It is as commander of the British Eighth Army in the Western desert during World War 2, and later as commander of Allied ground forces in Operation Overlord, the invasion of Normandy, that Bernard (‘Monty’) Montgomery is perhaps best known. What is less well known is that he loved to wager on almost anything. One of the best documented examples was Monty’s bet with Walter Bedell (‘Beetle’) Smith, later Chief of Staff of US General Dwight (‘Ike’) Eisenhower, that the Eighth Army would capture the strategically important Tunisian port of Sfax by April 15th, 1943. The terms of the wager were that the Americans would, if he was successful, deliver him a B-17 Flying Fortress, complete with an American crew. Sfax fell on April 10 and Montgomery cabled Eisenhower immediately, demanding full and immediate payment. Montgomery got the Flying Fortress but not before receiving a stinging dressing down from the Chief of the Imperial General Staff, General Alan Brooke (later Viscount Alanbrooke). So we learn from Alanbrooke’s diary entry for June 3rd, 1943. Smith is reported to have later remarked to Monty: “You may be great to serve under, difficult to serve alongside, but you sure are hell to serve over.” Still, the days of the wager were not over, as evidenced by the £5 wager struck between Montgomery and Eisenhower about the timing of the end of the war. Eisenhower describes the bet in his memoirs as follows: “I was personally so confident that we could launch ‘Overlord’ strongly and promptly in the spring of 1944 that I bet Montgomery five pounds that we would end the war by Christmas of that year. I lost the bet.” Now one of the potential pitfalls of betting comes about when one party to the wager has inside information that the other does not, or when one of the parties can influence the outcome in a way the other is unaware of. So could this £5 bet have influenced the timing or perhaps even the outcome of the Second World War? Can a man be so obsessed with winning a wager that he would be prepared to lose a war? Of course not! We are talking the real world here. As Eisenhower himself relates, he lost the bet because he failed to take account of two things. “The first of these”, he writes, “was the late date of the assault across the Channel, and second, was that I did not conceive that Hitler would continue fighting after we had once lined up the Allied Armies on the banks of the Rhine.” No, a £5 wager had absolutely no impact whatsoever on the conclusion of the war. Now make it a Flying Fortress and we might be talking!
“October”, wrote Mark Twain, “is one of the peculiarly dangerous months to speculate in stocks. The others are July, January, September, April, November, May, March, June, December, August and February.”
Yes, speculation in stocks is always risky. But are there some times of the year when it more advisable to buy or sell than other times? Some people think so and the classic saying, “Sell in May, go away, buy again on St. Leger Day” is one of the more famous aphorisms encapsulating this advice.
For those totally unacquainted with affairs of the turf, ‘St. Leger Day’ is the day on which the final, oldest and longest classic race of the annual calendar (the St. Leger Stakes) is run, traditionally the second Saturday in September. A variant of this adage is the ‘Halloween indicator’, which holds the same advice with regard to selling in May, but advocates holding on for a few weeks after St. Leger Day, till about October 31st, before buying again.
The assumption underlying both strategies is that stocks tend to underperform during the summer months. But is this true? Ben Jacobsen and Sven Bouman, writing in the prestigious American Economic Review, in 2002, certainly believe so – “… we find this inherited wisdom to be true in 36 of the 37 developed and emerging markets studied in our sample.
The ‘Sell in May’ effect tends to be particularly strong in European countries and robust over time. Sample evidence, for instance, shows that in the UK the effect has been noticeable since 1694”. Note that – since 1694! That was the year that the Bank of England was formed. Also the year (incidentally) that the great French philosopher, writer and dramatist Voltaire was born. So what about it? Is early autumn a good buy to buy? Well, it all depends on what you take to be strong evidence, and the academic jury really is out on this one.
This doesn’t stop the financial press trotting out the famous dictum whenever events seem to support it. Take May 2006, for example, when the US S&P index declined by 3 per cent and the Japanese Nikkei 225 by nearly 9 per cent. Forbes magazine duly declared on June 6th that the “axiom ‘sell in May and go away’ worked like a charm”. The Financial Times noted on July 14th that “this year [2006] ‘sell in May and go away’ would have been a great strategy”. The Economist on May 25th went further, arguing that the ‘sell in May’ adage was “an explanation of why investors the world over have been selling shares since May 11th”.
So what would have happened if you had sold your shares on May 1st, 2009? On that date the FTSE closed at 4,243. By St. Leger week the FTSE had broken the 5,000 barrier and has edged up further since, to stand at over 5,100 by the end of September. So much for what you should, or should not have done in May!
