Showing posts with label alpha. Show all posts
Showing posts with label alpha. Show all posts

Thursday, June 11, 2020

Warren Hatch on Seeing the Future in the Era of COVID-19: Manifold Episode #50



Steve and Corey talk to Warren Hatch, President and CEO of Good Judgment Inc. Warren explains what makes someone a good forecaster and how the ability to integrate and assess information allows cognitively diverse teams to outperform prediction markets. The hosts express skepticism about whether the incentives at work in large organizations would encourage the adoption of approaches that might lead to better forecasts. Warren describes the increasing depth of human-computer collaboration in forecasting. Steve poses the long-standing problem of assessing alpha in finance and Warren suggests that the emerging alpha-brier metric, linking process and outcome, might shed light on the issue. The episode ends with Warren describing Good Judgment’s open invitation to self-identified experts to join a new COVID forecasting platform.

Transcript

Good Judgment Inc
.

Good Judgment Open

Superforecasting: The Art and Science of Prediction

Noriel Roubini (Wikipedia)


man·i·fold /ˈmanəˌfōld/ many and various.

In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.

Steve Hsu and Corey Washington have been friends for almost 30 years, and between them hold PhDs in Neuroscience, Philosophy, and Theoretical Physics. Join them for wide ranging and unfiltered conversations with leading writers, scientists, technologists, academics, entrepreneurs, investors, and more.

Steve Hsu is VP for Research and Professor of Theoretical Physics at Michigan State University. He is also a researcher in computational genomics and founder of several Silicon Valley startups, ranging from information security to biotech. Educated at Caltech and Berkeley, he was a Harvard Junior Fellow and held faculty positions at Yale and the University of Oregon before joining MSU.

Corey Washington is Director of Analytics in the Office of Research and Innovation at Michigan State University. He was educated at Amherst College and MIT before receiving a PhD in Philosophy from Stanford and a PhD in a Neuroscience from Columbia. He held faculty positions at the University Washington and the University of Maryland. Prior to MSU, Corey worked as a biotech consultant and is founder of a medical diagnostics startup.

Sunday, September 30, 2012

Buffett's secret

Low beta + leverage. The leverage is obtained cheaply via Berkshire's insurance and reinsurance business. But I wonder whether low beta investing practiced algorithmically (i.e., without Buffet's stock picking skill, just taking a representative sample of low beta companies, or using some simple selection method) would work. I haven't yet read the AQR paper below and wonder how they adjust for "quality factors". Can I do that too?
Buffet's Alpha

Berkshire Hathaway has a higher Sharpe ratio than any stock or mutual fund with a history of more than 30 years and Berkshire has a significant alpha to traditional risk factors. However, we find that the alpha become statistically insignificant when controlling for exposures to Betting-Against-Beta and quality factors. We estimate that Berkshire’s average leverage is about 1.6-to-1 and that it relies on unusually low-cost and stable sources of financing. Berkshire’s returns can thus largely be explained by the use of leverage combined with a focus on cheap, safe, quality stocks. We find that Berkshire’s portfolio of publicly-traded stocks outperform private companies, suggesting that Buffett’s returns are more due to stock selection than to a direct effect on management.
More from the Economist.
Economist: ... Yet the underappreciated element of Berkshire’s leverage are its insurance and reinsurance operations, which provide more than a third of its funding. An insurance company takes in premiums upfront and pays out claims later on; it is, in effect, borrowing from its policyholders. This would be an expensive strategy if the company undercharged for the risks it was taking. But thanks to the profitability of its insurance operations, Berkshire’s borrowing costs from this source have averaged 2.2%, more than three percentage points below the average short-term financing cost of the American government over the same period.

A further advantage has been the stability of Berkshire’s funding. As many property developers have discovered in the past, relying on borrowed money to enhance returns can be fatal when lenders lose confidence. But the long-term nature of the insurance funding has protected Mr Buffett during periods (such as the late 1990s) when Berkshire shares have underperformed the market.

These two factors—the low-beta nature of the portfolio and leverage—pretty much explain all of Mr Buffett’s superior returns, the authors find. Of course, that is quite a different thing from saying that such a long-term performance could be easily replicated. As the authors admit, Mr Buffett recognised these principles, and started applying them, half a century before they wrote their paper.
See also If you're so smart, why aren't you rich?

