• Value investing is one type of positive asymmetry.
  • Other positive asymmetries exist and we need to open our minds.
  • Betting small amounts aggressively will minimize risk and enhance returns.
  • Safety lies in speculation, but only when the speculation is very aggressive.


The Limitations of Value Investing

Value investing is fairly well understood today.  The most basic definition is buying securities cheaply and selling when they become expensive.  The benefits are obvious to understand.  Your loss exposure is reduced when you buy cheaply.  Your returns are enhanced if the prices recover.  It’s one of the most powerful methods at your disposal to achieve high returns in the financial markets.

Value investing is also very limited.  It’s merely one type of positive asymmetry, a situation with low downside and high upside.  There are other ways to achieve positive asymmetries.  That’s what we’re going to discuss.  We need to open our minds to other methods.  My journey as an investor began with value investing.  That was not the end.

Let’s venture away from investing a while and expand our horizons.  We can return after a detour to the darker world of casinos, bookies, and sports betting.  There is much we can learn from this.


Lessons From Sports Betting

I’m going to state a big caveat at the very beginning of this discussion.  Do not bet on sports expecting to make money!  Due to high bookie fees and unfavorable tax treatment, each bet has a negative expected return.  Most people can’t win enough games to overcome these disadvantages.  Successful gamblers are more rare than successful investors because gambling hurdles are steeper.

With this caveat now stated, multi-game parlay bets are a good starting point for understanding power laws.  Parlays behave similarly to exchange traded options but are much easier to teach.  They embrace power laws and reduce your losses when your expected return is negative.  I aim to show this.

Let’s begin with the basics of sports betting.  The standard payout for winning a $1 bet on a single game is $1.91.  You get 100% of your initial bet returned plus a 91% profit.  The missing 9% of profit was paid as a bookie fee.  You lose 100% if your pick is wrong.  It’s also possible to tie.  For simplification I’m going to ignore ties in this discussion.

A parlay combines two or more games into a single bet.  You win the parlay if you win all the games.  If one game loses, the entire parlay is lost.  Parlays reduce your probability and frequency of winning.  In exchange, parlays reduce your risk exposure and dramatically increase your profits when you win.

For example, let’s say you bet $1 on a three game parlay and each game has a standard payout.  Your payout would be calculated by taking $1.91 times $1.91 times $1.91, which is equal to $6.97.  Your profit would be $5.97 after deducting your $1 bet.  Parlays actually give you a positive asymmetry; in this particular case you’re betting $1 to earn $5.97.  Parlays follow a power law.  Each game added to a parlay increases its payout exponentially.

Compare this to betting $1 on three games separately.  First of all, you must risk a total of $3.  If you win all three games, your profit would be $0.91 + $0.91 + $0.91, for a total of $2.73.  Betting $1 on three separate games has a negative asymmetry.  This is because you can lose $3 and win only $2.73.  Straight bets have linear payouts and do not follow power laws.  This is why most professional gamblers use parlays.

Let’s calculate the expected return of betting $1 on a single game. Assume a standard payout of $1.91 and a 50% chance of winning and losing.  Remember, we’re ignoring the possibility of ties for simplification; this will not effect the calculation.

The basic formula of expected returns for a two-outcome scenario is the following.

Expected Return = (Probability of Winning x Profit) + (Probability of Losing x Loss)

Since we have a 50% chance of winning and losing, let’s input these numbers into the formula.

Expected Return = (0.50 x Profit) + (.50 x Loss)

We know the standard profit on a $1 bet is $0.91.  We’d also lose $1 if we pick wrong.  Let’s update the equation.

Expected Return = (0.50 x 0.91) + (0.50 x -1)

Finally, we arrive at an expected return of -4.5 cents on every $1 bet.

If we bet three different times with $1, our expected return would be -13.5 cents.  This is calculated by taking -4.5 cents times 3 games.

What if we avoided three individual bets and placed $1 on a three game parlay?  Let’s calculate the expected return.  Again, we’re ignoring ties in the calculation.

Expected Return = (Probability of Winning x Profit) + (Probability of Losing x Loss)

You have a 12.5% probability of winning a three game parlay if you have a 50% probability of winning individual games.  This is calculated by taking 0.50 times 0.50 times 0.50.  Your probability of losing is then 87.5%.

Expected Return = (0.125 x Profit) + (.875 x Loss)

We calculated the profit of a three game parlay earlier at $5.97.  The loss is $1.

Expected Return = (0.125 x 5.97) + (.875 x -1)

The expected return betting $1 on a three game parlay is -12.9 cents.  As we calculated earlier, three straight bets of $1 had an expected return of -13.5 cents.  We reduced our expected loss over 4% by switching to parlay betting.

The expected losses reduce further as we increase the number of bets within our parlay.  For example, a ten-game parlay loses over 17% less than betting ten games straight.  The more you embrace power laws, the less you lose when your expected returns are negative.

The inverse applies when you have a positive expected return.  The more you embrace power laws, the more you win!  Power laws enable you to win more and/or lose less.  Either way, they’re far more potent than aiming low for linear returns!  This applies to sports parlays, exchange traded options, value investing, and everything else.


