Marketeers have been herding or stampeding recently. The NYSE up volume/down volume has been over 10:1 and over 1 million on one side. The days have been "trendy." Fish school and gazelles stampede for safety when under attack. Predators have to stand back or just pick off strays. Seems to be an effective survival type tactic. A question might be: when does the stampede start, and what triggers it?
Vinh Tu writes:
Virtual birds form flocks, when each bird individually follows three rules:
1. Separation: steer to avoid crowding local flockmates.
2. Alignment: steer towards the average heading of local flockmates.
3. Cohesion: steer to move toward the average position of local flockmates.
Here's a nice demo.
I'm looking for other good demos, for other types of herding behaviour.
Similarly, traders can stampede and trend as each individually decides that there is a trend going on. An exogenous shock that triggers a buy signal for enough traders would be able to trigger the stampede.
Adi Schnytzer writes:
In Australian and other bookmaker horse betting markets, herding is triggered by inside trades (plunges) and takes the odds lower than they the horse's true winning probability. This creates arbitrage opportunities. I have not yet gotten round to tote-only markets like the US or HK, but know that things there are more complicated by the absence of tradable updating prices. In the stock market, I'm sure it's also insiders or big money that triggers the herding and I hope to get around to this next year. Meanwhile, see A. Schnytzer and A. Snir, "Herding in Imperfect Markets with Inside Traders", Journal of Gambling Business and Economics, Volume 2, No. 2, 2008, 1-16. (available upon email request).
Why do you hypothesize the Tel Aviv market rose before the holiday? Yom Kippur prayer, as Prof. Schnytzer suggested? What else do they know?
Adi Schnytzer comments:
I simply couldn't come up with a better hypothesis. I guess you get so low that up is the only feasible direction left, right?
Nigel Davies responds:
I think there's a flaw in this logic. The concern here is 'system failure,' which if it happens can mean that the profits from being short may be worthless anyway. Who knows, under some kind of post system martial law, short-sellers might even be rooted out and put on trial…
In my view there are two long bets; long the system's surviving and long personal/familial survival in some post-apocolyptic nightmare. So the most reasonable hedge is to buy survival items like freeze-dried food, blankets, medicine, weapons, a horse, some chickens and a couple of goats.
Anatoly Veltman adds:
You are thinking of V-shaped bottom. Of course, other shapes of bottoms have occurred in history of every contract.
V-shaped bottom's dilemma is that environment created in course of a rout doesn't facilitate one's large reversal position - even if one correctly times reversal. The entire ecosystem deflates; so due pay-off will not be mathematically possible in favor of the bottom picker.
Theoretically, this should not be the case vis-a-vis a trendfollower, who correctly stays short all the way down, possibly even pyramiding. Except in 2008 — when shorting became restricted.
Sam Marx adds:
I agree regarding Cramer but in this downdraft we don't know how far it will go even if stocks are undervalued now. But stocks have a tendency to overshoot at opposite ends.
In '87 when there was a one day sell off of approx. 23% I was clearing through a firm that had its start in commodities and the head of the firm was almost in tears claiming that the stock market was vicious compared to commodities. He gave up clearing and bought a bank in Chicago.
I saw Mike Huckabee on Cavuto's Saturday program say that a "knowledgeable" friend of his suspects "economic terrorism" is behind this sell off.
In the end, undervalued stocks with growth potential will come back in price. That's the basis of Buffett's large purchase of KO (Coke) in '87. The stock was driven down by being part of an index where arbs bought the index future and sold a stock basket that included KO.
In '87 on the floor after that big one day down, I sold overpriced far month out of the money calls and bought an equal number of shorter month calls at the same strike price. Both were grossly overpriced. The plan was when the volatility dropped because of time the spread decreased and I unwound them. As a saving grace if the stock started to move up the volatility would've dropped and I could also unwind at a profit.
June 15, 2008 | 9 Comments
I found myself lying awake in my bed last night thinking about the Nobel Prize Winner. No! Not like that….but about what he said in Stockholm last week. Expected Utility Optimization. What he said is that the goal of asset allocation should be optimizing the expected utility for the actual investor in question, and that the mean variance model should just be looked upon as a special case. And of course he is right. I mean, by the way he sets it up, he is right by definition. But….I am thinking how it would play out in the real world. In my fantasy, a consultant would sit down with an investor, asking questions to find out his preferences. Of course this is already happening in a general sense but here it would end in a very specific investor utility function). Then the asset allocation would be done based on the utility function.
I am thinking that what will be overlayed on the usual return/risk models, are constraints (e.g cutting off tail risk, smoothing out fluctuations and what have you) and while the model presumably maximises return given a risk level and those added constraints; if we add constraints there must be risk premia transferred to someone else? By definition, since the investor specified his utility function (and given that the formulas and models held up and he got "what he wanted") he is better off than before, but so must someone else be?
I am not sure this new allocation model will start a revolution in the way asset allocation is done. I think however that finding situations where other investors are up against constraints, could help open up possibilities and profits. In the micro realm, many traders prefer to cut off the risk of gaps against them, by not holding overnight. This might open up possibilities for traders well capitalised and with good stomach, to do just that (this must be tested). Other suggestions are welcome.
Adi Schnytzer critiques:
It never ceases to amaze me that people who know markets and work in them don't realise that we don't know the probability that anything will happen tomorrow unless we are in a fair casino. So the idea that anyone can maximize expected utility is nonesense since you don't know the probabilities. I am currently working on developing a risk index as a follow-up to such an index developed recently by Aumann. He cutely argues that even though we don't often know the probabilities to assign to events, it's important that, in principle at least, we have an index. Well, I've been looking for real life examples of his index (and my follow-up) in stock and derivative markets, and simply cannot find one. As a top bookie once said to me: "If I only knew the winning probabilities of the horses, I wouldn't need to know winners; I'd be making a fortune anyway." Spot on.
Jim Sogi adds:
Martin talked about "…cutting off tail risk".
The thesis that outliers shape the future is intriguing, but also that the risk cannot be eliminated. The idea that one can cut left tail risk is an illusion that in itself creates a greater risk. As Phil says, it also cuts right tail return.
Jeff Watson concurs:
Risk can be quantified, assumed, bought, sold, transferred, created, subordinated, reassigned, split, delayed, diluted, fragmented, hedged against, and layed off……. Risk can respond to some methods, but it is still risk, and is near impossible to eliminate.
Speaking of planning in general, Stefan Jovanovich adds:
I have quoted this before, but it seems worth repeating, if only to add a mite to Adi's wisdom. Planning in business is all very well, but the trouble is that your plan's assumptions always turn out to be works of fiction. As John Wannamaker said, "I know half the money I spend on advertising is wasted. If someone would tell me which half, I would very much appreciate it."
Vince Fulco concurs:
This quote has always seemed appropriate…
Moltke's famous statement that "No campaign plan survives first contact with the enemy" is a classic reflection of Clausewitz's insistence on the roles of chance, friction, "fog," and uncertainty in war. The idea that actual war includes "friction" which deranges, to a greater or lesser degree, all prior arrangements, has become common currency in other fields as well (e.g., business strategy, sports). [Wikipedia].
Russ Humbert warns:
One of the hardest things to get people to see is that most people/businesses have a long term utility function but operate as if all risk is short term volatility. For example, I work for a company that has a niche market and is privately held. The owner wants to pass this business on to his great-grand kids so each will be as well off as he is now. He has only teen kids now. This niche has very little volatility of earnings and good ROEs. But this just encourages piling on the same long term risk, to minimize the short term risk. That is: grow the core business, not diversify. We already have the leading player in this niche. Barriers of entry: a learning curve, requires some marketing nimbleness, and need for stable size and reputation. However, long term this has no good ending. Best case we double our market share and flatline growth. But many worse cases. Bigger, deeper pocket competitor or many, learns our niche attracted by the ROE and stable vol. We are regulated out of the market. Products slowly go obsolete, replaced by Government safety net. We lose our reputation, etc. See this in spades throughout the fallen out of favor or failed businesses, due to subprime mess. Low vol high ROE business, until…. For the speculator this would be like choosing a strategy that 95% time gives "Alpha" in a beta model based on quarterly results of recent history. But all the "alpha" is hidden because, 5% time it causes you to go broke or close to it. It just hasn't happen yet, or recently. Basically volatility as a risk measure can hide long term complacency defeating most utility functions.
Going back to the military aspect Bill Egan adds:
An interesting aspect of the fog of war is the common mistake of not reevaluating the plan often. A major cause of this error is that people confuse perseverence towards a goal (a good thing) with sticking to the particular plan they are using at the moment to achieve that goal. Criticism of the plan and proposing actual changes to deal with new information or uncertainty are considered as defeatism or disloyalty and the operationally fluid are smacked down. The no longer relevant plan is then ridden on to failure to a loud chorus of "yes, sir! yes, sir! three bags full, sir!" A pleasant sight if it is your opponent doing this but awful if it is your leadership. I have fond memories of serving as a company commander under a battalion commander who always asked us to tell him if he wasn't making sense and meant it. Good man.
Phil McDonnell enlightens:
There are many deep questions in Mr. Lindkvist's ruminations on Expected Utility Optimization.
My first comment would be that there are at least two distinct classes of utility function. The first class might be what can be called the Ad Hoc Class. This would include the questionnaire method of approximating one's utility function.
Other methods might be classified as normative, as in what one should ideally want to use for a utility function. As a well known example we have the Sharpe Ratio. This is based upon the normative idea that one should maximize expected return but with a quadratic penalty for increased volatility which is treated as a surrogate for risk.