Wednesday, August 15, 2012

Better to be lucky than good

Shorter Taleb (much of this was discussed in his first book, Fooled by Randomness):
Fat tails + nonlinear feedback means that the majority of successful traders were successful due to luck, not skill. It's painful to live in the shadow of such competitors.
What other fields are dominated by noisy feedback loops? See Success vs Ability , Nonlinearity and noisy outcomes , The illusion of skill and Fake alpha.
Why It is No Longer a Good Idea to Be in The Investment Industry 
Nassim N. Taleb 
Abstract: A spurious tail is the performance of a certain number of operators that is entirely caused by luck, what is called the “lucky fool” in Taleb (2001). Because of winner-take-all-effects (from globalization), spurious performance increases with time and explodes under fat tails in alarming proportions. An operator starting today, no matter his skill level, and ability to predict prices, will be outcompeted by the spurious tail. This paper shows the effect of powerlaw distributions on such spurious tail. The paradox is that increase in sample size magnifies the role of luck. 
... The “spurious tail” is therefore the number of persons who rise to the top for no reasons other than mere luck, with subsequent rationalizations, analyses, explanations, and attributions. The performance in the “spurious tail” is only a matter of number of participants, the base population of those who tried. Assuming a symmetric market, if one has for base population 1 million persons with zero skills and ability to predict starting Year 1, there should be 500K spurious winners Year 2, 250K Year 3, 125K Year 4, etc. One can easily see that the size of the winning population in, say, Year 10 depends on the size of the base population Year 1; doubling the initial population would double the straight winners. Injecting skills in the form of better-than-random abilities to predict does not change the story by much. 
Because of scalability, the top, say 300, managers get the bulk of the allocations, with the lion’s share going to the top 30. So it is obvious that the winner-take-all effect causes distortions ...
Conclusions: The “fooled by randomness” effect grows under connectivity where everything on the planet flows to the “top x”, where x is becoming a smaller and smaller share of the top participants. Today, it is vastly more acute than in 2001, at the time of publication of (Taleb 2001). But what makes the problem more severe than anticipated, and causes it to grow even faster, is the effect of fat tails. For a population composed of 1 million track records, fat tails multiply the threshold of spurious returns by between 15 and 30 times. 
Generalization: This condition affects any business in which prevail (1) some degree of fat-tailed randomness, and (2) winner-take-all effects in allocation. 
To conclude, if you are starting a career, move away from investment management and performance related lotteries as you will be competing with a swelling future spurious tail. Pick a less commoditized business or a niche where there is a small number of direct competitors. Or, if you stay in trading, become a market-maker.

Bonus question: what are the ramifications for tax and economic policies (i.e., meant to ensure efficiency and just outcomes) of the observation that a particular industry is noise dominated?

Saturday, January 26, 2008

Fake alpha, tail risk and compensation in finance

I highly recommend this essay in the Financial Times. It notes that current banking and money management compensation schemes create incentives for taking on tail risk (which is really beta) and disguising it as alpha. The proposed solution: holdbacks or clawbacks of bonus money. This would probably be a big improvement over the status quo (although how long would one have to wait to be sure that risk was properly priced on a group of thirty year loans?). When will shareholders smarten up and enforce this kind of compensation scheme on management at public firms? Clawbacks already happen in VC when early success turns into losses for a fund.

A minor quibble with what is written about VCs: in many cases "activism" is too strong a characterization -- it is the inventor/entrepreneur who does all the work.

FT: Bankers’ pay is deeply flawed

By Raghuram Rajan

Published: January 8 2008 18:04 | Last updated: January 9 2008 16:21

Summary: Raghuram Rajan says bogus alpha is created by hiding long-tail risks, as with structured products linked to subprime mortgages. A solution would be to hold in escrow a big chunk of bonuses until the full risks play out, meaning only true alpha gets jumbo rewards and reducing the hidden risks in the financial system.


Banks have recently been acknowledging enormous losses, yet those losses are barely reflected in employee compensation. For example, Morgan Stanley announced a $9.4bn charge-off in the fourth quarter and at the same time increased its bonus pool by 18 per cent. The justification was that many employees had a banner year and their compensation should not be held hostage to mistakes that were made in the subprime market. The chief executive, John Mack, however, assumed some responsibility and agreed to take no bonus for 2007 – although he got a $40m payout for 2006.

