Consider These Two Trading Strategies...

Strategy 1 underperform Strategy 2
That's it.

Horizontal Axis (Y) is P(Gain) from 0 to 1
The vertical one is the expected profit.
X-intercept is break even ...

I assume you to risk 1%.

 

Expected value:

E(A) = 0.6(+1) + 0.4(-1) = 0.2

E(B) = 0.4(+2) + 0.6(-1) = 0.2

Kelly fraction:

K(A) = 0.6/|-1| - 0.4/1 = 0.2

K(B) = 0.4/|-1| - 0.6/2 = 0.1


A is clearly superior.

 

I agree that on paper A is superior.
But in practice I'd choose B.

 

Yes!

Consider doing half kelly bets. If so, after 100 bets, your acct is at 4.52x with strategy A compared to 2.09x for strat B.

A is definitely better. Food for thought.

 

The expected value is gain per unit bet. Same for both strats.

The Kelly fraction tells how many units to bet.

Clearly strategy A is superior.

 

The prob of a 5 straight losses is 1% in A and 7% in B. So for the same expected value you have less risk of permanent impairment of capital. Consistent with Kelly calculations above.

It's interesting to see who focuses on gains and who focuses on losses in this discussion.

 

On Paper Ok.
But in Practice, Especially Full Kelly, I'll bet on your Quick bankruptcy with A.

 

Use half kelly

 

I reformulate for half:

But in Practice, I'll bet on your bankrupty with A.

 

No you have more risk. You're more prone to be ruined with A than B.