The idea of using a square root function as a weighting for betting returns actually goes back several centuries to Cramer, a mathematician. His friend and frequent correspondent Daniel Bernoulli countered with the idea of a logarithmic weighting function, which is also what I espouse with extensions. Bernoulli's ideas were not translated into English until the 1950s and thus were lost to Western thinking until very recently.
Dr. McDonnell is the author of Optimal Portfolio Modeling, Wiley, 2008
Adi Schnytzer concurs:
It's time the world learnt how data collection functions. These numbers are produced by turkeys who never ask whether their numbers make sense. And to think that markets respond to them!
Bill Rafter adds:
Lots of the data put out are also seasonally adjusted. One of my big peeves is that the data monkeys who work for the gummint do not know how to properly do the seasonally adjustment. As a result there are a lot of bad data out there. The real problem comes when the bad data are released, and everyone follows them. In other words, perception becomes reality. You (having the good data) have to follow the bad data also, at least until some time elapses and the whole thing gets corrected. So you have to watch against being too clever for your own good.
Jason Thompson reveals:
I've developed a localized index of inflation that is actually reflective of folks' consumption baskets. It includes taxes, insurance, education, and healthcare in more accurate weights. It has shown me how far off the CPI has been versus reality since at least 2002. The spread has consistently grown! This local inflation measure focuses on prices in the Chicagoland area and so would be best compared with CPI-U. Further, the resolution is quarterly not monthly. The inflation measure for Q1 2008 will likely show an increase of 8.6% YoY.
Bill Fleckenstein of Seattle, where I live, has a book out now on Alan Greenspan showing the fake PhD for what he really is. Vic and Laurel always referred to Greenspan as a fake PhD. I watched the tele-circus every time Greenspan appeared before Congress. Just as in a circus the main clown was Greenspan and the crowd were the Congressmen who were the suckers P.T. Barnum referred to when he said "there's a sucker born every minute." My study of the Federal Reserve dove into many books written by Real PhDs with genuine insights into the nefarious activities of people claiming to be economists under guise of their position. I have shown that the Fed is not an independent agency but is a tool of politics. In view of that Fleckenstein should have pointed to the pseudo-science of economists and the gullibility of Congress as the culprit in the fiascos and bubbles, he writes about. Actually, at the heart of bubbles lies the economics of Chicago, the Friedmanist fantasy that mathematics makes economics a science and deregulation, hands-off, free markets, makes wealth grow for everyone. If massive deregulation had not occurred the criminal, crocodile brain stem of financiers would not have been freed to swindle everyone into accepting the Chicago fantasy. Flooding the world with fake money is not science, it is merely political policy. And bubbles, as in champagne, produce headaches; in this case, world-shaking headaches. Oil is up around $110 but it is there because the dollar is not worth anything. Oil has a value but dollars do not; that's the root of our problems; it takes more worthless dollars to buy oil. If the dollar were solid, oil could be bought with fewer dollars. And that is were Friedman's Chicago School has got us to.
Adi Schnytzer adds:
I disagree with Ken about lumping Friedman in with the Fake PhDs of this world. If Friedman's policies had been followed, the robber banks would be broke now, the US economy would be in a depression, but it would at least recover therefrom quickly. All of these attempts to save the thieving mongrel bankers is simply delaying the collapse, not preventing it. Free markets give good folks pain but the also take out the trash like nothing else.
"…Left off the balance sheet is the value of the asset that Gary Becker, Nobel Laureate in Economics, calls human capital. Professor Becker says that the skills and experience of our people are worth more than half a million dollars per person. By this calculation, traditional assets comprise less than 25 percent of the national balance sheet, which means that true U.S. assets exceed $180 trillion…" Mike Milken
I haven't had my morning coffee yet but here's an attempt at arithmetic along Beckerian lines:
A recent FT article put Japanese assets at 75% of its GDP. Pulling a totally random number out of nowhere, if the return on assets is 5%,
GDP = 5%*(total assets)
GDP = 5%*75%*GDP+5%*humancapital
19.25*GDP = humancapital
Looking at World Bank statistics
World GDP 2006 = 48.2 trillion
World financial assets = 170 trillion
Return on assets = 5% (can someone give me a better number?)
Return on financial assets = 8.5 trillion
Return on human capital = 39.7 trillion
Human capital = 794 trillion
population = 6.6 billion
Average human capital per capita (hheh..) = 120303.3
Anyway, very rough calculations with numbers plucked from the ether, but the order of magnitude at least is in line with Prof. Becker.
(Also, I left out something important - GDP is not just a return on capital (even human capital) because human ingenuity produces excess profits and increases the value of the capital. So you'd have to adjust the calculation of human capital to account for growing return. And risk adjustments. Etc. etc.)
Any real macro economists care to point me in the direction of more accuracy?
Phil McDonnell replies:
Rather than pulling an imaginary growth rate out of our … armpit, perhaps a better approach can be found. GDP is the goods and services produced by a society. However much of that is consumed as well. The number we are really seeking is the net 'profit' figure that can be carried forward into the next year. It is good to remember that any 'profit' carried over must be held in the form of an asset. Thus a reasonable measure of the rate of return would be the net increase in total assets year over year.
Yishen Kuik counters:
Maybe I'm too classical, but I've always thought that GDP is a flow measure of all the goods and services we produce, of which one portion is consumed to give us present utility and the remaining portion is invested to enhance our ability to increase GDP in the next period.
Presumably all goods have some aspect of both utility and investment ("school is fun and you learn something" or "bridges are beautiful and enable transportation"), but we can think of the investment portion of GDP as flowing into a stock of accumulated capital.
The stock of capital deteriorates over time, so some of that flow is just running to keep still. Part of the stock is human, part of it is physical plant, and part of it is institutional arrangement of society (courts, laws etc). The dollar figure we attach to capital stock is just a very rough attempt at measurement, and doesn't take into account the importance of having the right arrangement of the 3 kinds of capital stock. The right arrangement catalyzes a $100mm investment to return 15%, while the wrong arrangement will have no such catalyzing effect. That is why $100mm produces such different results when invested in America versus Africa.
I think it is this accumulated capital stock (human/physical/institutional) which is the right place to discuss big picture returns on investment. Unfortunately much of it is unquantified and unquantifiable.
Adi Schnytzer brings up the stock market aspect:
Surely the real issue here is that, however, we define GDP, it's notoriously unpredictable? After all, why has the market been shooting up and down so furiously lately? In part it's because every one has been wondering whether or not the US economy is moving into a recession. Well, if we could agree on a way to to measure and predict GDP, we'd have solved that issue for the market pretty quickly, wouldn't we?
Derek Gard dissents:
This assumes the market moves based on GDP at all.
From 1950 to 1960 GDP went from 1696.765 to 2517.365 (48%) and the DJIA went from 198.89 to 679.06 (241%)
From 1960 to 1970 GDP went from 2517.365 to 3759.997 (49%) and the DJIA went from 679.06 to 809.2 (19%)
From 1970 to 1980 GDP went from 3759.997 to 5221.253 (39%) and the DJIA went from 809.2 to 824.57 (2%)
From 1980 to 1990 GDP went from 5221.253 to 7112.100 (36%) and the DJIA went from 824.57 to 2810.15 (240%)
From 1990 to 2000 GDP went from 7112.100 to 9695.631 (36%) and the DJIA went from 2810.15 to 11357.01 (304%)
GDP during the 60s was higher than the 50s and yet the market barely budged. And GDP during the 60s and 70s surpassed the growth rates of the 80s and 90s, yet what decades saw the greatest gains in stocks? Stock market moves do not correlate well with actual GDP data over decades or even years, let alone the daily thoughts and musings of financial pundits.
To say stocks move on GDP data, or confusion thereof, is not supported by raw data. This is the same logic that says, "Stocks rose on a drop in oil prices" one day and then the very next day says, "Stocks fall despite a decline in oil prices." It is a fallacy promulgated by the same people who earned 3.5% per year in stocks during the 80s and 90s when the market was earning more than triple that.
Adi Schnytzer replies:
My argument was not that the market moves in line with GDP, rather that lately the market has been reacting to news suggesting either an imminent recession or not. To measure the relevance of this assertion you need to check whether or not the market falls some months before a recession (thus anticipating it) and not whether over a long period the market tracks GDP.
Nigel Davies opines:
As a simple chess player I must admit to being confused by the apparent
implication (seen everywhere right now) that positive GDP is good and
negative GDP is bad. In my own admitedly primitive pursuit one rarely
gets the opportunity to play expansive moves on a continuous basis,
there are periods when one must regroup in order to increase the
potential energy of a position.
So if I were an economist I would not be looking for answers in simple
linear relationships. Instead I'd try to study the interplay between
'potential energy' (one might try to define this in many ways, for
example by defining debt in 'real' terms) and GDP. And I'd hypothesise
that one of the most bullish economic times would be during a recession
in which personal debt was being reduced.
Vinh Tu tries to sum up and conclude:
Whether more GDP is "good" or "bad" is a normative judgment. To an
economist, however, since GDP by definition refers to the production of
"goods", it has to be good. (It is generally assumed that utility is
monotonically increasing with goods.) Whether the increase in goods
produced corresponds to an increase in share prices is an entirely
different matter. A share represents a claim on assets which, in turn,
yield a stream of goods (or money which can be exchanged for goods.)
