Put a value investor and a professional gambler together at a dinner party, and chances are they will have a hard time finding things to talk about. The risk-averse value investor often finds it difficult to relate to traders, let alone bottom-feeding sports bettors. The conversation would be awkward, with plenty of unspoken judging, and the two would likely do their best to politely end the encounter. But they would be missing out on some great conversation — especially the value investor — because the two disciplines employ strategies that are often complementary. (Even Warren Buffett spent a good part of his youth handicapping horse races.)
Based on the ideas originating on this site, which are often in line with strategies advanced by Gurus such as Joel Greenblatt, value investors are increasingly looking at special situations — mispriced securities where uncertainty and market ignorance are the primary source of value. These situations include high-leverage spinoffs1, bankruptcies, undeveloped oil plays2, and issues involving patents or pharmaceutical trials, to name just a few. They are value bets and although they can be wise investments, they require a fundamentally different strategy than what most of us typically employ with stocks that possess strong margins of safety.
Value investors are trained to think in terms of the quality of an idea. When a value guru fails, we often credit his failure to a flaw in the analysis. Rarely do we consider the role of chance and variance in an investor’s track record. There are simply not enough investment ideas in the average value investor’s career to definitively credit failure to pure randomness. The charge cannot be disproved, so we rarely level it. But in value betting with special situations, there is often no margin of safety and randomness takes on a much more significant role.
Enter the professional gambler — the sports bettor, card-counting blackjack player and poker grinder. These people make their living by identifying situations in which they have a small edge and then ruthlessly exploit it in as many repetitions as possible. Professional gamblers possess expertise in randomness and proper bet-sizing. Through involvement in tens of thousands of games or millions of hands, they have experienced the brutal, seemingly impossible downswings that are unavoidable in games of chance.
To illustrate my point, consider this graph. In the poker world this is considered a very good run.
3,000 heads-up tournament matches by a skilled, winning player against a single human opponent. Each match is winner-take-all and lasts about 10 minutes.
This skilled player wins nearly 55% of his matches. His long-term winnings of $80,000 were in line with his expectation during this run, but look at the downswings he endured along the way! Risking an average of $300 per match, he once suffered a downswing of over 30 units ($9,000). These were not paper losses (i.e. Mr. Market undervaluing a stock for a year). This was a permanent loss of capital. If he does not properly account for variance, he risks going bust.
So how does this relate to value investing? In many special situations, the market may overestimate failure due to fear or uncertainty, resulting in the mispricing of a security. For example, Mr. Market may estimate that a company in bankruptcy has a 70% chance of going to zero, but after conducting analysis, we conclude that there will probably be equity left over for shareholders, and the chances of going to zero are merely 50%. This is a value bet. There is no margin of safety, and our success depends on achieving results in line with our expected value. This sounds an awful lot like the sports bettor’s strategy! But it can still be a wise allocation of capital. We just have to size our bets properly, or eventually we WILL go bust due to variance.
Consider the average sports bettor who has just lost everything. Why did it happen? It was NOT because he couldn’t pick winners. Even a fool would have a hard time achieving a win-rate worse than 48% over the long run. Chances are it was not due to the commissions he paid to the sportsbook on each winning bet (that would have whittled away his bankroll, but taken a long time to get to zero). The most common cause of gamblers going bust is that they bet too much of their bankroll on each game, hand, or tournament. The first bad downswing knocks them out and they have no chance to achieve their expected value.
Value investors considering special situations in which there is no margin of safety would do well to draw some lessons from professional gamblers and learn to properly size bets. How do we determine proper bet size? It requires a departure from our standard concentrated portfolio strategy in which we often place 10% or more on a single position.
A sobering statistic: A hypothetical investor identifies 10 special situations in which he has a 60% chance of doubling his money and a 40% chance of the stock going to zero. Each event is independent (the result of one investment is not linked to that of the others). He decides to invest 10% of his portfolio in each of the 10 ideas. His expected return is excellent — an overall gain of 20%. But he will suffer a permanent capital loss 16.6% of the time, even when his analysis is absolutely correct. The strategy may work for a time, but eventually it will ruin the value investor. (Calculate your own probabilities here.)