Is October still a good time to buy? Well, I think Mark Twain sort of had it right all along.
Links:
There have been a number of fascinating articles on election forecasting published in ‘Foresight’, the magazine of the International Institute of Forecasters. Of these, perhaps one of the most accessible is that associated with the name of Professor Allan J. Lichtman. Lichtman’s unique approach to political forecasting revolves around what he terms the ‘The Thirteen Keys to the White House’, a historically based model that is both simple and seemingly successful. The theory underpinning the “Keys” is that the result of a US Presidential election turns almost entirely on the performance of the party controlling the White House. There are 13 keys, each of which Lichtman assesses as either true or false. When five or fewer keys are false, the candidate of the incumbent party will win. When six or more are false, the candidate of the challenging party will win. Key 1 is ‘Party mandate’ (“After the midterm elections, the incumbent party holds more seats in the US House of Representatives than it did after the previous midterm elections”). In fact, the party of the incumbent President (the Republicans) lost seats in 2006, so this is FALSE. Key 2 is ‘Contest’ (“There is no serious contest for the incumbent party nomination”). I don’t think Mitt Romney would agree with this. I would mark this as FALSE. Key 3 is ‘Incumbency’ (“The incumbent party candidate is the sitting President”). FALSE. Key 4 is ‘Third Party’ (“There is no significant third-party or independent campaign”). With all due respect to Ralph Nader and Bob Barr, I think we can say TRUE to this. Key 5 is ‘Short-term economy’ (“The economy is not in recession during the election campaign”). I think we can reasonably assign this to the FALSE column. Key 6 is ‘Long-term economy’ (Real per capita economic growth during the term equals or exceeds mean growth during the previous two terms.) FALSE. Key 7 is ‘Policy Change’ (“The incumbent administration effects major changes in national policy”). Economic crisis measures apart, I think it’s reasonable to mark this as FALSE. Key 8 is ‘Social Unrest’ (“There is no sustained social unrest during the term”). TRUE. Key 9 is ‘Scandal’ (“The incumbent administration is untainted by major scandal”). Some scandalous things have happened under Bush’s watch, to be sure, but we can mark this in the sense meant as broadly TRUE. Key 10 is ‘Foreign/military failure’ (“The incumbent administration suffers no major failure in foreign or military affairs”). FALSE, in spades. Key 11 is ‘Foreign/military success’ (“The incumbent administration achieves a major success in foreign or military affairs”). Well, the ‘surge’ had some success, to the benefit of McCain. Let’s be generous to the Republicans and tick it in the TRUE column. Key 12 is ‘Incumbent charisma’ (“The incumbent-party candidate is charismatic or a national hero”). McCain was shot down during the Vietnam war, captured and hailed as a war hero. Let’s be generous again and mark him down as a TRUE national hero. Key 13 is ‘Challenger charisma’ (“The incumbent-party candidate is not charismatic or a national hero”). Obama not charismatic? FALSE. Of course, it’s possible to disagree with a couple of the way I’ve marked these keys but whichever way you cut it, this adds up to six or more FALSE statements, which in turn adds up to a win for the Democrats. And so another success is chalked up for Professor Lichtman and his famous keys! And for the Betfair markets which never once wavered in pointing to a Democratic victory.