Whether an increase in GDP is beneficial for share prices has
everything to do with where that increase comes from. An increase in
efficiency, whereby the return on existing assets increases, would
probably increase share prices, all else being equal. On the other
hand, the creation of new capital assets would not increase the value
of pre-existing assets if it resulted in the assets being less
After recent discussions on the site about the levered index ETFs, I became curious as to how well these products are tracking their targets. So, using daily data for 9 Nov 2006 through 9 Nov 2007, each 1-day, 2-day, 3- , 4- , 5- , 10- , 15- and 20-day % change was calculated for both the relevant index (either S&P 500 or Nasdaq 100) and the positive and inverse ETFs.
Then the ratio of "ETF % move / index % move" was calculated. For the positive ETFs, the ratio should be ideally 2, and -2 for the inverse products. (The only tricky part is that if the index move is close to zero, the ratio can go to infinity. So, included were only x-day periods where the absolute value of the index move was at least 0.5%.)
Means and sd's were calculated for all the ratios in each x-day period. Below are the results for each of four ETFs:
length in days | mean ETF/index ratio | sd of ratios
1d 1.96 0.40
2d 1.96 0.38
3d 1.97 0.35
4d 1.99 0.28
5d 1.95 0.33
10d 1.94 0.31
15d 1.98 0.29
20d 1.97 0.30
1d -1.98 0.42
2d -1.95 0.45
3d -1.92 0.39
4d -1.97 0.35
5d -1.91 0.34
10d -1.87 0.43
15d -1.84 0.40
20d -1.81 0.42
1d 1.89 0.59
2d 1.91 0.45
3d 1.94 0.42
4d 1.98 0.36
5d 1.95 0.36
10d 1.96 0.38
15d 1.98 0.37
20d 1.99 0.53
1d -1.90 0.55
2d -1.91 0.45
3d -1.89 0.47
4d -1.93 0.38
5d -1.89 0.40
10d -1.94 0.41
15d -1.95 0.32
20d -1.93 0.36
Adi Schnytzer suggests:
Looks fairly good, but a more revealing test might be to regress daily % change in the relevant index (Y) on change in the relevant ETF (X). So we have Y=a+bX and the test would be not only b=0.5 (which is what you have done) but also the joint F test, a=0 and b=1. Why? Because if a is not zero, then there is a bias in the tracking, i.e. either there is an over/under-reaction to large changes in the index or to small changes in the index depending upon the sign of a.
Kim Zussman writes:
While waiting for this week's bombs to start flying, here is regression of (daily return = [c2/c1]-1 )SSO vs SPY since inception of SSO June 2006 (including dividends):
Regression Analysis: SSO versus SPY
The regression equation is
SSO = - 0.000217 + 2.00 SPY
Predictor Coef SE Coef T P
Constant -0.00022 0.00013 -1.64 0.101
SPY 1.99573 0.01630 122.44 0.000
S = 0.00245947 R-Sq = 97.7% R-Sq(adj) = 97.7%
Analysis of Variance
Source DF SS MS F P
Regression 1 0.090682 0.090682 14991.23 0.000
Residual Error 348 0.002105 0.000006
Total 349 0.092787
Obviously a significant slope coefficient, with beta of 2. Notice however that the intercept is almost significantly negative (alpha), suggesting the ETF manufacturer is skimming something every day (probably in the prospectus). Recall that SPY is the SP500 ETF which levies its own (tiny) fee, so you are paying more for the leveraged ETF and might rather consider futures (unless you treasure your sanity).
Adi Schnytzer explains:
What matters (in the way you have run it) is the joint F test a=0 and b=2, and I have no doubt you will be unable to reject it at any reasonable level of significance. Note also that 0.00022 is a teensy number. So it would seem that these are a good buy if one is bullish medium term and doesn't mind staying in the market. Mind you, there are those of us who got into the market just before the latest crash and so, mind or no mind, are in there till the recovery. That's the trouble with futures, unless you can pick your closing date far enough down the track.
Gordon Haave remarks:
Theoretically speaking, levered ETFs work in directional markets. That is, the constant leverage results in buying on up days and selling on down days. So, in certain market periods they work out just fine and are good short term trading vehicles.
Phil McDonnell summarizes:
There are three ways investors in leveraged ETFs incur costs. First, management fees, which are usually lower in non-leveraged ETFs, presumably because there is less juggling to do. Second, the leveraged half of the fund must pay interest at the going margin rate. Even if the fund uses futures or options the interest is implicitly built into the price of the derivative. Third, he constant leverage trap. The 2x funds are designed to give returns which are twice the daily return of the underlying. They rebalance daily, which means they sell low and buy high. In choppy markets and over multiple days this leads to slight under performance relative to the 2x benchmark. Mr. Mabry's study looked at multiple days and found this slight underperformance. In contrast, Dr. Zussman's study found a perfect 2.00 multiplier on a daily basis. That is exactly what they promise, 2x returns for the day. The negative alpha is due to the sum of all three costs above. Not to quibble with Prof. Schnytzer, but .00022 is about 5.5% per year in costs. Most of this is because of the leverage. It is either real or implied interest which must be paid.
I'm trying to collect the following daily data from around 1998 to the present: share price, volume, option prices, volumes and implicit volatilities. I would be prepared to pay if need be and the source is "official." I need these data for stocks traded on Wall Street, though I'm not yet sure which.
Sam Marx replies:
I recommend that you start with the CBOE itself and if you need more, they may be able to assist. Check with the CBOE website as a start.
I've been studying complex variables lately because I find the imaginary very important these days, and I had to brush up on them for one of my daughters.
It led me to consider the imaginary part of the moves during a day or week, and the real part. Consider last week. O/H/L/C:
9/28 1538.20 1545.20 1519.00 1538.10
9/21 1491.80 1552.00 1485.20 1534.40
The real part of the move, from 1534.40 to 1538.10 was 3.70. The low of the week 1519 so there was a -15.40 point imaginary negative part, and the high was 1545.20 so the imaginary positive part was 10.80.
A similar calculation could be done for the day, looking at the amount below the previous close, the amount above the close, and the final move.
We can look at the two points on an Argand like diagram. I claim that the length and the angle between the two lines connecting the negative and positive imaginary could be useful as a predictor. Better yet, the two angles themselves and the real part. Similarities might be useful. Such angles should be quantified , classified, and subjected to prediction and falsification.
Another example. The week of August 17 showed a real move of -1.10 and a negative imaginary of -76.00 and a positive imaginary of 21.50. A small real move but non-negligible imaginary moves.
Laurence Glazier adds:
I'd also be interested in trying volatility as the orthogonal parameter (it is to do with the imagination after all.)
Michael Cook follows up:
I love complex variables - it is one of the most beautiful subjects in mathematics. Everything comes together and illuminates and integrates everything that's gone before in the traditional mathematics curriculum.
I don't understand how you are defining the imaginary part of price moves - can you clarify? I am intrigued!
Alex Castaldo explains:
If I understand Vic correctly, he defines two complex numbers, the AboveMove and the BelowMove:
AboveMove = (c[t]-c[t-1]) + i (h[t]-c[t-1])
BelowMove = (c[t]-c[t-1]) + i (l[t]-c[t-1])
And plot these as two vectors on the Argand diagram. The real parts are the same, but the imaginary parts are different (and always of opposite sign). Next you can get the angles and the lengths.
Adi Schnytzer queries:
Are these the complex components of the change simply because they exceed the bounds of the price at the start and end of the week? If so, why a week and not a day or a month? And perhaps more to the point, can the maths of complex numbers then be used to predict? Analyze the moves?
What comes to be known as being unknowable may or may not be consistent with randomness, rather than, what is unknown. Let unknowns be distinct from the random lest the spirit of inquiry, scientific or even otherwise, be stifled.
Within the unknowables, there are many types of problems (for one example, those suffering data insufficiency) that are not worthy of achieving the classification of belonging to the random. By the way, why does the classification consistent with randomness carry that less worthy connotation?
It is the consistency with randomness that helps insurance companies buy risk, shop floor foremen decide that maintenance shutdown is yet not required, two surfaces are allowed to produce sufficient friction to make the value of work to be non-zero, etc. etc.
A generalized extension is that all cognitive systems including human traders and non traders are able to undertake risk and achieve when they recognize that their willingness to assume the ascertained level of risk is going to produce a draw down, a negative incursion, an unprofitable outcome etc., over a course of several such ventures consistent with randomness. Whenever there is a risk expectation inconsistent with randomness the system would stop and re-evaluate if that is rather an opportunity playing the negative system.
To be consistent with randomness is not useless but useful in specific decisions. It is more valuable than what we do not know or will not know or will not be able to know.
The negation of a negative expected outcome is the way to capture positive outcomes.
If a regression of the results of the trading activity of various participants on an information curve ranked by their seniority would produce an R square that would explain how much of that information seniority explains the trading outcome and thus help explain to those existing at the bottom of the curve that there was no randomness in the impact of information and trading.
Thus, consistent with random is a classification within the larger subset of the knowns rather than unknowns.
Therefore I would surmise that for trading as much as any other human endeavor the idea is to filter the potential impact of consistent with randomness fate and luck away, and focus on effort. Maybe this is what is implied by the saying "fortune favors the brave."
Adi Schnytzer responds:
I'm sorry, Sushil, but I don't buy it. Imagine that you knew every order that was going to be placed when the market opened today and also knew all the financial details of all the brokers and traders and market-makers. And that you knew all of the news of the world and inside info. And, further, that you had a serious computer at your disposal. I suspect that little in the way of randomality would remain. In other words, in a market, I would argue that the "error term" is basically missing variables, many of which won't ever be known to any single trader even if all are known to the aggregate of all analysts. Bottom line: get the info you can and learn really well how to analyze it.
