### Coin Toss Explained.

A Simple concept of coin toss (probability and risk data coming out of it) is a wonderful way to bring home the point of Risk Management.

This would appear to be kinder-garden stuff, but trust me, be it maths, poker, chess or stock markets, you gain BIG when you have got the basics right!!

Assumptions:

• The coin is fair: It has 02 sides, head and tail clearly demarked.
• You are Not Intoxicated or atleast sober enough to record the outcome of the coin toss.
• Basic Excel Skills

So, we know that Probability of a coin showing either HEAD or TAIL is 50%.

What is Probability, (It is simply the likelihood of an event to happen, expressed as a percentage ratio to number of attempts)

So for example, If I play chess with Magnus Carlsen a 100 times, chances of me beating him are 0 (unless I slip a roofie in his water bottle). And therefore Magnus has a probability of 100%.

Let us take a more even example, If somebody throws a difficult catch at me, I am likely to catch it 06 out of 10 times. This gives me a probability of 60%

NOW, you need to put the win rate of your trading system in this PROBABILITY column.

#### Rules of the Game:

We are LONG HEADS. (No shorting, that would complicate the example). We will earn if coin lands head and lose if it shows tail.

Our initial equity is Rs:1000/ and there are No table limits (you can bet as much/less as you want)

If you win, you get 2R and if you lose u lose 1R. (Where R is the amount you wagered). So if you go bizerk and bet the entire 1k on a single bet, you will either double your money or go bankrupt.

Now, there are basically 02 ways you can decide how much you want to bet. 01 is by way of your GUT feel and the other is probability based Optimized betting.

Lets admit it, 90% of us bet based on our “FEEL”. The conviction is developed based on narrative we are fed. (or as we would like to believe, the valuable information we have gathered by doing “Research” and “hard work”)

To improve this Gut based betting, we can come up with a system of allocation, without which we are subject and slave to our moods and fancies. Make no mistake, If you are going thru divorce, those court proceedings will show up on your equity curve.

A system is a logic and reason based method that tells you how much to wager. System removes ambiguity from the game. The biggest benefit of removing this ambiguity is the REMOVAL OF REGRET.

I know atleast 10 good to great investors who regret not betting enough on Avanti feeds. My partner regrets not betting big (enough) on symphony, relaxo and Kilpest when he spotted them dirt cheap.

Stock market is a game of regret. If your stock goes up, regret is you did not bet enough, if it goes down regret is you bet too much.  Selling the stock has same set of regrets.

System betting takes away the emotion of REGRET. You bet based on your historic probability.

Read this amazing article written by Ed Seykota where he Optimizes the coin toss with simulation.

Notice a fascinating thing about optimized betting. There is a SWEET SPOT that you need to arrive at. If you bet less, it won’t be worth your effort (Opportunity cost). If you bet big, you start losing money and fast.

In the above example, where probability is 50% and win/loss is 2:1. The optimal bet size is 25%.

How to calculate this,

Read this Paper Written by Mr Kelly Himself. (where he explains the maths behind the concept)

In short, it is

K = W – (1-W)/R

where K is your bet size, W is win rate and R is payoff.

You can plot your system’s parameters into this webpage and see what is the optimal bet size you should deploy.

## KELLY ON #MWM (MysticWealth momentum)

When we inserted our historic (backtest and Live) probability numbers into Kelly formula. Kelly told us to go ahead and bet 10% of our corpus into each bet.

BUT REMEMBER, Kelly is a Optimal bet sizing mechanism. It is optimized to generate maximum return, it doesn’t care about drawdowns.

We at MysticWealth (for MWM) therefore follow half Kelly . We bet less than 50% of what Kelly suggests and therefore you see every new bet is allocated 5% of the portfolio.

If you reverse engineer it, you would realize that a fund manager using kelly formula has a 1/3 chance of halving a bankroll before doubling it, and  a “half kelly” bettor only has a 1/9 chance of halving their bankroll before doubling it.

A lot of fund managers use Kelly betting to gather big AUM in bull markets only to suffer massive drawdowns later.

Position betting should be done in such a way that worse case scenario should not throw you out. You should be aware of your pain threshold at all times.

Here, Listen to this podcast I did with Ralph Vince (A pioneer in the field of Risk management, optimal betting) answering these questions.

Here are few book recommendations if this topic interests you.

Taking Chances

Fortune Formula

A man for All Markets

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