Even so, most readers would suspect something is not right here. Indeed, compensation practices in the financial sector are deeply flawed and probably contributed to the ongoing crisis.

The typical manager of financial assets generates returns based on the systematic risk he takes – the so-called beta risk – and the value his abilities contribute to the investment process – his so-called alpha. Shareholders in asset management firms, such as commercial banks, investment banks and private equity or insurance companies are unlikely to pay the manager much for returns from beta risk. For example, if the shareholder wants exposure to large traded US stocks she can get the returns associated with that risk simply by investing in the Vanguard S&P 500 index fund, for which she pays a fraction of a per cent in fees. What the shareholder will really pay for is if the manager beats the S&P 500 index regularly, that is, generates excess returns while not taking more risks. Hence they will pay for alpha.

In reality, there are only a few sources of alpha for investment managers. One of them comes from having truly special abilities in identifying undervalued financial assets. Warren Buffett, the US billionaire investor, certainly has it, yet this special ability is, by definition, rare.

A second source of alpha is from what one might call activism. This means using financial resources to create, or obtain control over, real assets and to use that control to change the payout obtained on the financial investment. A venture capitalist who transforms an inventor, a garage and an idea into a fully fledged, profitable and professionally managed corporation creates alpha.

A third source of alpha is financial entrepreneurship or engineering – creating securities or cash flow streams that appeal to particular investors or tastes. As long as the investment manager does not create securities that exploit investor weaknesses or ignorance (and there is unfortunately too much of that), this sort of alpha is also beneficial, but it requires constant innovation.

Alpha is quite hard to generate since most ways of doing so depend on the investment manager possessing unique abilities – to pick stocks, identify weaknesses in management and remedy them, or undertake financial innovation. Such abilities are rare. How then can untalented investment managers justify their pay? Unfortunately, all too often it is by creating fake alpha – appearing to create excess returns but in fact taking on hidden tail risks, which produce a steady positive return most of the time as compensation for a rare, very negative, return.

For example, an investment manager who bought AAA-rated tranches of collateralised debt obligations (CDO) in the past generated a return of 50 to 60 basis points higher than a similar AAA-rated corporate bond. That “excess” return was in fact compens ation for the “tail” risk that the CDO would default, a risk that was no doubt perceived as small when the housing market was rollicking along, but which was not zero. If all the manager had disclosed was the high rating of his investment portfolio he would have looked like a genius, making money without additional risk, even more so if he multiplied his “excess” return by leverage. Similarly, the management of Northern Rock followed the old strategy of taking on tail risk, borrowing short and lending long and praying that the unlikely event of a liquidity shortage never materialised. All these strategies essentially earn the manager a premium in normal times for taking on beta risk that materialises only infrequently. These premiums are not alpha, since they are wiped out when the risk materialises.

True alpha can be measured only in the long run and with the benefit of hindsight – in the same way as the acumen of someone writing earthquake insurance can be measured only over a period long enough for earthquakes to have occurred. Compensation structures that reward managers annually for profits, but do not claw these rewards back when losses materialise, encourage the creation of fake alpha. Significant portions of compensation should be held in escrow to be paid only long after the activities that generated that compensation occur.

The managers who blew a big hole in Morgan Stanley’s balance sheet probably earned enormous bonuses in the past – Mr Mack certainly did. If Morgan Stanley managed its compensation correctly those bonuses should be clawed back and should be enough to pay those who did well this year without increasing the bonus pool. At the very least, shareholders deserve better explanations. More generally, unless we fix incentives in the financial system we will get more risk than we bargain for. Unless bankers offer these better explanations, their enormous pay, which has been thought of as just reward for performance, will deservedly come under scrutiny.

The writer is a professor of finance at the Graduate School of Business at the University of Chicago and former chief economist at the International Monetary Fund

Wednesday, July 11, 2007

Hedge funds or market makers?

To what extent are Citadel, DE Shaw and Renaissance really just big market makers? The essay excerpted below is by Harry Kat, a finance professor and former trader who was profiled in the New Yorker recently.