Kim Zussman adds:
The big Wall Street firms, hedge funds, etc., have the most accurate and up-to-date research, and it's hard to imagine we can beat them at that game. But what makes it still a game is that the reaction can be quite hard to predict — even if you could know the future.
For example, Ben's 50bp cut — only now in hindsight do we get to weigh his put (about 50 S&P points). However it was also possible the market could have taken these cuts to mean the risk of unpreventable recession was higher than expected, and they sold. That the prior week was up also threw a false signal — that the market had already priced a big cut.
Perhaps panning for fear in its many disguises, even getting it right only 52% of the time, is the best place to prospect.
Someone invited him into the USA and Customs admitted his entry. Now we get him here and he is subjected to ridicule and verbal abuse. Two wrongs don't make a right! Even President Bush got his jabs in. The US should show we are the better people and not lower ourselves with verbal tirades while he is a guest in America. If his mind is ever to be changed (perhaps it cannot be) America and its leaders need to set a pristine example. I totally disagree with Iran's terriorist ties and abuses of human rights — but we did invite him here.
Nigel Davies writes:
Reminds me of a live televised discussion I once saw between a British and Russian school, back in the days of the USSR. The Brit kids were incredibly obnoxious, using it as an opportunity to lambast the USSR without really knowing what they were talking about. The Soviets kids, on the other hand, were really nice and polite and tried very hard to have a normal civilized conversation. As this was televised live in Russia too, it was quite a coup in demonstrating the superiority of the Soviet child.
This sensitivity might be a games player's thing. In our tournaments and travels we have to get on with a wide range of folk who can be culturally very different. I don't see much sign of it in the Western mainstream.
Eric Blumenschein responds:
I don’t believe appeasement as a geopolitical strategy works. Neville Chamberlain was very polite to Adolf Hitler and WW2 still came around. If I am correct, Ahmadinejad was invited to the UN, not to the USA. If he thought Columbia University was going to fold over like sheep and give him the podium unchallenged, then he was obviously mistaken. Kudos to that university to call him out in a way that would never happen at the UN.
Nigel Davies replies:
Chamberlain tends to be dredged up a lot with such issues, but there is middle ground between appeasement and plain rudeness. The way this has been handled the guy will look like a hero back home for sallying forth into a hostile land. And now if they invite Bush to Iran and he declines, it can be portrayed as cowardice back home. You’ve gotta consider the other guy’s moves.
Adi Schnytzer remarks:
My understanding is he came to visit the UN and as such the US government was forced to let him in. Columbia then decided to invite him and in the spirit of democracy (which was the original excuse for inviting him) they permitted an expression of views contra his own.
Nigel Davies responds:
The issue as I see it is one of strategy. He will soar in the opinion polls back home because of his 'courage' in going to a hostile land and fighting the infidel.
What about just not giving him quite so much attention? If he can't distract the Iranian population with his slanging matches with external enemies, they're more likely to judge him on his actual leadership qualities.
How sad what's happening in Burma (what the world insists on calling Myanmar) and how predictable. In the 1990s I published a paper that modelled the peaceful revolution in Eastern Europe and explained the numbers of demonstrators in different places fairly well. Freedom is a public good and people will only contribute to public goods provision if the price is low enough. Bottom line: If the dictator doesn't respond to demonstrations, they will grow in size over time until the dictatorship becomes non-viable. Why? Because when a soldier's wife or parents of kids are demonstrating, he won't fire on them. Therefore, in order to survive, the regime must put down the peaceful demonstrations brutally. Deng knew this and so we had Tien An Men. The Burmese dictator seems to know it as well. So, is there a solution? Only one: external miltary intervention. Boycotts are useless because Japan and China, to name just two, have been breaking all current boycotts against Burma, and will continue to do so. Now, who's got the guts to try military intervention? No one.
Does anyone know how to use Taqtic? I'm trying to extract options implied volatilities without much luck.
What theory exactly do I test, and how is it put together on the basis of history? In the physical sciences, the answer is, ironically enough, often gut feeling and intuition. Bohr's "crazy" ideas about atoms are an example. That is what makes counting so difficult: What the heck do I count? Statistics and econometrics are fabulous tools, but applying them to forecasting is tough!
Rod Fitzsimmons Frey adds:
I agree that is the crux of the issue. The inductive leap that all scientists must make is a mystery that is not itself explained by science. Francis Bacon, who convinced me to ditch philosophy and take up engineering, hand-waved it away by putting a philosopher-king at the head of the rational, scientific state, with all the other citizens scurrying about gathering data to test the hypotheses that he came up with.
Nigel Davies remarks:
The reason a chess player should practice analysing positions is in order to cultivate intuition. Many players wrongly believe that the idea is to find specific improvements from specific positions, but they rarely get the opportunity to spring their cooks.
I have come to believe that the same role is played by counting for traders, that the main goal should be to cultivate understanding and awareness rather than devise specific trades. And one can find many other examples in difficult human endeavours, such as the importance of kata to the martial artist.
Bill Rafter explains:
The answer to "what to test?" is "everything." You try to break everything down to its smallest components and test each. You keep records and their summaries on everything. If you learn of something new, you have to go back and test everything again using that new method.
Suppose you know with certainty that the market is headed up in the near future. A simple and intuitive strategy would be to buy the high beta stocks. But testing that strategy would prove you wrong. You cannot know that unless you test. Okay, now let's consider the reverse: you know with certainty that the market is headed down. What about selling the highest beta stocks? Test and you will find out.
One of the big topics now is volatility. How do most people define volatility? Are there any other ways to define volatility? Is there any symmetry to the various definitions of volatility? That is, does it work the same way in up days/weeks as it does in down days/weeks? If you define volatility as one-day rates of change, the answer is affirmative. But not so with other definitions.
Most researchers make the mistake of testing their ideas against "the market". Well, the market is just the average. You are not going to find any leading indicators by looking at the average. So let's say that instead of looking at the S&P 500, you do your research on the 10 Sectors. The results are different. So then you drill down a little more to the 24 Industry Groups, and then to the 60+ Industries. If you are "on to something" you will find that the results get better with additional focus. Your universe is the same 500 stocks, but you are no longer averaging to mediocrity. Note that I didn't say this was technical or fundamental research; it's just research rather than intuition.
Most people do research badly. Let me give some examples. (1) One of the major data suppliers (50,000 subscribers) gives its users the ability to construct their own portfolios. That's important, as you may just want to work with stocks of companies with positive cash flow. However a call to the support department of that data supplier will inform you that virtually none of their subscribers make their own portfolios. (2) The research software platform with the highest number of users does not even allow users to construct their own portfolios. They give them pre-constructed portfolios of the S&P, Russell, Dow, etc. Take it or leave it. (3) One of the leading (at least by reputation) institutional and retail providers of fundamental research allows its users to screen stocks on the basis of certain factors. Their screening tool does not work correctly; giving the wrong results. It's been that way for the two years that we have had a comp account. No one has fixed it, most likely because no one has noticed. We noticed, but of course we're not going to tell them.
So if flocks of "counters" or "quants" did poorly in the recent selloff, it may not be because counting or quant research is a flawed concept. It may because the researchers are not giving an honest day's work for their pay. They are pretending to do research. Their version of the scientific method is shoddy at best. But that's okay. To be a consistent winner, you need a supply of losers.
David Lamb writes:
"What to test" brings to mind the passages on counting in Vic and Laurel's books. In one, Artie, Vic's father, was writing on a yellow pad of paper while he was watching handball players. Upon a completion of a point Artie would notate: OTWK (off the wall killer); KW (killer, winner); DW (drive killer); A (ace); AW (angle winner). He was trying to calculate "the chances of winning the next point after runs of winning and losing points of different magnitudes."
And Dr. Rafter's comments on not testing ideas against the market, due to the market's being average, if further demonstrated by Artie's note taking during handball matches. He wasn't watching average players, he was watching a particular "sector" of players. In this case it was the best players.
I have two time series A and B with 120 monthly observations each. I want to test whether A's yearly changes predict B's yearly changes. But there are only 10 non-overlapping years. What is the least horrible method that would use overlapping 12-months changes? I am thinking of a bootstrap but looking around, I found mention of the Generalized Method of Moments (aka Generalized Estimating Equations) which looks complicated. Do readers have other suggestions?
Alex Castaldo replies:
The traditional approach used in the literature (by Shiller among others) is to do a rolling (i.e. overlapping) predictive regression and then correct for the overlap by using Newey-West standard errors (rather than the usual standard errors that regression software normally uses).
Victor and Laurel do not like the Newey-West approach, and the literature has been coming around to their point of view. The problem is that Newey-West is correct asymptotically (that is, as the number of data points goes to infinity) but in these problems we do not have a large amount of data (that is why we are resorting to using overlap). Simulation studies show that in small samples the Newey_West method can be biased.
What is the solution? I don't know; it is an open research problem. There is something called the Hodrick (1992) method which is said to be free from small sample bias. (It is different from the Hansen-Hodrick method). Also you might try to read recent papers on the subject, such as Ang and Bekaert "Stock Return Predictability" (2006) and the references therein.
Adi Schnytzer writes:
'LOMACKINLAY': module to perform Lo-MacKinlay variance ratio test
lomackinlay computes a overlapping variance-ratio test on a
timeseries. The timeseries should be in level form; e.g., to
test that stock returns vary randomly around a constant mean,
you consider the null hypothesis that the log price series is a
random walk with drift. The log price series would then be
given in the varlist. If the assumption of homoskedastic
errors in the process generating the differenced series is not
reasonable, the robust option may be used to calculate a
variance ratio test statistic robust to arbitrary
heteroskedasticity. This is version 1.0.5, corrected for errors
in logic identified by Allin Cottrell.
