May

21

 While the skeptical environmentalist Dr. Lomborg may contest trends in global warming and the increased frequency of natural disasters, I focussed on severe weather conditions in the US between 1955 and 2005. More specifically, having analyzed the annual frequency of hails and tornadoes in both Midwestern states and the whole US, I have come to the following conclusions:

(1) Both hail and tornado observations (not accounting for the severity or resulting economic costs) have risen since 1955. While the tornado frequency increased in linear fashion, hail observations however have grown exponentially over the same sample period.

(2) As one would expect, hail and tornado frequencies are co-integrated, whereby the latter are Granger-caused by the former.

(3) Rates of annual increases of both time series observations are slightly lower for the Midwest than the US on average.

However, my hypothesis that increasing numbers of hail and/or tornado observations might impact US grain markets was not confirmed. Having calculated annual volatilities (on a calendar rather than production year basis) for hard red spring and winter wheat varieties for Midwestern states of production, wheat volatilities were not correlated with either hail or tornadoes observations and consequently no regression yielded any significance.

Mar

31

What is the relationship between range and return? Using SPY intraday 1/04-present, %range and %return defined as:

day range = ((H/L)-1)*100
return =((close/open)-1)*100

Then regressing return vs (same day) range:

The regression equation is day rt = 0.246 - 0.262 day range.

Predictor      Coef    SE Coef      T      P
Constant    0.24619  0.05315   4.63  0.000
day range  -0.26152  0.05195  -5.03  0.000

S = 0.605558   R-Sq = 3.0%   R-Sq(adj) = 2.9%

Wee! The bigger the range, the more the drop. Seems obvious in that large range implies large variance, and there is contemporaneous negative correlation between variance and return. Logically big range can accompany big gain, big drop, or little change, yet it turns out most often to drop.

Optics trivia: this scatter plot resembles geometric spot-diagram of off-axis star image for system exhibiting the aberration known as coma.

In other regressions, tomorrow's day return had little correlation with yesterday's range or return.

The association of big range with contemporaneous negative returns is also seen if plotting range vs. date since 2006, the broad and (so far) narrow peaks corresponding with summer 2006 and recently, respectfully. 

Bernd Dittmann adds:

To further Kim's findings, it would be interesting to note that the daily range (as defined above) is strongly partially auto-correlated with a maximum lag of 10 trading days for the sample period since Jan. 2004, whereas intraday returns do not exhibit such a degree of auto-correlation. This would be in sync with findings of volatility clusters.

Day of high volatility or high daily trading ranges are likely to be followed by days of similar wide trading ranges. If one were to expand the sample period back to 2000, the above returns vs. daily range equation no longer holds. Neither the intercept (0.041, p=0.41) nor range (-0.026, p=0.38) is significant. 

Mar

20

I have to admit, bookshops are one of my weaknesses. They seem magically to attract me, and once I am in there, I am always delighted either to find, “The Education of a Speculator,” or “Practical Speculations” on the shelves. Another book, however had, intrigued me for a while and I finally gave in. It must have been titled: The UK Stock Market Almanac 2007.

While not having digested all tables and lists yet, here’s my brief review:

The content of the book is as ensnaring as its title suggests. The backbones of the author’s analysis are seasonal phenomena. Calendar months, days of the week, quarterly and sector specific behaviours are being examined. While it might be tempting to regard the title as shortcuts or extensions to the Chair’s seasonal analyses, I advice fellow Daily Specs to do the homework by themselves. Concepts of statistical significance, parametric vs. nonparametric methods, cross-correlations, are simply neglected. Results are not reviewed for robustness over time and Dr. Costaldo might be interested to know that the author includes January twice in his “January — Rest of Year” analysis. This book appears to have been written not with scientific precision but with inspiration of the Market Mistress, luring the reader into false security.

Mar

15

My true love gave to me,
A black eye and a kiss you'll see.

