Statistical Expectancy to Calculate Risk


The world does not run on absolute certainty, yet the strategic decisions we choose affects future outcomes somehow. The irony seems amplified with those who understand little toward statistical expectancy. Having adequate grasp of this subject makes a more informed investor for any business or personal desires.

The concept is simple.

E = Expectancy

P(w)= Probability of winners

S(w)= Average winner Size

P(l)= Probability of losers

S(l)= Average loser size

E = [P(w)*S(w)]-[P(l)S(l)]

E.g. let’s look at New Zealand finance companies. They pledge to provide retail investors a slightly above the government bond interest rate as long as their own investments do not experience corrections or draw-downs. Historically speaking, credit markets have a positive correlation to the general economy, and the world has experienced at least 2 years of recession each decade, or 2 out of each 10 years. From this we can conclude that these companies will not end every single year profitably.

I.e. the rough probability of a losing year is then 2/10=0.2 or 20%, and the probability of them ending each year profitably stands at 1-2/10=0.8 or 80% at best. They offer retail investors annual rates of roughly 9.x% (I’ll round it up to 10%) in the years they make performance targets, and in a bearish year the average investor looks to take a loss of 30% to 70%, averaging 50%.

So can the average retail investor “expect” to profit over the long run using these companies?

Probability of a profitable year: (80% or 0.8)

Average investor profit: (10% or 0.1)

Probability of a bad year: (20% or 0.2)

Average investor loss: (50% or 0.5)

E= (0.8)(0.1)-(0.2)(0.5)


E= -0.02

A negative expectancy suggests a net loss will likely occur in the long run. In fact the average roulette player has a less negative expectancy than the above; in other words you would likely lose less money playing roulette at the casino than investing with the finance companies.

To make profit or receive greater reward consistently, you need the odds on your side. Having a positive expectancy remains one of few ways to verify that. So learn the math, and make wiser decisions.


Source by Rocko Chen

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