# Financial Math FM/Sharpe ratio

## Sharpe ratio

Sharpe ratio is defined as follows:

${\displaystyle S={\frac {{\bar {r_{p}}}-r_{f}}{\sigma }}}$

where

${\displaystyle {\bar {r_{p}}}}$: Expected portfolio return
${\displaystyle r_{f}}$:Risk free return rate (such as that of the 10-year US treasury bond)
${\displaystyle \sigma }$:Portfolio standard deviation

Sharpe ratio is the equation above developed by Nobel laureate William F. Sharpe to measure risk-adjusted performance. The Sharpe ratio tells us whether a investment is smart or not. The higher the sharpe ratio is, the more return the asset gives for the same risk. In other words, the higher the sharpe ratio is, the better the investment becomes.

Graphically, you're on the straight line joining cash to the Efficient Frontier, and moving to the left.