Probability of loss is the most significant factor in determining bet size. The higher the probability of loss, the lower the bet size must be to remain within an acceptable Risk of Ruin (RoR). For example, a long shot can have a positive expected value, but the low frequency of success makes extended downswings far more likely. To survive long enough to achieve long-run results, we must employ a small bet size. This logic also explains why value investors can safely accumulate large positions in companies where there is a large margin of safety — the probability of loss is small.
Example from an idea posted on Joel Greenblatt’s Value Investors Club website in July 2011. “Statistical analysis of the inadvertently released enrollment curve for Oncothyreon's ("ONTY") lung cancer vaccine, Stimuvax, shows there is a 50%+ probability Stimuvax is working. At $8.84/sh, ONTY's EV is $350mm, but if Stimuvax works, the company is worth ~$1.8b, resulting in a stock price of ~$39/sh, ~340% above today's close.”
If ONTY has no other assets or prospects, this would be a binomial outcome. The drug either works or it doesn’t. If there is a 50% chance of the drug not working, then we’ll assume for simplicity’s sake that there is a 50% chance of a total loss of capital. With the estimated payoff at 340%, this coin-toss situation appears to be a very attractive. But we must also look at overall portfolio exposure to determine how to size the bet. What percentage of the portfolio is exposed to random outcomes? The more a portfolio is exposed to simultaneous random events, the less one should bet on each event.
For example, a portfolio exposed to eight simultaneous coin-toss situations will lose at least six of eight nearly 15% of the time. Simultaneous losses prevent the investor from adjusting bet sizes down during downswings in order to properly manage risk. Downswings can often exceed what many consider possible. But over the long run, extended losses can and do occur. Streaks of seven to nine consecutive coin-toss losses are quite normal in the world of gambling. (Amateurs experiencing protracted downswings often become convinced that the gods are against them, but this is simple probability.)
In his 2007 book, "The Dhando Investor," Mohnish Pabrai argued that rather than assigning a single “fair value” dollar amount to a company, it is often useful to express value in terms of possible outcomes (e.g. 30% bankruptcy, 50% base case success, 20% sale of company). This approach is also helpful when attempting to determine a stock’s probability of loss. It looks something like this:
A working version of this spreadsheet can be downloaded from GoogleDocs here. If this stock is currently priced at $0.16, we estimate that there is a 40% probability of loss. We run some probability figures here, and then examine our portfolio to measure our exposure to simultaneous value bets in order to determine proper bet size.
What bet size should we use in the typical coin-toss situation with a 47% probability of loss? As a yardstick, many professional gamblers would advise risking no more than 1% of the bankroll per bet in this situation. Some would recommend a more conservative approach of 0.5% if the bankroll cannot be easily replenished. If your bet size on coin-flips is larger than what most professional gamblers feel comfortable with, it may be time to re-examine your tolerance for risk.
In summary:
1) If value investors considering special situations have one weakness, it is that they underestimate the Risk of Ruin, misapplying the concentrated position strategy to value betting.
2) Professional gamblers understand how to survive downswings. If the average value investor becomes involved in 100 value situations over a decade, the gambler is involved in tens of thousands or even millions. He understands that bet size destroys far more quickly than poor analysis.
3) When determining proper bet size, probability of loss is the most important factor.
4) Multiple, simultaneous bets require an even smaller bet size.
5) Above all else, survive! When in doubt, be conservative.
Stay tuned for Part II, which will examine if value betting is a worthwhile use of time for value investors.
[1] In You Can Be a Stock Market Genius, Greenblatt argues that bets on high-leverage spinoffs can reward shareholders with large gains without any obligation to repay debt in the event of bankruptcy.
[2] GuruFocus Article, 1 March 2013. "HNR: Bargain and Speculative Hybrid."