Daily range is high when volatility spikes, and decays over time. Yesterday was day 12 since the 4% decline in stocks. Checking the SPY intraday high/low as range (actually (H/L)-1), I used linear regression to measure the rate of decline. Here is a plot of SPY daily range since 2/27/07 (inclusive):

One might argue that range or volatility decay is not linear since it cannot progress continuously downward. In fact tests using quadratic regression showed better RSQ by adding **2 term, though linear term explained most of the variance. For simplicity the 1st 12 days are modelled as linear.

As a check on the current daily range decline against historics, I repeated regressions of the intraday range vs. the day following (analogous) declines; defined as 1day cl-cl drop worse than -3%, preceded by 5 days without a drop worse than -1% (SPY since 1993). Here is a table of the regression slopes and T-values for the range vs. the day following big declines, by year:

Yr       slope      t
2007  -0.0011  -1.8
2003  -0.0001  -0.2
2002  -0.0018  -2.4
2000  -0.0019  -2.8
1998  -0.0027  -1.5
1997  -0.0004  -0.9
1996  -0.0018  -2.4

It looks like the current change in range lies mainly in the plain, and is consistent with prior such events.

Bernd Dittmann adds:

As Kim outlined, both daily volatilities and daily high-low ranges decline after a spike. I estimated for the S&P 500 between Jan 03, 2000 and today a simple garch based on daily returns rather than daily range. The equation of the conditional variance ("h") seems to be consistent with his findings: Its regressor of lag 1 is 0.9276. A one-off vola spike (with subsequent error terms of the equation of the mean being zero) feeds through the model and decays as shown below:

day h
1 0.9276
2 0.8604
3 0.7981
4 0.7404
5 0.6868
6 0.6370
7 0.5909
8 0.5481
9 0.5084
10 0.4716
11 0.4375
12 0.4058
13 0.3764
14 0.3492
15 0.3239

This yields a similar picture as declines in daily high-low ranges.

Mar

14

While Prof. Gregory Mankiw 's Principles of Economics still maintains its high popularity as an introductory textbook for first year undergraduate students, I also strongly recommend Dr. Yoram Bauman's refreshing exposition of Mankiw's fundamental principles.


Mar

5

Pi, from Tom Larsen

March 5, 2007 | 1 Comment

 Pi is one of my 2 favorite movies with a trading theme. When I watch that movie, I think, "I know people like that!" Charts and computers everywhere and nobody knows what they're talking about. Their heads are pounding. So the hero is a little obsessed with the market…which reminds me of a favorite quote from the book, "The World According to Garp," when the wrestling coach tells Garp, "You've got to get obsessed and stay obsessed!"

The other movie is Trading Places, which I first saw in the theater with other members of the Pacific Stock Exchange after the close one day back in the 80s. What a great time we had! Here are a few lines where the evil Duke brothers cross-examine the street person they plan to turn into a trader. Billy Ray cuts through market analytical baloney to get to the real psychology of the market:

Randolph Duke: "Exactly why do you think the price of pork bellies is going to keep going down, William?"

Billy Ray Valentine: "Okay, pork belly prices have been dropping all morning, which means that everybody is waiting for it to hit rock bottom, so they can buy low. Which means that the people who own the pork belly contracts are saying, 'Hey, we're losing all our damn money, and Christmas is around the corner, and I ain't gonna have no money to buy my son the G.I. Joe with the kung-fu grip! And my wife ain't gonna f… my wife ain't gonna make love to me if I got no money!' So they're panicking right now, they're screaming 'SELL! SELL!' to get out before the price keeps dropping. They're panicking out there right now, I can feel it."

Randolph Duke: [on the ticker machine, the price dropping] "He's right, Mortimer! My God, look at it!"

Bernd Dittmann adds:

Bearing in mind Dr. Niederhoffer's enthusiasm for the book "Secrets of Turf Betting", I propose to add 1973’s "Sting," starring Redford, Newman et al to the Specs’s movies list. The similarity between the "Sting's" plot, bucket shops from the early twentieth Century and present day counterparts (spread betting firms and alike) is striking. Besides the movie's relevance to speculation, both Newman's and Redford's performances are stellar, even in their earlier years.