KW: variance ratio test
KW: random walk
KW: time series
Requires: Stata version 9.2
I was saddened by the death of Luciano Pavarotti, not only because he was the greatest tenor of the past 50 plus years, but because I was fortunate enough to see and hear him at his very best. What makes him the greatest is simple: none of the other tenors is/was capable of singing bel canto and Verdi's Otello. An amazing voice.
A recent broadcast of Rossini's William Tell reminded me of Pavarotti's superb recording. This really puts his greatness into perspective: How many tenors have recorded (or performed) this opera or the main, brutal tenor arias and Otello? To the best of my knowledge no one has done this between Pavarotti and Tamagno! And Tamagno was the first Otello.
Larry Williams adds:
These words are from the wife of one of Pavarotti's competitors and fellow singers, retired now, whose name is legendary in opera circles. Many purists were not wild about Pavarotti — but here's as inside a look as you can get:
Luciano had a beautiful, clear voice, with an excellent technique, and a real connection to the Italian style. He did whatever he wanted. His control went beyond music and he understood his place and mission with no pretensions, unlike, say, Callas. I loved the individuality of his voice. You could never mistake him for anybody except himself. I loved the ease with which he sang and the joy he took in performing. He was an outsize personality that was able to spread the love of opera to many people, and for that the operatic world should be forever grateful. Operatic singers seem to be blander now, more cookie-cutter alike. I wonder if he would have made it in these times.
Eli Zabethan rues:
Despite having a parterre center box at the Met for many years, sadly I never got to hear the Maestro except on CDs. I was always traveling and missed his performances.
The doc who runs the "real age" site at the University of Chicago was once asked whether sex could replace exercise. He opined that if you could have 120 or so orgasms a week, you wouldn't need to do any other exercise! This is a tough one, of course. My wife and I keep getting tired after about 100 and we have to do some rowing to make up the shortfall. (Just kidding - we don't row!)
My collaborator and I have just completed a paper on loss aversion and would be happy to send a copy to anyone who may wish to read it. It is entitled "Painful Regret and Elation at the Track" by Adi Schnytzer and Barbara Luppi.
One interesting result that may mess up a lot of thinking about the relationship between bias and stake is that whereas many relatively small horse betting markets display a favorite-longshot bias, the biggest of them all in terms of pool sizes, Hong Kong, does not — and it once had a reverse bias (favorites were over-backed relative to longshots), but this disappeared in around 1990.
I suspect, and hope to demonstrate sooner rather than later, that this bias is due not to psychology, but to information asymmetry. I have already found (with Barbara Luppi) that Hong Kong bettors do display loss aversion. Now since there is no favorite-longshot bias, the latter can't be due to prospect theory or other such behavioral mess-ups.
Adam Robinson remarks:
Size of stake is relative. It is "in the eyes of the investor." A wealthy individual may view a $1m stake as small, whereas a middle-class investor might view the same stake as enormous.
As described in Fortune's Formula, large, "scientific" gambling syndicates migrated to Hong Kong because of the larger pool of money available, which may at least partially account for persistent anomalies being rigorously exploited away.
Adi Schnytzer replies:
The syndicates have removed the reverse favorite-longshot bias, but are even more loss averse than the regular outsiders!
I would be really grateful for answers to the following …
- When there is a sudden increase in demand for an ETF do the managers have to buy the constituents and thereby push up the price of those so that the EFT's price continues to reflect that of the constituents?
- Is this different from a closed-end fund?
- Is the price of an ETF a function of sudden changes in volume in the same way that the price of a typical share is influenced by sudden changes in volume?
David Wren-Hardin explains:
- An ETF is just a container for a basket of stocks. I'm not sure whom you mean by the manager. If you mean the trust, the trust holds the stocks, but doesn't have to do anything if people buy ETFs on the open market. If people are buying an ETF, though, and a specialist or marketmaker sells them, he will typically hedge with the underlying basket or with the equivalent future. So the buying pressure is passed on. But no one has to buy the underlying.
- I believe it's different, because ETFs can be created and redeemed. You can hand the trust the basket of stocks and get ETFs, or you can break up your ETF and get the basket of stocks back. Potentially, the number of ETFs is limited only by the amount of underlying stock in the open market. Mismatches in demand can lead to impaired rebates of ETFs for those who are short, especially around dividend times. Clearing firms will then sometimes create ETFs to ease the impairment for their customers. Or customers will create ETFs themselves to cover it.
- The short answer is yes. The ETF and its underlying stocks trade as an arb, and changes in demand quickly move back and forth between the two universes.
Kevin Depew adds:
From the iShares Web site:
iShares ETFs are traded like stocks on an exchange where investors buy and sell them just as they would any other publicly traded security. And because iShares ETFs trade like a stock, investors can benefit from features like intraday pricing and trading, the ability to place stop and/or limit orders, and the opportunity to sell iShares ETFs short.
Like other exchange-traded securities, iShares ETFs will trade subject to a bid-ask spread. Spreads may fluctuate in response to supply and demand forces, overall market volatility, and other factors ? in other words, the same factors that influence the prices and spreads of stocks. But unlike stocks, the ETF's creation and redemption process not only helps to minimize the bid-ask spreads, but may also reduce the premiums and discounts that can develop between the iShares ETF market price and the Net Asset Value (NAV).
ETFs are very different from closed-end funds. A closed-end fund's shares are fixed, which is why they frequently trade at a premium or discount to NAV. Although they both trade on an exchange, the ETF shares can be created and redeemed throughout the day.
Also, it's important to get a handle on the composition of ETFs. The Biotech HLDR, with fewer than 20 members, is two-thirds weighted in AMGN and DNA. On the other hand, IBB, with more than 150 members, is only about 12% weighted in AMGN, has no exposure to DNA. That's a significant difference for two funds labeled Biotech. David Wren-Hardin replies:
Kevin makes a great point. HOLDRS were invented by Merrill Lynch, and unlike other ETFs from the Spyder family (SPY, DIA, XLE, et al.), they never rebalance, and their composition does not change unless a company is taken over or goes bankrupt. That's why AMGN and DNA have taken over the BBH, as opposed to IBB, which is rebalanced from time to time.
In addition, it's more costly to create/redeem out of a HOLDR than a SPY, It costs $10.00 per 100 HOLDRS to create or redeem, That works out to a dime a HOLDR share, a pretty hefty premium. SPY, on the other hand, is a flat $3000.00 charge. The minimum creation unit is 50,000 shares, so that's only six cents, 40% cheaper already. But its $3000,00 for 50,000 or 5,000,000, and at that level the fee becomes a much smaller cost.
Also, HOLDRs pay their dividends straight through. If INTC goes ex-dividend, the owner of the SMH gets the dividend the same day as a regular INTC owner, minus a touch since fees are taken out of the dividend stream. Spyder products and their ilk accumulate the dividends over time, and pay it out quarterly.
Art Cooper remarks:
An excellent resource is Russell Wild's Exchange Traded Funds for Dummies.
Dean Parisian remarks:
I bought into the ETF story early on. So far so good with the love of my financial life, RSP, the Rydex S&P Equal Weight ETF, doing what it is supposed to do.
But all is rosy neither in love nor in the financial markets. I'd like to think I was hoodwinked in shares of USO, the United States Oil Fund. Contango has pinned me down so far, can backwardation bail me out? The fund manager said I should have read the prospectus better.
Sometime one doesn't need to count. Here is an example. Once I was considering buying a very illiquid small cap with a huge dividend. I called the CFO and said I was an investor interested in their stock. I asked him why such a dividend? He told me it was a one-off; they were getting rid of cash they didn't need. There was no chance of such a high dividend in the future.
Then I told him his stock was too illiquid anyway. He said they could do something about it. The next morning there were 100,000 shares for sale, instead of the usual 1,000 or 2,000. Needless to say, I never bought this stock. There was no need for counting.
There are plenty of examples like that, but to my knowledge they are always in opaque markets, with few players. I could give similar examples in physical oil or even swaps.
However, when it comes to huge markets like stocks indices, big caps, or WTI (even the oil majors or OPEC don't try to call the price of oil), how can anybody believe that he knows more than the market, that he has an information advantage? In those cases, counting is the only solution.
You could reply that information is not enough; you need to process it. And someone with experience and interest in the markets is able to process information better than the rest of the financial community. This may be true. Still, for the rest of us, with less experience and wits, isn't it safer to do what scientists do when confronted with time series, that is, count?
Besides, nobody can deny the incredible efficiency of the scientific method. Just look at its positive impact on everybody's lives from the Age of Enlightenment. To deprive oneself of such a tool doesn't make sense, even if one is a superior analyst.
Adi Schnytzer replies:
I'd like to present my critique of counting. I assume that we wish to predict where the market is heading, be it in an hour's or a year's time. Counting — as exemplified by Vic and Laurel — generally involves regressing the returns or prices of stocks on one or, at most, two explanatory variables and testing for significance. Thus, using daily data, we may ask was has happened to the S&P500 over the past few years if, on Groundhog Day, the little beast saw its shadow.
We may check what happened the next day or daily for the next month or whatever. The problem is that rarely are other explanatory variables added to the regression and this is OK if those missing variables are uncorrelated with shadow viewing. But, if this does tell us about a cold winter remaining, it affects energy prices and these should appear in the regression since the S&P 500 is clearly affected by energy stocks which are known to be related to the weather. But this is not the real problem.