First, from the New Yorker piece:

It is notoriously difficult to distinguish between genuine investment skill and random variation. But firms like Renaissance Technologies, Citadel Investment Group, and D. E. Shaw appear to generate consistently high returns and low volatility. Shaw’s main equity fund has posted average annual returns, after fees, of twenty-one per cent since 1989; Renaissance has reportedly produced even higher returns. (Most of the top-performing hedge funds are closed to new investors.) Kat questioned whether such firms, which trade in huge volumes on a daily basis, ought to be categorized as hedge funds at all. “Basically, they are the largest market-making firms in the world, but they call themselves hedge funds because it sells better,” Kat said. “The average horizon on a trade for these guys is something like five seconds. They earn the spread. It’s very smart, but their skill is in technology. It’s in sucking up tick-by-tick data, processing all those data, and converting them into second-by-second positions in thousands of spreads worldwide. It’s just algorithmic market-making.”

Next, the essay from Kat's academic web site. I suspect Kat exaggerates, but he does make an interesting point. Could a market maker really deliver such huge alpha? Only if it knows exactly where and when to take a position!

Of Market Makers and Hedge Funds

David and Ken both work for a large market making firm and both have the same dream: to start their own company. One day, David decides to quit his job and start a traditional market-making company. He puts in $10m of his own money and finds 9 others that are willing to do the same. The result: a company with $100m in equity, divided equally over 10 shareholders, meaning that each shareholder will share equally in the companyís operating costs and P&L. David will manage the company and will receive an annual salary of $1m for doing so.

Ken decides to quit as well. He is going to do things differently though. Instead of packaging his market-making activities in the traditional corporate form, he is going to start a hedge fund. Like David, he also puts in $10m of his own money. Like David, he also finds 9 others willing to do the same. They are not called shareholders, however. They are investors in a hedge fund with a net asset value of $100m. Just like David, Ken has a double function. Apart from being one of the 10 investors in the fund, he will also be the fundís manager. As manager, he is entitled to 20% of the profit (over a 5% hurdle rate); the average incentive fee in the hedge fund industry.

At first sight, it looks like David and Ken have accomplished the same thing. Both have a market-making operation with $100m in capital and 9 others to share the benefits with. There is, however, one big difference. Suppose David and Ken both made a net $100m. In Davidís company this would be shared equally between the shareholders, meaning that, including his salary, David received $11m. In Ken's hedge fund things are different, however. As the manager of the fund, he takes 20% of the profit, which, taking into account the $5m hurdle, would leave $81m to be divided among the 10 investors. Since he is also one of those 10 investors, however, this means that Ken would pocket a whopping $27.1m in total. Now suppose that both David and Ken lost $100m. In that case David would lose $9m, but Ken would still only lose $10m since as the fundís manager Ken gets 20% of the profit, but he does not participate in any losses.

So if you wanted to be a market maker, how would you set yourself up? Of course, we are not the first to think of this. Some of the largest market maker firms in the world disguise themselves as hedge funds these days. Their activities are typically classified under fancy hedge fund names such as ëstatistical arbitrageí or ëmanaged futuresí, but basically these funds are market makers. This includes some of the most admired names in the hedge fund business such as D.E. Shaw, Renaissance, Citadel, and AHL, all of which are, not surprisingly, notorious for the sheer size of their daily trading volumes and their fairly consistent alpha.

The above observation leads to a number of fascinating questions. The most interesting of these is of course how much of the profits of these market-making hedge funds stems from old-fashioned market making and how much is due to truly special insights and skill? Is the bulk of what these funds do very similar to what traditional market-making firms do, or are they responsible for major innovations and/or have they embedded major empirical discoveries in their market making? They tend to employ lots of PhDs and make a lot of fuzz about only hiring the best, etc. However, how much of that is window-dressing and how much is really adding value?

Another question is whether market-making hedge funds get treated differently than traditional market makers when they go out to borrow money or securities. Given prime brokersí eagerness to service hedge funds these days, one might argue that in this respect market-making hedge funds are again better off then traditional market makers.

So what is the conclusion? First of all, given the returns posted by the funds mentioned, it appears that high volume multi-market market making is a very good business to be in. Second, it looks like there could be a trade-off going on. Market-making hedge funds take a bigger slice of the pie, but the pie might be significantly bigger as well. Obviously, all of this could do with quite a bit more research. See if I can put a PhD on it.


HMK
04-02-2007

Sunday, July 01, 2007

Hedge fund engineering

The New Yorker's John Cassidy has a great piece on hedge funds here. He makes a number of important points, largely based on academic research.

