Author: rgearyiii

Subject: NASDAQ NH/NL and Tick Size

Date: 8/20/2015

Recommendations: 37

In May I posted in http://boards.fool.com/wider-spreads-are-good-for-you-317475... about the SEC mandating a pilot program during which stock exchanges impose a minimum tick size of $0.05 for a large sample of US stocks. One consequence of increasing the minimum tick size that you may not have considered is the impact on probabilities that less liquid stocks repeatedly revisit their 52-week highs or lows. With a larger tick size, those non-negligible probabilities are increased, and consequently, the dynamics of market timing indicators like the NASDAQ New High/New Low Ratio are altered. I`ve put together some backtests that demonstrate the surprising non-triviality of this issue. First, the investment used for bullish periods (when the ratio is at least 1) is the same in all backtests, and I call it "gSPYQQQ": 1. From 19251231 through 19570227, it is a market cap-weighted portfolio of all S&P 90 stocks. 2. From 19570228 through 19731216, it is a market cap-weighted portfolio all S&P 500 stocks. 3. From 19731217 through 19850130, it is a market cap-weighted portfolio of all "Pseudo-NASDAQ 100" stocks. The latter group consists of NASDAQ`s current NASDAQ 100 inclusion rules applied to the NASDAQ exchange over the period. These rules, as applied by the GTR1 backtester, are able to replicate current NASDAQ 100 constituents with about 96% overlap, and are therefore believed to produce a good simulation of the NASDAQ 100 universe prior to its inception. 4. From 19850131 through the present, it is a market cap-weighted portfolio of all NASDAQ 100 stocks, trimmed of secondary share classes. My reason for these choices is to track the trendiest indexes available at each time while including dividends, which the official indexes do not. Weighting by market capitalization ensures that the portfolios would have been tradable with low turnover. Consider these three backtests over the period when sufficient NASDAQ data is available (one year of price history), but prior to the completion of decimalization on 20010409: (1) (2) (3) 1st Trades: 19731217 1st Trades: 19731217 1st Trades: 19731217 End: 20010409 End: 20010409 End: 20010409 CAGR: 15.86 CAGR: 13.01 CAGR: 20.31 TR: 5533.35 TR: 2749.49 TR: 15704.06 GSD(20): 28.35 GSD(20): 15.24 GSD(20): 17.83 DD(20): 18.19 DD(20): 8.42 DD(20): 8.68 MDD: -69.38 MDD: -32.17 MDD: -26.82 UI(20): 12.39 UI(20): 6.82 UI(20): 5.50 Sharpe(20): 0.46 Sharpe(20): 0.47 Sharpe(20): 0.80 Beta(20): 1.15 Beta(20): 0.40 Beta(20): 0.57 TI(20): 9.86 TI(20): 16.93 TI(20): 23.82 AT: 0.45 AT: 2.51 AT: 2.54(1) http://gtr1.backtest.org/2013/?s19731217e20010409lf-1lp-1h1:... (2) http://gtr1.backtest.org/2013/?s19731217e20010409lf-1lp-1h1:... (3) http://gtr1.backtest.org/2013/?s19731217e20010409lf-1lp-1h1:... The first backtest (1) is simply of buying and holding gSPYQQQ with no timing. Backtests (2) and (3) are for applying two different versions of the NASDAQ NH/NL Ratio, holding gSPYQQQ when the ratio is bullish (at least 1) and holding Cash (with returns matching the interest rates on 3-month US Treasury Notes) otherwise. In both versions of the NH/NL Ratio, only closing prices are used. Where they differ is in how New Highs and New Lows are counted: In (2), the current close only needs to be equal to the maximum (in the case of New Highs) or minimum (in the case of New Lows) close over the last 252 market days, meaning it may be a repeat of that maximum or minimum. I call these "Loose" New Highs and New Lows. By contrast, in (3), New Highs are only counted if the current close is strictly greater than all closes in the previous 251 market days, and New Lows are only counted if the current close is strictly less than all closes in the previous 251 market days. I call these "Strict" New Highs and New Lows. As you can see, the strict version of the indicator clobbers the loose version. It stands to reason that should larger tick sizes return (even if they are still only $0.05, as opposed to the 1/8ths that were in effect for most of the pre-decimalization history), the importance of which method of measuring News Highs