The real problem is that since the variance of stock price returns is relatively large in all models that have ever been built, any exogenous shock can turn ups into downs and vice versa. And it is precisely exogenous shocks (e.g. what will the Iranians do tomorrow, what will Bush do, what will the big boys do?) that counting and its big brother econometrics cannot handle at all! But the world is full of these. How many of the news items in today's newspaper have you predicted?
To be sure, many turn out to be irrelevant, but not all. And once they have happened, it's too late for the model! Now, there are people who evidently know in advance things that are not in the public domain. The Iranians know what they'll do to the sailors tomorrow, but most of us don't.
Suppose they are each given $1 mil in gold and sent home first class tomorrow after seeing the Iran nuclear sites destroyed tonight. One suspects the market might react and counting will have proven utterly useless. Suppose, on the other hand, the Iranian Navy, having proven that it is superior to the Royal Navy, decides to blockade all oil exports from the Gulf. Hmmmm…
Mar 14, 2007 11:57 AM Reuters News Agency
BERLIN — A brothel in Germany hopes to capitalise on the growing number of pensioners interested in "matinee" s-x by offering them a 50 percent discount during the afternoon hours.
The "Pascha" in the western city of Cologne has introduced reduced rates for s-x sessions for clients aged 66 and above — provided they can prove they are old enough.
"All clients need to do is show us some proof of age," said a spokesman for the brothel's managing director Armin Lobscheid. "A 'normal session' costs 50 euros with us — and we're now paying 50 percent of that for these older guests."
"Life begins at 66!" it says in an advert for its "senior citizens afternoon" next to a picture of a motorcycle rider.
Brothels have Managing Directors? Wow, I bet those MDs at Morgan Stanley feel super-special now.
Gordon Haave replies:
And I'd bet the "talent" are all vice-presidents.
Roger Arnold queries:
How does this get accounted for in GDP? Is it a deflationary indicator or indicative of an increase in productivity? Are there any hedonic adjusters that need to be accounted for? Looks like free market animal spirits are beginning to reawaken in Europe!
George Zachar responds:
Simplistically, I'd say it would show up as a decline in productivity, as seniors will simply shift their s-x purchases to the earlier time slot, with the establishments earning only half their prior revenue per session. GDP would similarly take a hit, and assuming quality remains constant, this would show up as a price decline.
So look for Trichet, at his next press conference, to be asked about stag-de-flation.
Marion Dreyfus explains:
George's explanation is a wrong take entirely. The early bird special is income that would be extra, since these are men who would not be coming in at all, short of lowered price per assignation. These are men who are thus providing income in the slow early afternoon hours when nothing much else is happening. Since the wear and tear on the females is supposedly less (I don't know from experience what the difference is in men from 20s, 30s, to 70s, etc.) than from the younger males that give them a harsher workout, maybe the lower price is fair, since they are not working as hard for the money.
Thus it seems like a win-win, actually. Management is selling product in normally slow hours, and the clientele will be doubly pleased at low-priced but professional action and can get a workout without having to be especially nice to their wives. Or if single, they can feel manly again, despite not being able to date perhaps, at their age or with a paucity of date-objects around. And likely as not, some of the men will use the opportunity to simply talk, as a surrogate for therapy, and bloviate on topics they can't share comfortably with their wives or friends without censorious responses.
I think the whole thing a fit subject for a PhD, actually, when one considers all the ramifications.
Adi Schnytzer adds:
I agree entirely. This is very definitely a topic for a PhD in sexual economics, a field I will be delighted to pioneer if anyone wants me as a supervisor and who isn't scared of fieldwork. Marion's gritty microanalysis makes a lot of sense and an econometric analysis of the wear and tear caused by different age males on working females is long overdue.
Shin (1993) proposed a method to calculate the extent of insider trading in bookmaker markets, with z as the measure of insider trading. He assumed that bookmakers manipulate the supply-side of the market to protect themselves against the risks of adverse selection involving counterparties with proprietary or inside information and against excessive payouts from wins by high odds horses. This article uses a large sample of thoroughbred races (n = 1796) over 4 years on Saturdays at major venues in Melbourne to validate the Shin methodology. Analysis derives a z-measure of insider trading in bookmaker markets of just over 2% (which closely matches results from multiple UK analyses). The surprise is that an almost identical value (p < 0.001) is obtained for z in the Tote market which does not have a supply side and so should have a zero value of z. It seems that factors driving a nonzero value of z arise in the demand side of wagering markets and not the supply side as assumed. This conclusion illustrates the risks associated with what Fama (1991, p. 1575) termed 'the joint hypothesis problem' where the conclusions of a mis-specified market model are likely to be invalid.
I have published an empirical refutation of Shin and can supply it to anyone interested. But more to the point, if the extent of insider trading in horse betting markets is really 2% (2% of what? turnover?) then insider trading is a trivial and unimportant phenomenon. Now, since such trading is legal in horse betting markets, it would be expected to be even less in markets where it is illegal. This is a load on rubbish. Read Shin's paper and think about his assumptions. Then decide whether you think he ever saw either end of a horse! He's a brilliant economic theorist, but knows little about betting markets. Les Colemen's work is interesting and he and I are planning to hunt down insiders in the stock market when I take a sabbatical in Melbourne in 2009.
On a television channel dedicated to religious topics, a clip of Daily Spec contributor Larry Williams appeared within a segment on Bible Codes. Larry, a journalism graduate, dug up information about Moses and wrote a whole book on the material he found. I was surprised to learn of Larry in this context, since he is best known for other marvelous achievements.
The Bible, according to cryptographers, is replete with predictions written centuries ago and found to be accurate by the events unfolding in our time.
Kudos to Larry for investing his time and expertise, his flair for language, in this remarkable project.
Nigel Davies writes:
This is highly analogous to searching for Codes within the markets, with many of the same problems applying. I understand that one of the bones of contention is the asking of the questions and that sceptics have found apparently similar Codes in Moby Dick and elsewhere.
One of my acquaintances ended up becoming ultra-religious on the strength of Bible Codes. I guess he might have wanted them to be there or he'd have tried to falsify them before donning the black hat.
Such proof would also contradict one of the major philosophical ideas of Judeo-Christianity in that any 'struggle with G-d' would essentially be over once 'proof' were discovered. I guess they figured it was more important to get bums on seats.
Adi Schnytzer replies:
There have been (unsuccessful) attempts by statisticians (but what would they know, right?) to refute the Codes, but I don't want to spoil Nigel's day with facts. If he really cared about this beyond heaping contumely on it, a little Googling would go a long way.
Gordon Haave responds:
Please! Let's not get into fantasy. Numerous statisticians have shown what a fraud the Bible Code is. But, even if you want to go back and forth between competing websites, all you need to know is that there have been no "predictions" at all. After certain things happen, the Bible Coders go back and data-mine the bible to see if the event was predicted. When they predict something unlikely in advance (not a vague "there will be trouble between Israel and Palestine") then get back to me.
Adi Schnytzer retorts:
Well, I guess I'm going to have to blind you with facts! The paper that studied the Codes was written by Doron Witztum, Eliyahu Rips, and Yoav Rosenberg and is entitled Equidistant Letter Sequences in the Book of Genesis. It was published in the very respectable journal Statistical Science in 1994. An attempted rebuttal was published by Brendan McKay, Dror Bar-Natan, Maya Bar-Hillel, and Gil Kalai in 1999. See Ralph Greenberg's site for links. For myself, this will do:
"The present work, represents serious research carried out by serious investigators. Since the interpretation of the phenomenon in question is enigmatic and controversial, one may want to demand a level of statistical significance beyond what would he demanded for more routine conclusions… The results obtained are sufficiently striking to deserve a wider audience and to encourage further study."
H. Furstenberg, the Hebrew University
I. Piatetski-Shapiro, Yale University
D. Kazhdan, Harvard University
J. Bernstein, Harvard University"
Laurent Glazier remarks:
I am not sure what this particular example might mean, but because a Canadian academic has succeeded in finding similar patterns in the text of Moby Dick it has been widely assumed that this invalidates all Bible Code findings. Similarly the artificial construction of small scale crop circles in England has led people to conclude that all such formations, including those on a huge scale, are artificial. These conclusions are appealing, and may be true, but are not logical.
The Bible Code discovery I found most intruiging was that the encoded occurrences of the Hebrew names for tree species are nearly all found hidden in the verses describing the Garden of Eden. Designing statistical tests to prove the likelihood or otherwise of such patterns, found in context, has caused great difficulty in the past to fine minds, largely because preconceptions can interfere in setting up the tests.
Testing for geometric patterns in star formations is another matter, especially Mark Vidler's unpublished discovery of the clustering of bright stars at multiples of 10 degrees from Regulas, as seen from Earth. Another issue entirely would be looking for a cause of any established patterns.
Kim Zussman adds:
The movie "Pi" (3.14159…) is about a mathematician who suffers from severe migraine and mental illness, and is deciphering hidden numerical codes like Fibonacci series in The Kabbalah. He is pursued by a rabbi who is also a mathematician.
G-d's commandment is to index: shouldering the risk of capitalism while not attempting to gamble or covet other people's wives is written in the WSJ between the mutual fund quotes.
There are several things going on down under I thought Daily Spec readers might enjoy hearing about…
The first of course is the incredibly strong performance of the stock market. This is due in part to the fact that all Australians must pitch in part of their earnings to an investment program. It is privately managed, meaning a huge amount of money comes into their market month after month after month and keeps driving prices higher. Also, for the most part, their stocks are undervalued versus other stock markets in the world.
