SPXEW S&P 500 Equal Weighted Index (Survey S1)
  2. $SPX S&P 500 Index versus the $BKX Banking Index (Survey S2)
  3. $SPX S&P 500Index versus the $NDX Nasdaq 100 Index (Survey S3)
  4. $SPX S&P 500 Index versus the $SOX Semiconductor Index (Survey S4)
  5. $NDX Nasdaq 100 Index versus the $SOX Semiconductor Index (Survey S5)

Methodology:

I checked if the n-day summation of the daily index versus index performance exceeds a specific bar (which more or less equals the index versus index under-(out-)performance over the course of n days)

Example: running 5-day summation of [(today’s close(SPX) – yesterdays’s close(SPX)) /yesterdays’s close(SPX)  – (today’s close(SPXEW) – yesterdays’s close(SPXEW)) /yesterdays’s close(SPXEW)]  > 5%
(which more or less equals the $SPX’ versus $SPXEW under-(out-)performance over the course of n days)

Study (exemplary)

  1. $SPX outperforms $SPXEW by at least 2% over the course of the last 5 sessions (Survey S1)
  2. $SPX outperforms $BKX by at least 5% over the course of the last 5 sessions (Survey S2)
  3. $SPX outperforms $NDX by at least 5% over the course of the last 5 sessions (Survey S3)
  4. $SPX outperforms $SOX by at least 5% over the course of the last 5 sessions (Survey S4)
  5. $NDX outperforms $SOX by at least 5% over the course of the last 5 sessions (Survey S5)

Assumption: Survey 2, 3, 4 and 5 should have negative implications concerning the SPX’ performance over the course of the following couple of sessions due to the significant under-performance of those sector indexes ($BKX, $SOX) which should lead the market on the upside (or on the downside).

Table I below shows the SPX‘ performance (since 01/02/1990) over the course of the following 5 sessions (means profit/loss 5 sessions after those sessions where the respective setups had been triggered) after surveys 1 to 5 had been triggered.

20090514-S1

For exemplary purposes, figure II shows the SPX‘ (bell curve) distribution of profits and losses over the course of the following 5 sessions concerning survey 5 ($NDX outperforms $SOX by at least 5% over the course of the last 5 sessions). The bell curve is slightly left-skewed, which means a bigger part of the distribution is concentrated on the right -the profit side- of the figure. The bottom line is that there is NO historical evidence that any under-performance of the $SOX Semiconductor Index versus the $NDX Nasdaq 100 might have negative implications for the S&P 500‘s performance over the course of the following 5 sessions.

20090514-S15g

And the same conclusion holds true if checked against the $NDX’ (not $SPX’) performance over the course of the following 5 sessions. Figure II shows the NDX‘ (bell curve) distribution of profits and losses over the course of the following 5 sessions concerning survey 5 ($NDX outperforms $SOX by at least 5% over the course of the last 5 sessions). The bell curve is again slightly left-skewed, which means a bigger part of the distribution is concentrated on the right -the profit side- of the figure. The bottom line is that there is NO historical evidence that any under-performance of the $SOX Semiconductor Index versus the $NDX Nasdaq 100 might have negative implications for the Nasdaq 100‘s performance over the course of the following 5 sessions.

20090514-S15gndx

Over the last 5 sessions the $SPX has lost -3.9% while the $SOX has lost -12.5%. So I additionally checked for those occurrences where the $SOX under-performed the $SPX by at least –8.0% during the last 5 sessions, and the respective implications concerning the $SPX’ performance over the course of the next couple of sessions.

Table I below shows the SPX‘ performance (since 01/02/1990) over the course of the following 5 sessions whenever the $SOX had under-performed the $SPX by at least -8.0% during the last 5 sessions.

20090514-S2

Win/Loss Ratio and profit factor do NOT (significantly, if at all) differ from the respective at-any-time probabilities and odds, so again there is no statistical evidence that any tremendous under-performance of the $SOX versus the $SPX  like the –8.0% we just experienced has negative implications concerning the $SPX’ performance over the course of the next couple of sessions in comparison to the respective at-any-time probabilities and odds for a higher/lower close and profits/losses up to 5 sessions later.

________________________________

But now the other way around: Does any significant out-performance of the $SOX or $BKX versus the $SPX and/or $NDX have positive implications for the major market indexes’ performance over the course of the next couple of sessions ?

Study (exemplary)

  1. $SPXEW out-performs $SPX by at least 2% over the course of the last 5 sessions (Survey S1)
  2. $BKX out-performs $SPXby at least 5% over the course of the last 5 sessions (Survey S2)
  3. $NDX out-performs $SPX by at least 5% over the course of the last 5 sessions (Survey S3)
  4. $SOX out-performs $SPX by at least 5% over the course of the last 5 sessions (Survey S4)
  5. $SOX out-performs $NDX by at least 5% over the course of the last 5 sessions (Survey S5)

Assumption: Survey 2, 3 4 and 5 should have positive implications for the SPX’ performance over the course of the following couple of sessions due to the significant out-performance of those sector indexes ($BKX, $SOX) which should lead the market on the upside.

Table II below shows the SPX‘ performance (since 01/02/1990) over the course of the following 5 sessions (means profit/loss 5 sessions after those sessions where the respective setups had been triggered) after surveys 1 to 5 had been triggered.

20090514-S3

Contrary to what one might have expected concerning a significant positive outcome, the S&P 500 did NOT perform better than random even if those ‘leading’ sector indexes like the $SOX and $BKX significantly outperformed during the last couple of sessions.

And although the following figure III which shows the NDX‘ (bell curve) distribution of profits and losses over the course of the following 5 sessions concerning survey 5 ($SOX outperforms $NDX by at least 5% over the course of the last 5 sessions) might suggest that the bell curve would be slightly left-skewed, which would mean that a bigger part of the distribution would be concentrated on the right -the profit side- of the figure (indicating a more bullish outcome for the $NDX over the course of the next 5 session), the bell curve shows a long tail on the left side (with losses exceeding the -10% mark)  for an overall profit factor of 0.83 only (sum of all profit divided by the sum of all losses).

20090514-S35g

________________________________

Bottom line:

The stats shown above are for exemplary purposes only. I checked survey 1 to 5 for different investment periods and different bars, but probabilities and odds only slightly differed from each other and never signifcantly changed the following conclusions (in compariosn to the respective at-any-time probabilities and odds):

  • any under-performance of the $SOX versus the $SPX and/or $NDX does -from the market’s historical perspective- NOT have any negative implications for the S&P 500′ and Nasdaq 100′ performance over the course of the next couple of sessions, as any significant out-performance does NOT have any positive implications concerning the major market indexes’ short-term performance.
  • any under-performance of the $BKX versus the $SPX shows some slightly negative implications concerning the probabilities for a higher $SPX close 5 sessions later, but not concerning the odds (profit factor / expectancy), and
  • any under-performance of the $SPXEW versus the $SPX in fact shows (being part of a couple of my previous posts) (significant) negative short-term implications concerning the probabilities and odds for a higher $SPX close one and two days later.

But although -averaged over the course of the last 20 years- there is no statistical evidence that any significant out- or under-performance of the $SOX and/or $BKX versus the $SPX and/or $NDX had significant (if any) positive or negative implications concerning the short-term performance of the major market indexes, there might have been shorter time periods in the market during which such out-/under-performance in fact showed any positive or negative implications.

Successful trading,

Frank

P.s.: WordPress recently implemented a Twitter widget, so I’ll regularly make some intraday updates as well using Twitter. If you’re interested in, please have a look at the blog during the trading session as well or subscribe directly to Twitter (recommended).

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