Links:
http://forecasters.org/foresight/
On 24 May, 2000, during a meeting held at the College de France in Paris, the challenge was made. A million dollars would be paid to anyone offering a proof or a counterexample to any of seven mathematical conjectures. The offer was made by Arthur Jaffe, co-founder (with Landon Clay) of the Clay Mathematics Institute. In the same year, British publisher Tony Faber offered a million dollars to anyone who could prove that every even integer greater than 2 can be expressed as the sum of two (not necessarily different) prime numbers, e.g. 74 can be expressed as the sum of the prime numbers 31 and 43. This is the ‘Goldbach Conjecture’, first formally proposed in a letter dated 7 June, 1742, from Prussian mathematician Christian Goldbach to Leonhard Euler. The purpose of the Faber offer was to publicize ‘Uncle Petros and Goldbach’s Conjecture’, a novel on the Faber and Faber publishing list by Apostolos Doxiadis. What is especially interesting about all these million dollar prizes is that they have the potential to incentivize and focus the minds of a diverse set of amateur and professional mathematicians around the world. In other words, to tap into the wisdom of the crowd. So nine years later, where are we with Goldbach and his primes? Faber and Faber have sold quite a few books. That much is known and could have been predicted. It has also been shown by computer that Goldbach’s Conjecture is true for all even numbers up to 1,200,000,000,000,000,000. Even so, we are no closer to a formal proof than we were when the prize was announced. How about the conjectures identified by the Clay Mathematics Institute? Better news here. Of the seven one has been proved, the one that states in simple terms that ‘a sphere is a sphere is a sphere’, i.e. no matter what you do to it other than tearing it (punch it, pinch it, kick it, twist it, squeeze it, squash it, poke it, inflate it, deflate it), it remains a sphere, even when the surface of the sphere is in three dimensions (the surface of an ordinary sphere is two-dimensional, of course, though it encloses a three-dimensional volume). Put more rigorously, the conjecture can be expressed as ‘Every simple connected, compact three-dimensional manifold (without a boundary) is a three-dimensional sphere.’ Got it? Anyway, this is the Poincare conjecture, named in honour of French polymath Jules Henri Poincare, and proved in 2003 by Grigori Perelman, though he’s declared that he doesn’t want the prize. The other six conjectures remain unresolved. For the record, these relate to the Hodge Conjecture, the Birch and Swinnerton-Dyer Conjecture, the Riemann Hypothesis, Yang-Mills Theory, the Navier-Stokes Equations and the P versus NP Problem. So here we have a market the size of the world and a total of 8 million dollars worth of liquidity, and only one of the conjectures has been proved, and that by someone who shuns the crowd and hasn’t even bothered to pursue the formal conditions required to pick up the prize. So we are left with the obvious question. If crowds are so clever, why can’t they solve a million dollar maths challenge?
James Boswell, the acclaimed diarist and biographer of Dr. Samuel Johnson, reportedly dropped to his knees and kissed the play. Henry James Pye, the Poet Laureate, wrote a prologue for it, as did the noted poet James Bland Burgess. It was championed by the critic and classical scholar, Joseph Warton, and Irish playwright Richard Brinsley Sheridan purchased the rights to its first production at London’s Drury Lane Theatre, for the princely sum of 300 pounds. The play was called ‘Vortigern and Rowena’, and was proclaimed as a lost work of William Shakespeare. With sceptics in the minority, chief among them being Shakespearean scholar, Edmond Malone, the play opened to a packed, enthusiastic audience on April 2, 1796. The part of Vortigern himself was played by no less a light than the fine Shakespearean actor, John Philip Kemble, brother of the legendary Sarah Siddons. He was also the manager of the Drury Lane Theatre. The widespread excitement and anticipation among the audience soon turned, however, to bemusement and then literal disbelief, so that by the time Kemble was drawn to hint at his own opinion, repeating with emphasis Vortigern’s line “and when this solemn mockery is o’er”, the catcalls of the audience told its own story. The play ends with the entrance of the Fool, who admits that the play is not very tragic, as “none save bad do fall, which draws no tear.” In fact, there were tears, but these were tears of laughter from those members of the audience charitable enough not to boo it off the stage. The real author, William Henry Ireland, soon admitted to the hoax and promptly left for France. So here we have a ‘lost play’ by Shakespeare examined by notables of the day, most of whom were convinced of its authenticity, or at least willing to put their name to that belief. One performance before a crowd of ordinary theatregoers, however, was enough to kill off that notion and indeed kill off the play. Indeed, it was not to see the stage again for over 200 years, when it experienced a so-called ‘comedic revival’ on November 19, 2008, by the Pembroke Players at the Pembroke College New Cellars in Cambridge. So what we can learn here about the ‘wisdom of crowds’? Was it perhaps the case that Shakespeare is to be played, not read, and the 18th century experts who examined it simply took it on trust that it would appear better when played than read? Could it be that they were not so expert as they were given credit for? Could it be that the real experts were the performers who had played much of the canon of the authentic William Shakespeare, and that their sceptical performances tipped the wink to the theatre-going crowd? Or could it be that the crowd simply is as wise as many give it credit for, especially when it has paid hard-earned money to get through the doors. More than 200 years on, we can’t be sure what the ‘Vortigern’ fiasco tells us. But of one thing we can be sure. One crowd was enough. ‘Vortigern and Rowena’ didn’t open for a second day.
Optimism bias may be defined as the systematic tendency for people to be over-optimistic about the outcome of planned actions. This includes over-estimating the likelihood of positive events and under-estimating the likelihood of negative events. Put another way, it is the tendency to see a glass as half full instead of half empty.
David Armor and Shelley Taylor highlight a number of examples of what they consider to be optimism bias in an interesting paper called ‘When Predictions Fail: The Dilemma of Unrealistic Optimism’, published in 2002.