But all is not that well here…
At dinner the other night a friend told me he had a knee operation. I said, "Well that didn't cost anything; that must've been nice." His reply was, "It cost me quite a bit. I had to pay cash because in the publicly supported medical system it would've taken a couple of years to get an appointment." I confirmed that with a jogging buddy today, who said the same thing. There is a fast track for emergencies, for instance if you're in a car wreck. But for any significant discretionary operation you will wait a long time
His wife added that since there is no cost to go to a doctor, the doctors are flooded, as there is no disincentive to seek care.
This was the one that got me: After employing someone for 12 months it is mandatory to give him a one-month vacation. I've never had a one-month vacation in my life. Who would want one? You couldn't work. Nonetheless, when the worker gets that vacation he gets it with pay plus 19%. In other words, he earns 119% of his base salary on his off month. The thinking of the labor union leaders is that the vacation will cost him more money than staying at home. So he is entitled to more.
One of the big issues in the upcoming election will be free dental care. My dentist here doesn't do anything for free. I don't blame him, and we both wonder: who's going to pay for it? Obviously, it will be paid in some form of higher taxation, something politicians here and everywhere seem to enjoy. There is a 40% tax on wine made here, which means I can buy the same bottle of wine cheaper in America.
I could go on and on with other examples of the difficulty of running a business here.
It is a lovely country with great people and great future, but it seems to have been overrun by socialists and labor union leaders, which certainly will have an impact on the economy at some point.
Adi Schnytzer writes:
And just imagine, there are millions of people all over the world just wishing they could get a visa for Australia. Go figure!
Larry Williams replies:
Sure! Can't get fired for stealing, get a month's paid vacation at 119% of base after 12 months of lounging around, free stuff! Ya, man let's go!
My point is that business people have read Atlas Shrugged and see it taking place here.
Adi Schnytzer adds:
Larry, how many people die for lack of operations, medicines, and doctors in Australia? What is the per capita number in the U.S.? No health system is perfect and no economic system is perfect and, yes, there are some stupid taxes, but how many homeless have you tripped over lately? If you want to compare Australia with the U.S's, the former being too socialistic for some tastes, why not do it properly?
Larry Williams replies:
I see about 100 homeless people here every day. Some are real characters to talk with. Come on a walkabout with me. They are flagrant and stink like heck but are courteous. They are all over here, on every major street. I certainly see more homeless people here than in San Diego, a city very similar to Sydney.
I do not know how many people die for lack of operations, but I suspect it's the same as in the U.S or U.K.
If an employee is caught stealing from you, all you can do is write a letter. It is not until the third time you can fire him.
Virtually every older Aussie I know vents these same complaints. I am just the reporter here!
I suggest that learning to play a game (poker, backgammon, chess, checkers or go) might teach far more than studying game theory. The big problem with drawing boards is that there's no opponent, so ideas are never subject to quite the same level of criticism, and they do not have to be quite as relevant to the very serious matter of winning.
Adi Schnytzer comments:
Game theory is not about drawing boards. People do not study game theory to help them in their game playing, believe it or not. They study it in order to understand the process of more perceived importance than board games.
Nigel Davies adds:
Please excuse my ignorance, I am a mere player. So what exactly is 'game theory' good for? And I'm talking a usable practical application that doesn't include getting a salary for teaching it to others. Please be very specific as I am very primitive.
Adi Schnytzer replies:
I recently posted the following note, which will introduce you to game theory and comment on its uses. Since it's written by the masters, it should help you out. There's nothing I can add to their wisdom.
Bob Aumann's Nobel Prize Lecture ("War and Peace") and his piece "On the State of the Art in Game Theory" are both worth reading … He also has a piece called "Consciousness," which is rather nice. These may all be downloaded here … In my view, the least (not non-mathematical) and most intuitive text available is Luce and Raiffa.
Nigel Davies adds:
There is still the problem of practical application which is what I've been going on about from the start.
In 'A Beautiful Mind,' we see that Nash figures that he and his friends should not go for the blonde because they will block each other, and somehow or other this later got him a Nobel Prize. However, it seems that Nash thought up his 'strategy' without any knowledge of the game, and from all indications, he was a virgin at the time. This sums it up - he thought he could win without any knowledge of how the pieces moved.
In a previous discussion, I brought up a similar error by a mathematician who gave a figure on the number of possible chess games. It's obvious to anyone who actually plays and knows the rules that the number has to be infinite. The guy was so arrogant and/or naive that he didn't bother to learn the rules properly before coming up with his number.
Frankly, I have the same problem with Robart Aumann's paper. It's all very well theorizing about peace, but has he actually tried to apply this? I suggest that without knowing the territory, too many assumptions will be wrong.
If it's any consolation, it seems that Lasker had a similar problem with Einstein and the theory of relativity. In Einstein's foreword to Hannak's biography of Lasker, you see that Lasker thought that there was no justification for claiming that the velocity of light in a vacuum would be infinite, unless this had been verified in practice.
This, incidentally, was one of my few moments of agreement with the Elizabethan ghost.
Ross Miller comments:
It is worth noting that the "real" John Nash never did this, just the John Nash invented by a screenwriter who got to write this movie based on his ability to write Batman movie screenplays. The example in the movie is not a Nash equilibrium. In a Nash equilibrium, you do the best you can taking everyone else's actions as given and ignoring responses to your own actions. If everyone else goes for the inferior females, you make a beeline for the superior one in a Nash equilibrium. As stated, this game has no Nash equilibrium if everyone believes that multiple hits on the same target generates no payoff from that target, but a single hit will. Nigel is correct in pointing out that solutions to this game require thinking beyond the game theoretic formalisms.
The best reason for the Nash equilibrium to get a Nobel Prize was that it facilitated the Arrow-Debreu work on a competitive equilibrium. It was because his equilibrium is an intrinsically competitive (and not collusive) concept. The screenwriter is not to be entirely faulted since the book from which the movie was based is full of technical errors and misstatements. Of course, technical correctness does not make for bestsellers and the average moviegoer is never going to understand what Nash did anyway, nor is much of anyone for that matter.
Peter Grieve offers:
My take on game theory (based on long but elementary study) is that:
1. It's not very useful in sequential games like chess, poker, etc. In chess it might help a computer make decisions based on a look ahead tree if the branches have some evaluation number. Game theory can't, of course, actually generate these evaluations, and they are quite important.
2. It's not very useful in games in which anyone has any experience. The simplifying assumptions are too great. Once in a while it could illuminate a connection that would not otherwise be obvious. But as far as selecting a detailed strategy in a real world, complex game, it would be madness to rely on game theory.
Game theory is a lot like the rest of applied mathematics. It's really strong on the simple stuff, things where its many simplifying assumptions are valid. It can act as an initial guide when there is no experience in an area. Occasionally it can suggest something new in known areas (which must then be extensively tested by experience, and often found lacking).
The problems arise when academic folks (who mostly talk to each other) get inflated ideas about the real world strength of their ideas.
An example of a situation where game theory would be valuable is the following. Suppose you where playing a game of Rock-Scissors-Paper with a really smart, vastly superior opponent who knew a lot about your mind. How can you at least break even in this game? Game theory tells us the answer. Roll a die, if it comes up 1-2, choose Rock, if 3-4, Paper, if 5-6, Scissors (roll the die in secret, of course). You can even tell the opponent that you will use this selection method, and it doesn't help him beat you (unless he can guess the way the dice will come up). He can use this same strategy on you, making sure he breaks even, and the game is at equilibrium. This seems intuitively obvious, but what if Rock breaks Scissors wins double? What sort of die should one roll then? Game theory will tell us.
Of course if Nigel reads this, he will immediately think of several possible strategies to bamboozle game theoretically inclined, mammoth brained opponents in Rock-Scissors-Paper. But if he is to win anything, he will have to bluff the opponent out of using the above strategy (perhaps by artfully convincing the opponent that his (Nigel's) mind is "primitive").
During the Cold War, everyone wanted to hire Air Force generals with lots of nuclear war experience, but there were none (General Ripper was long gone). The think tanks used some game theory. Thank goodness we never found out how valuable it was.
Adi Schnytzer comments:
Three points only:
1. Game Theory was used successfully to win a battle in the Pacific during WW2, though I don't have the details on hand.
2. Without game theory, a simple dumb computer would never have beaten the World Chess Champion!
3. Aumann's insights on war are useful, but make sense only to those living somewhere nuts like the Middle East. Those in cocoons who believe that the problem rests in a failure to love their fellow man (read: "Liberal Europe At Large") will never understand.
Nigel Davies adds:
Without game theory, a simple dumb computer would never have beaten the World Chess Champion!
How do you come to the conclusion that 'game theory' should take the credit? Why not Faraday, Edison or Graham Bell? As far as I know, none of the programmers studied game theory, but there were a few chess players on the Deep Blue team. If game theorists are claiming this, then by the same token shouldn't one be able to claim that the big bang was only possible thanks to physics professors? Now that would really be a feather in their cap - they might get two Nobel prizes!
Aumann's insights on war are useful, but make sense only to those living somewhere nuts like the Middle East. Those in cocoons who believe that the problem rests in a failure to love their fellow man (read: "Liberal Europe At Large") will never understand.
Ghengis Khan would probably have sorted the Middle East out in no time - old Ghengis was a good player in his day. OK, I guess you're going to claim that the Mongolian hordes had their own 'game theory' which enabled them to win their battles etc. So the academics can take the credit after all …
Game Theory was used successfully to win a battle in the Pacific during WW2, though I don't have the details on hand.
As should be clear from the above, I think specifics are needed in order to see why game theorists are taking credit for this one and why it's good shooting with one's howitzers, or even luck. And how many battles were lost by the way? Or weren't these retrospectively scored?
