Of an Expected Value Mindset

It is not whether you are right or wrong that’s important, but how much money you make when you’re right and how much you lose when you’re wrong. – Stanley Druckenmiller

Take the probability of loss times the amount of loss from the probability of gain times the amount of the possible gain. That’s what we’re trying to do. It’s imperfect, but that’s what it’s all about. – Warren Buffett

Q: How does a value investor evaluate a given investment opportunity? In baseball parlance, how does he choose either “to swing for the fences” or “make a pass”?

We begin with the definitions of Risk and Reward. Risk is often meant to refer to the “size of the loss” that could be potentially incurred. Reward is traditionally meant as the potential “size of a positive outcome”. Terms such as a higher reward or a bigger loss are common. However, for each Risk and Reward an additional variable needs to be considered.

For Reward:

  • the “Likelihood” or the “Probability” of winning to be referred as “p”
  • the size of the “Reward” or the “Payoff” in case of a win, referred as “+ve ODDS”

Similarly, for Risk:

  • the probability of failure or loss as the “q”
  • the size of the “loss” or the risk as “–ve ODDS”

The Expected Value Mindset

Value Investors ought to evaluate every investing opportunity in terms of these 4 variables. Unfailingly considering every financial situation in probability and outcome terms forms the core of a sound investment process. “While a great many people accept the concept of probabilistic decision making and even think of themselves as practitioners, very few have internalized the mindset.” – Robert Rubin

Expected value demonstrates that you can’t just focus on how often you’re right, you have to think about how much you make when you’re right versus how much you lose when you’re wrong. Put simply, always evaluate an opportunity in terms of its –ve probability (q) along with its –veOdds AND the +ve probability(p) and its accompanying +veOdds.

Expected Value = –(q*-veODDS) + (p * +veODDS)

More formally, expected value equals the weighted average value for a distribution of possible outcomes. Here’s a simple example:

Probability                  Outcome                  Weighted Value
40%                                    +20%                          +8%
30%                                    +5%                            +1.5%
30%                                    -10%                           -3%
100%                                                                     +6.5% = Expected Value

Consider the expected value for a stock that’s “priced for perfection” just prior to an earnings release. Say there’s a 70% probability that the company will meet the market’s expectations leading to a 1% stock rise. Alternatively, there is a 30% chance the company will disappoint the market, resulting in a 10% stock decline. How does this investment look?
The bet has a high +veEDGE (70%) but a poor expected value. Although the chances of a favorable outcome are high, asymmetric outcomes keep the expected value negative (70% x 1% + 30% x –10% = – 2.3%).

Take the inverse case of a downtrodden value stock. The probability of a poor outcome is 70%, resulting in a 1% decline, while a favorable outcome has a 30% chance and will produce a 10% gain. This scenario has a poor probability of a positive outcome but an attractive expected value (70% x –1% + 30% x 10% = +2.3%). See attached.

Fat Pitches by definition mean a Low:Low High High scenario. Needless to add, they result into the highest positive Expected Values.

The Expected Value WagonWheel

We can combine the 4 variables to create 16 permutations and depict them in a WagonWheel. See attached. It is worth considering the risk-reward scenario for each of the pie slices.

  • 7 sections marked “X” are termed “passes” or “rejects”. Of these, 2 are marked “XX” which means they are “unmistakably passes”.
  • 2 sections marked “S” indicate high-adrenaline areas where gamblers and speculators reside. Value investors choose to make a “pass”.
  • 2 sections marked “F”, which value investors would rather ignore. They represent a waste of his time and opportunity cost. The investor asks “Why bother?”
  • 2 sections marked “E” apply to start-up ventures and entrepreneurs (also see a case study later in this article.)
  • We are left with 3 sections out of the total 16. These are labeled the “VI-ZONEs” where a value opportunity would qualify. Of these, there is only ONE section which we shall term the “RED PITCH”. Here we find a “High p * Big +ve ODDs” coupled with “Low q * Small –ve ODDS”. In these areas, the probability of losing is small and in case of a loss the size is not large either. In addition, the probability of winning is big, and the size of the reward is large too. In coin toss parlance:
    + Heads is far more likely to show up than Tails …AND
    + In case of Heads we win big and in case of Tails we lose little.

The Art

This is ofcourse is the math which is easy to understand if we were dealing with a dice-roll or a roulette wheel whereby the Odds and the probabilities can be neatly and objectively defined. But life and investing are not a dice-roll. Determining the 4 variables in each case is the “art”.

Determining the quality and the size of Risk and the Reward are highly subjective and influenced greatly by an investor’s circle of competence, his skill and his temperament. Lastly, there is the important element of Time. In case of a dice roll, the outcome is instantaneous. In investing, the gap between an investment commitment and its outcome, often termed as the “time arbitrage” also significantly affects an investor’s behavior and the investment’s outcome.
A Case Study: Start-up Ventures

Consider the Edge/Odds criterion for “Start-up ventures” using the EV-WagonWheel. Start-ups by nature are highly “uncertain” undertakings. The probability of their success is Low. Rather, the probability of failure or the “q” is high. That is the nature of entrepreneurial ventures.

However being uncertain is NOT the same as being RISKY. Risk is defined as a “permanent loss of capital”. A venture maybe highly uncertain of success and yet may not end up losing a lot of money in case of a failure or not highly risky.

A start-ups high “q” and a low “p” is a given, but if the –ve ODDS are low AND if the +ve ODDS is high, then the venture could possibly be undertaken.

Eg. When Gates/Allen started Microsoft, the venture was highly “uncertain” of its success. But the capital that they had to invest was not high. If the venture succeeded they could win big BUT if it had failed then the loss would not lead to the founders financial ruin. (using the revolver to the head analogy, if the shot had fired, it would hurt but not kill).
– Husain Kothari
January 16th, 2013

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