Mar

2

 Soaring UK property prices, especially in Greater London, have motivated me to investigate these growth rates in more detail. The initial question at hand was to see whether house prices UK-wide or in Greater London have beaten the FTSE100 performance over the last years. Based on the Halifax House Price Index, RPIX and annual FTSE100 return data between 1986 and 2006. I have come to surprising conclusions:

First, all annual return rates (UK properties, Greater London properties and FTSE100) do not significantly differ between each other either in nominal or (real) terms: average annual returns are +8.3% (+5.2%), +8.6% (+5.6%) and +8.4% (+5.4%) respectively.

Second, given the difference in price volatility, both UK-wide and Greater London have outperformed the FTSE100, both nominal and real. The annualized nominal (real) standard deviations each are: 1.9% (2.0%), 2.2% (2.5%) and 3.3% (3.2%).

Third, although properties in London may appear more attractive than in other parts of the country, Greater London returns have exhibited a slightly inferior return-to-risk ratio, both in nominal and real terms. I found nominal (real) Sharpe Ratios of 0.869 (0.539), 0.890 (0.489) and 0.351 (0.215) for UK-wide properties, Greater London and the FTSE100.

Bear in mind, though, that Sharpe Ratios for properties as an asset class are biased upwards, since transaction costs (stamp duty and other dead-weight costs), their relative illiquidity and heterogeneity are not accounted for.

Feb

28

 Having continued with Jay Pasch's counting of the Chinese carnage of Tuesday (as published here on Feb 28th), and instead of using confidence intervals, I looked at extreme values. Based on daily returns from the 2nd of January 1987 utill today (4992 obs.), here are the left and right tails of the return distribution:

%return    <-% obs        normal dist    >+% obs

0.1            2184              2321                2418
0.5            1466              1865                1663
1                876               1337                1041
2                334                 596                  371
3                140                 182                  136
4                  69                   50                   61
5                  36                    9                    27
6                  23                    1                    15
7                  18                    0                     9
8                  12                    0                     5
9                   8                     0                     2
10                 6                     0                     2
 
What is clearly striking is that declines of three percent or more have been observed more frequently than 3+ percent increases. If one were to use a normal distribution to describe Hang Seng daily returns (which is rejected at any level of significance), one would clearly underestimate the frequency of extreme returns of ± 4 and surely of ± 7 percent. Which distribution would thus fit Hang Seng returns, and also its asymmetry in extreme values? 

Dec

11

Motivated by Mr. McCauley’s article Market Irony and the October 1987 Crash, I inquired whether stock indices might exhibit non-random behavior around “significant” dates. More specifically, I investigated the returns of the S&P500 index around the 4th of July as a major secular US holiday.

In the years between 1950 to 1977, S&P500 percentage returns on the trading day before 4th of July have been significantly positive, on average by 0.43%. Percentage returns on the trading day after Independence Day (”ID”) have also been positively correlated to pre-ID returns by 0.40, albeit no significance of those returns is found. The late 70’s however present a break for this relationship. Between 1978 and 2006 neither pre-ID nor post-ID returns are significant. Similarly, correlation between both returns is merely 3.6% whereby both return series exhibit significantly higher variances than between 1950 and 1977.

Had I not investigated the robustness of my results, I might have inferred that S&P500 pre-ID returns are significantly positive, even nowadays. In fact, testing for the whole period 1950 to 2006 would support this: returns lie between 0.08% and 0.42% with 95% confidence. Pre-ID returns would not significantly differ from zero, had it not been for the pre-’78 period with a 0.45% return on average.

This short study of equity returns around Independence Day once again illustrates the nature of market phenomena and the notion (not theory) of ever-changing cycles and the resulting necessity to investigate the robustness of estimates. What was a profitable strategy till the late 70’s no longer works today (post-’78 returns are positively biased solely by the previous sample interval). I found it furthermore striking to observe S&P500 pre-ID returns to be positive for 17 consecutive years (’53 - ‘69).

Before opening the discussion to the floor, it might be of interest to investigate equity or bond returns around “significant” days, be they major secular or religious holidays or certain anniversaries. Similarly, perhaps fellow DailySpecs might want to expand on my findings, testing various other US indices for perhaps a longer sample period to see whether we can establish corresponding return behavior.

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