and New Lows will grow significant again as well. Demonstrating that the issue was mostly eliminated with decimalization is somewhat complicated by the fact that the NASDAQ NH/NL Ratio by itself has not worked anywhere near as well since 2001. Nevertheless, the differences between the Loose and Strict versions of the indicator essentially vanished since 2001, as my hypothesis would predict: (4) (5) (6) 1st Trades: 20010409 1st Trades: 20010409 1st Trades: 20010409 End: 20150819 End: 20150819 End: 20150819 CAGR: 7.83 CAGR: 3.34 CAGR: 3.88 TR: 194.60 TR: 60.24 TR: 72.60 GSD(20): 24.75 GSD(20): 15.01 GSD(20): 15.34 DD(20): 17.02 DD(20): 10.58 DD(20): 10.73 MDD: -56.71 MDD: -51.82 MDD: -47.99 UI(20): 20.30 UI(20): 21.75 UI(20): 18.15 Sharpe(20): 0.39 Sharpe(20): 0.21 Sharpe(20): 0.24 Beta(20): 1.15 Beta(20): 0.38 Beta(20): 0.40 TI(20): 7.51 TI(20): 7.49 TI(20): 8.51 AT: 0.48 AT: 4.03 AT: 3.94(4) http://gtr1.backtest.org/2013/?s20010409lf-1lp-1h1::gSPYQQQ:... (5) http://gtr1.backtest.org/2013/?s20010409lf-1lp-1h1::gSPYQQQ:... (6) http://gtr1.backtest.org/2013/?s20010409lf-1lp-1h1::gSPYQQQ:... (4), (5) and (6) are backtests of the same strategies as (1), (2) and (3) respectively. Finally, here are backtests of the same strategies from 19260104 through the present, where the NASDAQ NH/NL Ratio is computed over the NYSE/AMEX (ordinary common shares of domestically-incorporated companies and REITs) instead of the NASDAQ prior to the latter`s first full year of existence: (7) (8) (9) 1st Trades: 19260104 1st Trades: 19260104 1st Trades: 19260104 End: 20150819 End: 20150819 End: 20150819 CAGR: 10.69 CAGR: 9.99 CAGR: 12.76 TR: 895640.31 TR: 507553.75 TR: 4719962.50 GSD(20): 24.91 GSD(20): 13.44 GSD(20): 15.34 DD(20): 16.61 DD(20): 7.99 DD(20): 8.36 MDD: -84.58 MDD: -65.86 MDD: -60.23 UI(20): 30.89 UI(20): 18.21 UI(20): 14.99 Sharpe(20): 0.42 Sharpe(20): 0.55 Sharpe(20): 0.66 Beta(20): 1.09 Beta(20): 0.36 Beta(20): 0.47 TI(20): 8.56 TI(20): 19.12 TI(20): 20.51 AT: 0.34 AT: 3.45 AT: 3.74(7) http://gtr1.backtest.org/2013/?lf-1lp-1h1::gSPYQQQ:gt0:gSPYQ... (8) http://gtr1.backtest.org/2013/?lf-1lp-1h1::gSPYQQQ:gt0:cashi... (9) http://gtr1.backtest.org/2013/?lf-1lp-1h1::gSPYQQQ:gt0:cashi... Finally, since someone is likely to ask, here are backtests comparing the Loose (10) and Strict (11) NASDAQ NH/NL Ratio where daily High/Low values are used instead of closes. That is, by the loose definition, a stock is at a new high if its high for the day is equal to the maximum daily high over 252 market days, whereas by the strict definition, a stock is at a new high only if its high for the day is strictly greater than all daily highs over the previous 251 market days; and similarly for loose and strict new lows. Keep in mind that NASDAQ started out as simply a quotation service for OTC stocks, reporting only bids and offers (i.e., no trades, and thus no highest or lowest trades, and no "close" either in the modern sense, just closing Bid/Ask) until late 1982, when it created two tiers (the NASDAQ National Market and the NASDAQ Smallcap Market), with time & trade reporting (including high and low) for the top tier only. Time and trade reporting for the second tier did not begin until June 1992, and only from that point is High/Low data for the NASDAQ complete. When actual traded highs and lows are not available, my GTR1 linearizer sets both equal to the close (or more precisely, the closing Bid/Ask midquote). (10) (11) 1st Trades: 19260104 1st Trades: 19260104 End: 20150819 End: 20150819 CAGR: 10.44 CAGR: 12.51 TR: 731593.63 TR: 3875888.25 GSD(20): 13.84 GSD(20): 15.82 DD(20): 8.24 DD(20): 8.88 MDD: -60.28 MDD: -56.19 UI(20): 16.13 UI(20): 15.93 Sharpe(20): 0.57 Sharpe(20): 0.64 Beta(20): 0.39 Beta(20): 0.50 TI(20): 19.16 TI(20): 19.11 AT: 3.19 AT: 3.67(10) http://gtr1.backtest.org/2013/?lf-1lp-1h1::gSPYQQQ:gt0:cashi... (11) http://gtr1.backtest.org/2013/?lf-1lp-1h1::gSPYQQQ:gt0:cashi... A similar long-term advantage for strict definitions of new highs and new lows is seen using the intra-day high/low data, and interestingly, daily high/low data (where it is available) does not appear to offer any advantage over close data. Robbie Geary