1) most funds don't generate alpha, net of fees. Hey, what happened to the efficient market? Why, then, is so much money flowing into hedge funds? If qualified investors (multi-millionaires) can't sort out the alpha question, who can? Apparently, it's left to a few academics...

...only eighteen per cent of the funds outperformed their benchmarks, and returns even at the most successful funds tended to decline over time. “Our research has shown that in at least eighty per cent of cases the after-fee alpha for hedge funds is negative,” Kat told me. “They are charging more than they are adding. I’m not saying they don’t have skill; I’m just saying they don’t have enough skill to make up for two and twenty.”

2) most funds are implementing a strategy that can be replicated much more cheaply (previous discussion)

3) although the very best funds do generate alpha, most of them are closed to new investors

4) finance professors, although among the best paid academics, make an order of magnitude less than financiers :-(

The article also discusses a program called FundCreator, which seeks to replicate any particular fund based on vol and correlations. The general theoretical framework is nice, but the idea of cloning, say, SAC Capital, seems nutty given changing market conditions and limited statistics.

However, Kat remained skeptical. As he conducted his research on hedge funds, he became convinced that it might be possible to generate similar returns in a mechanical way and with much less effort. Two years ago, he and Palaro began to sketch out ideas for a software program that could mimic the returns of individual hedge funds by trading futures. “We may be able to do without expensive hedge-fund managers and all the hassle, including the due diligence, the lack of liquidity, the lack of transparency, the lack of capacity and the fear of style drift”—changes in a fund’s strategy—“which comes with investing in hedge funds,” Kat and Palaro wrote in a working paper about the project which they published last year.

Kat provided many of the mathematical ideas. Palaro, an experienced programmer, did most of the computer work. Rather than trying to emulate a hedge fund’s monthly return—a nearly impossible task—the researchers sought to match the fund’s results over a period of several years, as well as the other statistical properties of its performance that investors were likely to care about most: the volatility of the returns, their correlation with the stock market, the likelihood of suffering extreme losses.

In the spring of last year, Kat sent me an e-mail in which he expressed confidence that he and Palaro would succeed. “It is possible to design mechanical futures-trading strategies which generate returns with the same, and often better, risk-return properties as hedge funds,” he said. “This means investors can have hedge-fund returns but without the massive fees and all the other drawbacks that come with the real thing.”

By the end of 2006, Kat and Palaro had finished writing their software program, which they called FundCreator, and have conducted several successful trials...

...Some scholars remain skeptical. “As a renegade statistician, I am a little bit suspicious of Kat’s methods,” Stephen Brown, of N.Y.U., said to me. He pointed out that, unlike Quantum, many hedge funds have been around for just a few years and there is little information about their performance. “On the basis of very limited data, it is a real challenge to construct an accurate and robust model of hedge-fund returns,” Brown said. Andrew Lo said that using FundCreator may not be as straightforward as it seems. “From the point of view of theory, there is nothing wrong with what Kat is doing,” he said. “But all dynamic trading strategies involving derivatives carry some risk. They rely on very specialized mathematical assumptions. If the assumptions turn out to be wrong, you can be mis-estimating the risks in a big way.” Faulty assessments of risk contributed to major financial losses suffered by Long-Term Capital Management and several other companies that have encountered problems trading derivatives.

Veryan Allen, an investment adviser and former hedge-fund executive who writes a blog about hedge funds (hedgefund.blogspot.com), said in a post last December, “If Goldman Sachs, Dow Jones, Merrill Lynch, Andrew Lo, or Harry Kat think they can do it, great . . . but I suspect investors will end up disappointed if they think the returns from hedge-fund clones will be anywhere near the performance of the best hedge funds.” Allen went on, “No matter what occurs in the markets, well-managed ‘expensive’ hedge funds operating proprietary strategies with skilled traders, robust risk management, and technology will perform, even under pessimistic economic scenarios. . . . That is why it is worth paying the two and twenty. . . . Average or generic hedge funds can certainly be replicated, but not the best hedge funds.”