Stefan Jovanovich adds:
There are only two reasons why the Americans had any chance in the Battle of Midway:
(1) Admiral Nimitz trusted his Navy code breakers and their analysis of the limited decryptions they had under Commander Rochefort. By translating messages and studying operational patterns, the code breakers predicted future Japanese operations. Relying on those predictions, Nimitz sent to sea the only three American carriers he had at Pearl Harbor and positioned them on the flank of the predicted Japanese line of attack.
(2) When an American scout plane sighted the Japanese fleet, Admiral Spruance put all of the American planes in the air for an all-out attack. In terms of conventional doctrine at the time, this was a highly suspect move, and its initial results were terrible. The Japanese fleet's air cover fighters and anti-aircraft gunnery annihilated the attacks by the Marine Corps scout bombers, Navy torpedo bombers, and U.S. Army Air Force torpedo-carrying "Marauder" bombers. The Army Air Force "Flying Fortress" high altitude bombers also failed but did not suffer any losses. The next attack by Navy torpedo bombers was literally wiped out; there were no planes and only one pilot survived. Only the last attack - by Navy dive bombers - succeeded.
If "game theory" includes cryptographic analysis, then its contribution to the Pacific War effort was, indeed, invaluable; but it required the willingness of Admiral Spruance to go "all in."
Adi Schnytzer replies:
Thanks Stefan. No, it wasn't the cryptography I had in mind. According to Careers in Mathematics,
Game theory, a part of operations research, was used to select a strategy for the Battle of Midway, a turning point in the Pacific arena during World War II. The U.S. Navy was on one side of Midway Island, and the Japanese Navy on the other. We calculated our probability of winning in the four cases of our going north of the island or south of it, and the same for the Japanese. Game theory was then used to select the winning strategy.
As I recall, breaking the codes told the U.S. where the Japanese fleet was going, and game theory told them how to place their limited resources optimally. But since this isn't nearly as important as winning a chess game, why are we bothering?
The US is six-for-six for the prize so farr, which means the Literature prize will go the the North Korean press release describing the "happiness caused by the bomb test."
Economics goes to "expectations-weighted Phillips Curve" dude. An odd choice, since a Phillips by any other name still a Phillips… Once you introduce expectations into economics you get its bastard child: finance!
Gregory van Kipnis replies:
The 'new' Phelps isn't like the one we remember, the 'old' Phelps, who wrongly theorized that inflation was inversely related to unemployment.
I especially like the way Phelps balances Rawlsian theories of social justice for the least advantaged with the injustice of depriving entrepreneurial types of their need for self-expression. Should a society be limited by serving the needs of the least at the expense of the best, or does it not follow that by bringing out the best from the best, all of society, including the least, benefit?
Prof. Adi Schnytzer adds:
Does fear in sport , as in the market put your opponent in the drivers seat? or does it depend on the personality of the warrior / trader, as to how this will effect the final outcome? I forward to you an article from Buenos Aries:
We hate Hewitt, says Nalbandian — From correspondents in Buenos Aires. September 20, 2006.
FORMER Wimbledon finalist David Nalbandian stirred the seeds of animosity ahead of the Davis Cup semi-final clash between Argentina and Australia by claiming his teammates don't like Lleyton Hewitt.
Hewitt has been at the centre of several spats with Argentina over the past few years and the ill feeling has grown to such an extent that he has reportedly employed two Australian bodyguards for the trip to Buenos Aires this week.
"No-one is friends with Hewitt and he does not worry me at all," Nalbandian, who was beaten convincingly by Hewitt in the 2002 final at the All England Club, said.
"We won last year over there (4-1 in Sydney) and now we will win here."
There had been talk that Hewitt would pull out over security fears but Nalbandian thinks his presence in the team will make little difference.
"With Hewitt, this tie will be a little more difficult but that doesn't change much really," added the world No.4.
"Whichever team comes here to play knows that at home, we are very strong, and now we have a great chance to make the final."
Argentina captain Alberto Mancini echoed Nalbandian's sentiments, claiming the circus surrounding Hewitt's appearance would not distract his team.
"The issue of Hewitt and his security (which includes six local security personnel) is something that everyone is talking about but it's not something our team is worrying about," he said.
"We respect Hewitt but my players can beat him."
Earlier, Argentina's Jose Acasuso blasted Hewitt for overreacting to the perceived animosity he will encounter.
"Hewitt seems to think that he's come to Iraq, that they are going to plant a bomb," Acasuso said.
"But we're not bothered because this is the circus that he wanted to set up. Nothing's going to happen and we shouldn't pay any attention to it.
"We're just worried about Argentina. Whether Hewitt has one bodyguard or 500 bodyguards, that's up to him."
Former world No.1 Hewitt, who was named alongside Mark Philippoussis and doubles specialists Wayne Arthurs and Paul Hanley for the tie, had previously expressed reservations about playing in the tie because of security concerns.
The bad blood between Hewitt and Argentina began at last year's Australian Open when Juan Ignacio Chela took exception to the Australian's histrionics and spat at him as they changed ends in their third round match, copping a fine for unsportsmanlike conduct as a result.
John O'Sullivan answers:
Yes and no, if we take cricket as the sport in case. There are few more exciting sporting spectacles than a contest between a hostile fast bowler and an aggressive batsman in international test cricket. A truly fast bowler is capable of delivering the 5 1/2 oz hard leather ball at speeds approaching 100mph. Over a 22 yd pitch that takes just over 0.5 seconds to arrive at the batsman. The batsman must select and execute his shot in that very short interval. Remember that in cricket, it is perfectly legitimate for a fast bowler to deliver a "bouncer": a short pitched delivery aimed at the batsman's chest, throat or head. Obviously, the aim is to intimidate and unsettle the batsman. Often a simple, straight ball aimed at the wicket will follow. This is a classic fast bowling sucker punch - a scared batsman will fluff the shot, and get bowled out.
From personal experience I know that no other sporting experience produces an adrenaline surge like going in to bat against a really fast bowler. The ball may be traveling so quickly that you can barely see it. In the amateur game the pitch may well be uneven, leading to dangerously unpredictable bounce. As a batsman you know that when the bowler releases the ball it may well be flying toward your face or ribs at 90mph half a second later. If you get your shot wrong, you'll get hit, and it will hurt like heck.
The fear causes a massive adrenaline rush. As a batsman you must harness that rush, as it sharpens your perception and quickens reactions. You must concentrate totally and absolutely on the ball in the bowler's hand as he runs up. And you must try to play freely and naturally.
When an aggressive batsman faces a hostile fast bowler, they will seek to dominate each other. The bowler will bowl bouncers to intimate the batsman. The batsman may "hook" those bouncers. The hook shot requires tremendous nerve and skill. The batsman doesn't attempt to duck or swerve the ball, but stands in line, allowing it to approach his face. He then plays a cross bat shot hitting the ball high, behind and to the right ("to leg") just as the ball comes on to his face. If he can execute this shot correctly he will score heavily, and dominate the bowler. If not, the bowler dominates, and the batsman may be hit in the face.
All batsmen where padded gloves, pads on the legs and a "box" to protect the groin. In recent years helmets have become common place. Less confident batsmen may add arm guards, thigh pads and chest guards.
The more heavily padded a batsman is, the less free his movement. Helmets can hinder vision. So the more protection a batsman has, the less able he is to apply technique to deal with the threat.
If a batsman is confident in his own abilities, he won't hinder his movement with too much protective padding. Market analogy: confident traders will not use stops.
A great batsman must have natural ability: eagle eyesight, quick reflexes, strength and nerves. Market analogy: a great trader must be a quick & confident thinker and have iron nerves.
A great batsman must practice endlessly. He must have a complete array of shots that he can select instantly and instinctively in response to the bowler. One can only learn by doing over and over again. Market analogy: a great trader's instinctive reactions can only be honed by being in the market in all conditions.
Cricket is a team sport, but a lopsided one: the batsman is on his own against the 11 men of the fielding side - the bowler, the fielding captain, and the fielder are all conspiring to get him out. The batsman stays alive and prospers by wit, skill and judgment. Market analogy: the trader relies on his wits to survive against the combined force of the market.
One mistake, and the batsman is a failure. To be a success, he must get it right over and over again. One error, and the batsman gives a catch to the fielding side, or he is run out. Or he is bowled out. To build a big innings, to score heavily, maybe a century, he must get it right over and over again. He might face hundreds of deliveries from several bowlers over the course of several hours, with the fielding side constantly conspiring against him, in order to build a big score. His concentration must be unremitting, and application of technique fluent and correct. One error and he is gone. Market analogy: the successful trader must constantly make correct judgments on placing, pulling and sizing orders and positions. One mistake and he is underwater, maybe even wiped out.
Craig Mee responds:
I believe the great Vivian Richards who averaged 50 runs every time he walking out onto the pitch with bat in hand, and faced some of the fastest bowlers ever to play the game, never wore a helmet in international cricket. Maybe the answer lies here, in this one individual, though I believe he may have been two standard deviations away from the mean, as the downside of getting hit, well for us mere mortals, is 'there goes the account.!'
Adi Schnytzer comments:
Although, to be fair, the nastiest fast bowlers in Richard's era were on his team! Donald Bradman, the greatest batsman that ever lived, and by a fair stretch, claimed in an interview that he was only ever hit once on the body by a ball! He wore no body protection to speak of and evidently needed none. Even the fast bowlers were scared of him! I once saw Richards make 200 in a Test match at the MCG and watching that innings I could not help wondering how anybody could ever make 300 in a Test in one day (Bradman at Leeds way before my time). Watching his interviews, one gets the feeling that the man had no need for adrenalin at all.
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