Safety Lies In Speculation

Gerald Loeb said in “The Battle For Investment Survival” that safety lies in speculation.  He believed that aiming for returns of several multiples with a small portion of your portfolio was safer than aiming for small returns with your entire portfolio.  Most value investors rejected this idea.  Value investors believe in the margin-of-safety provided by purchasing undervalued securities and diversifying across several of these investments.  Benjamin Graham created a big dichotomy between investors and speculators in “Security Analysis.”  Speculators were stigmatized as foolish gamblers and amateurs by the value investing community.

This was unfair to Loeb.  Loeb’s definition of speculation was misunderstood.  A speculator was not a foolish amateur in his context.  His definition of speculation means investing small sums of money into high payout opportunities.  He advocated risking less to earn more.  Does this sound familiar?  Loeb’s method was equivalent to using parlays in sports betting and exchange traded options in today’s markets.  Gerald Loeb was one of the earliest financiers to embrace power laws and write about it.

Loeb and Graham were both right.  Incompatible definitions of speculation caused a misunderstanding.  Both gurus advocated the use of positive asymmetries to reduce losses and enhance returns.  Their methodologies differed in significant ways but they were both successful by embracing power laws.

Both gurus had something valuable to teach.  However, if I had to choose between Loeb’s methodology and Graham’s, I would go with Loeb.  Loeb embraced power laws to a greater degree and that is why I admire him.  Graham failed to appreciate the advantages of betting small amounts to win big.  You get to keep most of your capital out of the equity markets!  During the crash of 1929, Loeb escaped with incredibly small losses while Graham nearly went bankrupt.  Paradoxically, high aggression enables better defense.

Back in Loeb’s day, he would purchase initial positions into a security and add to the position as the price went up.  He would begin selling as the price went down.  He created an early form of portfolio insurance, otherwise known as a synthetic option.

Nowadays, we have access to exchange traded options.  We can create a very high positive asymmetry by purchasing far out-of-the-money options with short expiration dates.  You can be as aggressive or tame as you like, but remember the lesson we learned from sports parlays.  You can risk less by being more aggressive!  You can also increase returns by being more aggressive!

Case Study:  Aiming For Super High Returns

Recently I decided to partake in an inverse value investment.  This is usually called a short sale.  I was looking at shares of Facebook trading with a price-to-earnings (P/E) ratio over 100 and a market capitalization near $300 billion.  Facebook is an extraordinary company but it’s clearly overvalued.  At current prices, the company needs about ten years before it could start earning an annual 10% per share, assuming it grew earnings 25% annually until 2026.

How could it grow earnings 25% another ten years?  It’s already a multi-billion dollar company! This growth rate is highly unlikely.  Facebook could be the exception and prove me wrong, but the market is pricing it as a certainty and throwing an additional premium on top! Even if Facebook maintains 25% growth another ten years, the return is still mediocre because you’re starting with such a steep P/E ratio.

I would not short sell a company based solely on overvaluation, especially a high quality one such as Facebook.  You need something else such as accounting fraud.  However, I am willing to place a long-shot bet against it.  I will risk a small amount to make high returns on the improbable event of a sharp market decline.  This is where far out-of-the-money put options become useful.

Based on its growth rate, I believe Facebook would be fairly valued with a P/E ratio of 20.  Maybe a P/E of 30 is justified but you’d have a small margin-of-safety.  That means Facebook is worth about $20-$30 per share while it trades in the market at over $100.

I look at put options with six-month expirations.  A strike price of $55 is the furthest out-of-the-money put option I can select on the exchange.  At the time, $55 puts are priced at $0.45.  If Facebook falls to $20 per share, my options would increase from $0.45 to $35.  The profit would be 76 times my initial investment.

This is clearly a long shot with a very low probability of happening.  I decide to risk a small amount, about 0.3% of my portfolio.  More than likely I’ll lose the investment.  If it does strike, it could return a potential 23% to my portfolio if Facebook shares drop to $20.

Let’s not forget that worldwide public and private debt is high.  Interest rates are low.  The stock market is overvalued.  The world is incredibly fragile.  Anything could happen to crash the market.  Overvalued companies fall much faster than undervalued ones during market panics.  My Facebook puts provide cheap insurance against such calamities.

This is one example of the long-shot bets I take with distressed securities and speculative options.  My portfolio is positioned with a positive asymmetry. The majority of my money is left out of the markets and defensively positioned.

Attribute Value
Enterprise Value/Revenue
Return on Assets
Return on Equity
Enterprise Value
Total Cash
50-Day Moving Average
200-Day Moving Average


Two things are achieved by embracing power laws very aggressively with your investments.  Most of your money is kept out of the market and not exposed to risk.  You are well positioned to take advantage of a market crash.  Second, the money you are investing has higher expected returns than a more linear strategy.  You will win far less frequently, but your big winners can make up for this in a big way.  You’ve created a positive asymmetry with low downside and a high upside, one more potent than a value investing strategy could produce in isolation.