Examples include students’ estimates of the likely starting salary of their first job in the graduate market and newlyweds’ thoughts on how long their marriage will last. It is interesting, therefore, that evidence of the existence of this very same bias has been identified in ‘internal’ company prediction markets, notably in a 2008 paper co-authored by Bo Cowgill, of Google, Justin Wolfers of the Wharton School and Eric Zitzewitz, based at Dartmouth College.
The distinguished authors of the study examine the results generated by what they call the Google corporate prediction market experiment. The primary goal of these markets is, as they put it, to generate predictions that efficiently aggregate many employees’ information and augment existing forecasting methods.
In support of previous investigations into the value of internal prediction markets, they were able to confirm that prices in the Google markets closely approximated event probabilities, i.e. that the markets were reasonably efficient. Even so, they were not perfect, and one notable reason was an apparent ‘optimism bias’ which, according to their findings, “was more pronounced for subjects under the control of Google employees, such as whether a project would be completed on time or whether a particular office would be opened.”
Optimism bias was also found to be more evident in new emplyees and in the immediate few days following a good news day for the Google stock price.
Still, what is a cost in terms of unadjusted predictive efficiency may be a benefit in terms of motivation and entrepreneurial zeal, a feedback mechanism the value of which it is perhaps easy to under-estimate.
In any case, if we are able to identify and measure the source and extent of the bias, it should be possible (in whole or part) to adjust and compensate for this particular inefficiency in generating the objective forecasts.
So is ‘optimism bias’ a particular issue for internal prediction markets? The Google paper identifies the bias as particularly evident where the subject of evaluation was to some extent under the control of the players. This is less evident in the case, for example, of political prediction markets. Each individual player is likely to contribute only a tiny fraction to the total outcome.
So can we identify an optimism bias in these macro-markets and if so what impact is it likely to have, and can we adjust for it? Are supporters of one political party or football team, for example, more optimistic than another, and how might that affect the forecasts of US elections? And how can we distinguish over-optimistic trading of one candidate from straight market manipulation? These are important questions. The challenge now is to help provide the important answers.
Links:
Armor, David A.; Shelley E Taylor. “When Predictions Fail: The Dilemma of Unrealistic Optimism” in Gilovich, Thomas; Dale Griffin, Daniel Kahneman (Eds.) (2002). Heuristics and biases: The psychology of intuitive judgment. Cambridge, UK: Cambridge University Press. ISBN 0-521-79679-2.
http://www.nber.org/public_html/confer/2008/si2008/LS/cowgill.pdf
Follow on Twitter: @leightonvw
The idea of a so-called favourite-longshot bias at the racetrack was first identified as long ago as 1949 by Richard M. Griffith, a psychologist based at the Veterans Administration Hospital in Lexington, Kentucky. What Griffith found, in a study of thousands of horses running at US racetracks, was that the shorter the odds at which a horse started a race, the better on average the value. In other words, a strategy of betting on horses starting at shorter odds would over the long-term tend to yield a better return than betting at longer odds. What was so startling about this discovery was the implication that it is possible to earn above-average returns by following a simple betting system which requires no knowledge of anything about the horses running other than the available odds. In a way, though, this is not so surprising, since it accords with the conclusions of a series of laboratory experiments dating back to a classic study by Professors Preston and Baratta, published in 1948. These experiments all found that subjects (under controlled conditions) tend to undervalue (or bet relatively too little on) events with a high probability of occurring (short odds), and to overvalue (or bet relatively too much on) events with a low probability of occurring (long odds). To this day, dozens of subsequent studies in the US and UK have confirmed the existence of this favourite-longshot bias at the racetrack, for bets placed with bookmakers and on the Tote. In a paper I co-authored, published in 2006 in ‘Economica’, we found there was some evidence of this bias even on Betfair, though much less pronounced. There are many theories as to what causes the bias and in what arenas it exists, but not until recently has any serious analysis been conducted into its existence in election betting markets. What evidence there is seems so far to points not just to a bias but to a super-bias. This was first highlighted in the 2004 US Presidential election when the favourite to win each of the states of the Union and the eventual winner was in every single case the same person. This is the equivalent of the favourite in 50 successive 2-horse races winning. Favourite-longshot bias or not, it just won’t happen at the racetrack! Move forward to the 2006 Senate elections and the feat was replicated, as every single contested seat fell to the polling day favourite. In the 2008 US Presidential election, the betting markets were a little less perfect – they got it right in just 49 of the 50 states. If this is not just an amazing set of coincidences, we are witnessing here a bias so extreme that a strategy of backing the favourite in every general election race is a sure-fire strategy for winning nearly every single bet placed. Does this mean you can pretty safely bet the market favourite to win every election to come? My view is that there’s some logic in betting what you can afford to lose according to such a strategy, but before you do (especially at very short odds), just bear one thing in mind. There’s only one thing you can be certain of – that there’s no such thing as certainty!
