Kelly Portfolio Analysis

user portfolio weights

x

1

0.3

x

2

0.2

x

3

0.4

expected returns [/yr]

r0

0.1

r

1

0.2

r

2

0.17

r

3

0.14

volatility 

1/2

yr



σ

1

0.3

σ

2

0.26

σ

3

0.17

correlations

ρ

12

0.25

ρ

31

0.19

ρ

32

-0.22

horizon [yr]

t

1

Given a set of assets (characterized by their expected returns, volatilities, and correlations), the Kelly criterion says to choose the asset weights that maximize expected portfolio return.

In the plot,

R

is the continuously compounded portfolio return (a random variable), the

x

axis is the standard deviation of

R

, and the

y

axis is its expectation. Further, the Kelly portfolio is shown in red (and its asset weights are tabulated at the top, starting with the risk-free asset weight, with leverage allowed), the user portfolio is shown in yellow, and the individual assets (including the risk-free asset) are shown as blue dots. The solid blue line is the boundary of all possible portfolios; the upper boundary is the Kelly efficient frontier. (It rolls over because the Kelly efficient frontier, unlike the Markowitz efficient frontier, is multi-period.)

In this Demonstration, a portfolio weight of 1 means 100% (shorting of assets is also allowed), a return of 0.10/yr means 10%/yr, and a volatility of 0.20 means 20%/

1/2

yr

(which means that in 1 year the standard deviation of return is 20%/yr and that in 4 years the standard deviation of return is 10%/yr).