Based on the ideas originating on this site, which are often in line with strategies advanced by Gurus such as Joel Greenblatt, value investors are increasingly looking at special situations — mispriced securities where uncertainty and market ignorance are the primary source of value. These situations include high-leverage spinoffs1, bankruptcies, undeveloped oil plays2, and issues involving patents or pharmaceutical trials, to name just a few. They are value bets and although they can be wise investments, they require a fundamentally different strategy than what most of us typically employ with stocks that possess strong margins of safety.
Value investors are trained to think in terms of the quality of an idea. When a value guru fails, we often credit his failure to a flaw in the analysis. Rarely do we consider the role of chance and variance in an investor’s track record. There are simply not enough investment ideas in the average value investor’s career to definitively credit failure to pure randomness. The charge cannot be disproved, so we rarely level it. But in value betting with special situations, there is often no margin of safety and randomness takes on a much more significant role.
Enter the professional gambler — the sports bettor, card-counting blackjack player and poker grinder. These people make their living by identifying situations in which they have a small edge and then ruthlessly exploit it in as many repetitions as possible. Professional gamblers possess expertise in randomness and proper bet-sizing. Through involvement in tens of thousands of games or millions of hands, they have experienced the brutal, seemingly impossible downswings that are unavoidable in games of chance.
To illustrate my point, consider this graph. In the poker world this is considered a very good run.
3,000 heads-up tournament matches by a skilled, winning player against a single human opponent. Each match is winner-take-all and lasts about 10 minutes.
This skilled player wins nearly 55% of his matches. His long-term winnings of $80,000 were in line with his expectation during this run, but look at the downswings he endured along the way! Risking an average of $300 per match, he once suffered a downswing of over 30 units ($9,000). These were not paper losses (i.e. Mr. Market undervaluing a stock for a year). This was a permanent loss of capital. If he does not properly account for variance, he risks going bust.
So how does this relate to value investing? In many special situations, the market may overestimate failure due to fear or uncertainty, resulting in the mispricing of a security. For example, Mr. Market may estimate that a company in bankruptcy has a 70% chance of going to zero, but after conducting analysis, we conclude that there will probably be equity left over for shareholders, and the chances of going to zero are merely 50%. This is a value bet. There is no margin of safety, and our success depends on achieving results in line with our expected value. This sounds an awful lot like the sports bettor’s strategy! But it can still be a wise allocation of capital. We just have to size our bets properly, or eventually we WILL go bust due to variance.
Consider the average sports bettor who has just lost everything. Why did it happen? It was NOT because he couldn’t pick winners. Even a fool would have a hard time achieving a win-rate worse than 48% over the long run. Chances are it was not due to the commissions he paid to the sportsbook on each winning bet (that would have whittled away his bankroll, but taken a long time to get to zero). The most common cause of gamblers going bust is that they bet too much of their bankroll on each game, hand, or tournament. The first bad downswing knocks them out and they have no chance to achieve their expected value.
Value investors considering special situations in which there is no margin of safety would do well to draw some lessons from professional gamblers and learn to properly size bets. How do we determine proper bet size? It requires a departure from our standard concentrated portfolio strategy in which we often place 10% or more on a single position.
A sobering statistic: A hypothetical investor identifies 10 special situations in which he has a 60% chance of doubling his money and a 40% chance of the stock going to zero. Each event is independent (the result of one investment is not linked to that of the others). He decides to invest 10% of his portfolio in each of the 10 ideas. His expected return is excellent — an overall gain of 20%. But he will suffer a permanent capital loss 16.6% of the time, even when his analysis is absolutely correct. The strategy may work for a time, but eventually it will ruin the value investor. (Calculate your own probabilities here.)
Probability of loss is the most significant factor in determining bet size. The higher the probability of loss, the lower the bet size must be to remain within an acceptable Risk of Ruin (RoR). For example, a long shot can have a positive expected value, but the low frequency of success makes extended downswings far more likely. To survive long enough to achieve long-run results, we must employ a small bet size. This logic also explains why value investors can safely accumulate large positions in companies where there is a large margin of safety — the probability of loss is small.