Reference:
Griffith, R. (1949), Odds Adjustment by American Horse Race Bettors, American Journal of Psychology, 62, 290-294.
I was once told a story about the value of crowd wisdom in turning up buried treasure. The story was that by asking a host of people, each with a little knowledge of ships, sailing and the sea, where a vessel is likely to have sunk in years gone by, it is possible with astonishing accuracy to pinpoint the wreck and the bounty within. Individually, each of those contributing a guess as to the location is limited to their special knowledge, whether of winds or tides or surf or sailors, but the idea is that together their combined wisdom (arrived at by averaging their guesses) could pinpoint the treasure more accurately than a range of other predictive tools. At least that’s the way it was told to me by an economist who was in turn told the story by a physicist friend. To any advocate of the power of prediction markets, this certainly sounds plausible, so I decided to investigate further. Soon I was getting acquainted with the fascinating tale of the submarine USS Scorpion, as related by Mark Rubinstein, Professor of Applied Investment Analysis at the University of California at Berkeley. In a fascinating paper titled, ‘Rational Markets? Yes or No? The Affirmative Case’, he tells of a story related in a book called ‘Blind Man’s Bluff: The Untold Story of American Submarine Espionage’ by Sherry Sontag and Christopher Drew. The book tells how on the afternoon of May 27, 1968, the submarine USS Scorpion was declared missing with all 99 men aboard. It was known that she must be lost at some point below the surface of the Atlantic Ocean within a circle 20 miles wide. This information was of some help, of course, but not enough to determine even five months later where she could actually be found. The Navy had all but given up hope of finding the submarine when John Craven, who was their top deep-water scientist, came up with a plan which pre-dated the explosion of interest in prediction markets by decades. He simply turned to a group of submarine and salvage experts and asked them to bet on the probabilities of what could have happened. Taking an average of their responses, he was able to identify the location of the missing vessel to within a furlong (220 yards) of its actual location. The sub was found. Sontag and Drew also relate the story of how the Navy located a live hydrogen bomb lost by the Air Force, albeit without reference in that case to the wisdom of crowds. Perhaps, though, that tale is too secret yet to be told!
Links:
http://www.er.ethz.ch/teaching/RationalMarkets_Rubinstein.pdf
Derren Brown, the magician, is no stranger to the use of the idea of the wisdom of crowds as part of his entertainment package. A couple of years ago, for example, he selected a group of people and asked them to estimate how many sweets were in a jar. All conventional ‘wisdom of crowds’ stuff, albeit wrapped as part of a magical mystery tour. His more recent venture into this world of apparent wisdom went down a rather singular avenue, however, as he explained how a group of 24 people could predict the Lotto numbers better than one. The idea in essence was that each of the 24 would make a guess about the number on each ball in turn and the average of each of these guesses would in each case converge on the correct chosen numbers. It appeared to work – but that is the thing about illusionists; they are good at producing illusions. I will not go into how he did generate the effect of predicting the lottery draw, because there is no point if you already know, and because it would spoil the fun if you don’t. What is sure, however, is that the musings of the crowd had nothing to do with it. But why not? After all, if the crowd can accurately guess the weight of an ox or the number of jelly beans in a jar, why not the numbers on the lottery balls? The simple answer, of course, is because the lottery balls are drawn randomly. And the thing about random events is that they are unpredictable. This is at the heart of what economists term ‘weak form market efficiency’, i.e. that future movements in share prices cannot be predicted from past movements. In this sense, the series has no memory. So what is likely to happen if you do get a group of friends around and ask each to guess the number that will appear on each of the Lotto balls drawn next Saturday? If you take the average of the guesses about each of the balls in turn, my best estimate is that you are likely to end up with a prediction for each ball that is about 30 or less. Why so? Partly this is because people tend to pick birthdays but it’s also because the averaging of a large number of guesses is likely to produce a number somewhere nearer the mid-point of the set of numbers than the extremes. But if you do use these numbers and just happen to win, you’re likely to be sharing your winnings with a lot of other people who’ve chosen birthdays. The better strategy is to populate your ticket with bigger numbers, which are likely to be less popular. This strategy won’t alter your chance of winning but it will increase how much you can expect to win if you do win. And that is no illusion!
Professor Leighton Vaughan Williams 