Also, some interesting stuff about Renaissance and others:

It is notoriously difficult to distinguish between genuine investment skill and random variation. But firms like Renaissance Technologies, Citadel Investment Group, and D. E. Shaw appear to generate consistently high returns and low volatility. Shaw’s main equity fund has posted average annual returns, after fees, of twenty-one per cent since 1989; Renaissance has reportedly produced even higher returns. (Most of the top-performing hedge funds are closed to new investors.) Kat questioned whether such firms, which trade in huge volumes on a daily basis, ought to be categorized as hedge funds at all. “Basically, they are the largest market-making firms in the world, but they call themselves hedge funds because it sells better,” Kat said. “The average horizon on a trade for these guys is something like five seconds. They earn the spread. It’s very smart, but their skill is in technology. It’s in sucking up tick-by-tick data, processing all those data, and converting them into second-by-second positions in thousands of spreads worldwide. It’s just algorithmic market-making.”

Almost by definition, there can be only a handful of genius investors, Kat continued. “And even if they are there, the chances that you will find them and that they will let you in are very, very slim,” he said. “That’s what I tell people. If you are really convinced that you can find those super managers, then don’t waste your time with our stuff. Go look for them. But if you are a bit more realistic, if you know that eighty per cent of hedge-fund managers aren’t worth the fees they charge, then the rational thing to do is to give up trying to find a super manager, and just go for a good, efficient diversifier instead.”

Not so long ago, Kat recalled, one hedge-fund manager, a “global macro” investor who specializes in betting on currencies and stock markets around the world, approached him with an offer. “He said, ‘Harry, I want to buy your thing so I can replicate myself. Then I’ll be able to enjoy life a bit more and keep sending my clients bills for two plus twenty. It’ll take them years to figure it out, if they ever do.’ ”

Sunday, July 02, 2006

Hollywood genius

Physicist turned author and screenwriter Leonard Mlodinow has a nice article in the LA Times on the hit or miss nature of the movie industry. He recapitulates the myth of expertise as it applies to studio executives, whom he compares to dart throwing monkeys (a la fund managers in finance).

Mlodinow wrote a charming memoir about his time as a postdoc at Caltech in the early 1980s. Fresh from Berkeley, having written a PhD dissertation on the large-d expansion (d is the number of dimensions), he was in over his head at Caltech, but found a friend and mentor in the ailing Richard Feynman.

We all understand that genius doesn't guarantee success, but it's seductive to assume that success must come from genius. As a former Hollywood scriptwriter, I understand the comfort in hiring by track record. Yet as a scientist who has taught the mathematics of randomness at Caltech, I also am aware that track records can deceive.

That no one can know whether a film will hit or miss has been an uncomfortable suspicion in Hollywood at least since novelist and screenwriter William Goldman enunciated it in his classic 1983 book "Adventures in the Screen Trade." If Goldman is right and a future film's performance is unpredictable, then there is no way studio executives or producers, despite all their swagger, can have a better track record at choosing projects than an ape throwing darts at a dartboard.

That's a bold statement, but these days it is hardly conjecture: With each passing year the unpredictability of film revenue is supported by more and more academic research.

That's not to say that a jittery homemade horror video could just as easily become a hit as, say, "Exorcist: The Beginning," which cost an estimated $80 million, according to Box Office Mojo, the source for all estimated budget and revenue figures in this story. Well, actually, that is what happened with "The Blair Witch Project" (1999), which cost the filmmakers a mere $60,000 but brought in $140 million—more than three times the business of "Exorcist." (Revenue numbers reflect only domestic receipts.)

What the research shows is that even the most professionally made films are subject to many unpredictable factors that arise during production and marketing, not to mention the inscrutable taste of the audience. It is these unknowns that obliterate the ability to foretell the box-office future.

But if picking films is like randomly tossing darts, why do some people hit the bull's-eye more often than others? For the same reason that in a group of apes tossing darts, some apes will do better than others. The answer has nothing to do with skill. Even random events occur in clusters and streaks.

...If the mathematics is counterintuitive, reality is even worse, because a funny thing happens when a random process such as the coin-flipping experiment is actually carried out: The symmetry of fairness is broken and one of the films becomes the winner. Even in situations like this, in which we know there is no "reason" that the coin flips should favor one film over the other, psychologists have shown that the temptation to concoct imagined reasons to account for skewed data and other patterns is often overwhelming.

...Actors in Hollywood understand best that the industry runs on luck. As Bruce Willis once said, "If you can find out why this film or any other film does any good, I'll give you all the money I have." (For the record, the film to which he referred, 1993's "Striking Distance," didn't do any good.) Willis understands the unpredictability of the film business not simply because he's had box-office highs and lows. He knows that random events fueled his career from the beginning, and his story offers another case in point...

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