Example from an idea posted on Joel Greenblatt’s Value Investors Club website in July 2011. “Statistical analysis of the inadvertently released enrollment curve for Oncothyreon's ("ONTY") lung cancer vaccine, Stimuvax, shows there is a 50%+ probability Stimuvax is working. At $8.84/sh, ONTY's EV is $350mm, but if Stimuvax works, the company is worth ~$1.8b, resulting in a stock price of ~$39/sh, ~340% above today's close.”
If ONTY has no other assets or prospects, this would be a binomial outcome. The drug either works or it doesn’t. If there is a 50% chance of the drug not working, then we’ll assume for simplicity’s sake that there is a 50% chance of a total loss of capital. With the estimated payoff at 340%, this coin-toss situation appears to be a very attractive. But we must also look at overall portfolio exposure to determine how to size the bet. What percentage of the portfolio is exposed to random outcomes? The more a portfolio is exposed to simultaneous random events, the less one should bet on each event.
For example, a portfolio exposed to eight simultaneous coin-toss situations will lose at least six of eight nearly 15% of the time. Simultaneous losses prevent the investor from adjusting bet sizes down during downswings in order to properly manage risk. Downswings can often exceed what many consider possible. But over the long run, extended losses can and do occur. Streaks of seven to nine consecutive coin-toss losses are quite normal in the world of gambling. (Amateurs experiencing protracted downswings often become convinced that the gods are against them, but this is simple probability.)
In his 2007 book, "The Dhando Investor," Mohnish Pabrai argued that rather than assigning a single “fair value” dollar amount to a company, it is often useful to express value in terms of possible outcomes (e.g. 30% bankruptcy, 50% base case success, 20% sale of company). This approach is also helpful when attempting to determine a stock’s probability of loss. It looks something like this:
| Outcome | Description | % Probability | Fair Value (Weighted Average) | ||
| Scenario A | $0.00 | Total Loss of Equity | 20% | $0.23 | |
| Scenario B | $0.10 | Liquidation | 20% | ||
| Scenario C | $0.30 | Sale of Company, Base Case | 40% | ||
| Scenario D | $0.40 | Sale of Company, Optimistic Case | 20% |
A working version of this spreadsheet can be downloaded from GoogleDocs here. If this stock is currently priced at $0.16, we estimate that there is a 40% probability of loss. We run some probability figures here, and then examine our portfolio to measure our exposure to simultaneous value bets in order to determine proper bet size.
What bet size should we use in the typical coin-toss situation with a 47% probability of loss? As a yardstick, many professional gamblers would advise risking no more than 1% of the bankroll per bet in this situation. Some would recommend a more conservative approach of 0.5% if the bankroll cannot be easily replenished. If your bet size on coin-flips is larger than what most professional gamblers feel comfortable with, it may be time to re-examine your tolerance for risk.
In summary:
1) If value investors considering special situations have one weakness, it is that they underestimate the Risk of Ruin, misapplying the concentrated position strategy to value betting.
2) Professional gamblers understand how to survive downswings. If the average value investor becomes involved in 100 value situations over a decade, the gambler is involved in tens of thousands or even millions. He understands that bet size destroys far more quickly than poor analysis.
3) When determining proper bet size, probability of loss is the most important factor.
4) Multiple, simultaneous bets require an even smaller bet size.
5) Above all else, survive! When in doubt, be conservative.
Stay tuned for Part II, which will examine if value betting is a worthwhile use of time for value investors.
[1] In You Can Be a Stock Market Genius, Greenblatt argues that bets on high-leverage spinoffs can reward shareholders with large gains without any obligation to repay debt in the event of bankruptcy.
[2] GuruFocus Article, 1 March 2013. "HNR: Bargain and Speculative Hybrid."
