# 感悟沉甸甸，心智亮晶晶

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## Sharpe ratio and Kelly formular

(2011-06-08 09:44:46) 下一个

Sharpe ratio to choose a good game and Kelly formular to decided how to play.

Sharpe ratio

The Sharpe ratio is a measure of the excess return (or risk premium) per unit of risk in an investment asset or a trading strategy.
S = (R – r) / σ：

R = Return（ave return）

r = Non risk return（e.g bond）

σ = Standard Deviation

http://en.wikipedia.org/wiki/Sharpe_ratio

In general, a good game has Sharpe ratio over 1.

Example :
R=10%
r=3.5%
σ=16%
S=(10-3.5)/16=0.406

in every 6 years (averagely), there is a year that the return is lower than -6% (beyond 1σ)

2. Kelly Formula
http://en.wikipedia.org/wiki/Kelly_criterion
f^{*} = (bp - q)/b
where:

* f* is the fraction of the current bankroll to wager;
* b is the net odds received on the wager (that is, odds are usually quoted as "b to 1")
* p is the probability of winning;
* q is the probability of losing, which is 1 − p.

f* = 投注金额占总资金的比例

p = 获胜的概率

q = 失败的概率，q = 1-p

b = 赔率，例如在轮盘赌中押单个数字，b = 35，押红黑，b = 1。

\$10000 * (1 * 0.51 - 0.49)/ 1 = \$200

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