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# Evaluating Risk Vs Reward With Kelly

|Includes: Tonix Pharmaceuticals Holding Corp. (TNXP)

BESTFIT data is fast approaching for Tonix Pharmaceuticals (NASDAQ:TNXP) and we got a question about evaluating the risk vs reward, so we wanted to do a quick post about the Kelly Criterion.

This is a formula that prescribes the optimal % of assets to wager given the risk vs reward:

a formula used to determine the optimal size of a series of bets. In most gambling scenarios, and some investing scenarios under some simplifying assumptions, the Kelly strategy will do better than any essentially different strategy in the long run (that is, over a span of time in which the observed fraction of bets that are successful equals the probability that any given bet will be successful). It was described by J. L. Kelly, Jr in 1956

Some more:

The History
John Kelly, who worked for AT&T's Bell Laboratory, originally developed the Kelly Criterion to assist AT&T with its long distance telephone signal noise issues. Soon after the method was published as "A New Interpretation Of Information Rate" (1956), however, the gambling community got wind of it and realized its potential as an optimal betting system in horse racing. It enabled gamblers to maximize the size of their bankroll over the long term. Today, many people use it as a general money management system for not only gambling but also investing.

So given the probability of an event, and the ratio of the upside vs the downside of that event, the Kelly formula prescribes the optimal % of assets to wager.

Here's the Formula:

% to wager = [(R times W) - L)] / R

R is the Ratio of the upside vs the downside

W is the probability of Winning

L is the probability of Losing (which is calculated as 1 − W)

For example:

Let's say someone gives you favorable 3 to 1 odds on a coin flip, what do you do? Things are clearly in your favor, but you still have a 50% chance of losing. Let's ask Kelly:

The W and L are both .5 because there is a 50% chance of predicting a coin flip (1 would be 100% chance), and the R is 3 (upside to downside is 3:1).

% to wager = [(R times W) - L)] / R

% to wager = [(3 times .5) - .5] / 3

% to wager = [(1.5) - .5] / 3

% to wager = 1 / 3

% to wager = 33.3%

So if somebody gives you 3 to 1 odds on a coin flip, Kelly says you should bet one third of your assets.

What if it is 10 to 1 odds on a coin flip? So tempting, yet a 50% chance of losing. Kelly?

% to wager = [(10 times .5) - .5] / 10

% to wager = [(5) - .5] / 10

% to wager = 4.5 / 10

% to wager = 45%

A big chunk, but more than half stays safe.

Tonix

So we can apply this to Tonix at each step of the way with a (1) post-data price target and (2) odds of good data.

R is calculated:

Price Target on Good Data / (Current Price - Price Target on Bad Data)

All for now, one caveat is that we think the Kelly formula is a good input, but nothing like the final word, which of course should have more to do with one's own personal risk tolerance.

PS

We happen to think the odds of good data are considerably better than 50%, we are not trying to imply anything with the coin flip example.

Disclosure: The author is long TNXP.