Sharpe ratio and Sortino ratio

Financial Trading in Python

Chelsea Yang

Data Science Instructor

Which strategy performs better?

Strategy 1:

Return: 15%
Volatility (standard deviation): 30%

Strategy 2:

Return: 10%
Volatility (standard deviation): 8%

Risk-adjusted return

Make performance comparable among different strategies
A ratio that describes risk involved in obtaining the return

Risk vs. reward

Sharpe ratio

$$ \text{Sharpe Ratio} = (R_p - R_r)/\sigma_p $$

$R_p $: Return of a strategy, portfolio, asset, etc.
$R_r $: Risk-free rate
$\sigma_p $: Standard deviation of the excess return ($R_p-R_f$)

The bigger the Sharpe ratio, the more attractive the return

Now choose again

Strategy 1:

Return: 15%
Volatility (standard deviation): 30%
Sharpe ratio: 15%/30% = 0.5

Strategy 2:

Return: 10%
Volatility (standard deviation): 8%
Sharpe ratio: 10%/8% = 1.25

Obtain Sharpe ratio from bt backtest

resInfo = bt_result.stats

# Get Sharpe ratios from the backtest stats
print('Sharpe ratio daily: %.2f'% resInfo.loc['daily_sharpe'])
print('Sharpe ratio monthly %.2f'% resInfo.loc['monthly_sharpe'])
print('Sharpe ratio annually %.2f'% resInfo.loc['yearly_sharpe'])

Sharpe ratio daily: 0.49
Sharpe ratio monthly 0.48
Sharpe ratio annually 1.34

Calculate Sharpe ratio manually

# Obtain annual return
annual_return = resInfo.loc['yearly_mean']

# Obtain annual volatility
volatility = resInfo.loc['yearly_vol']


# Calculate Sharpe ratio manually
sharpe_ratio = annual_return / volatility
print('Sharpe ratio annually %.2f'% sharpe_ratio)

Sharpe ratio annually 1.34

Limitations of Sharpe ratio

Penalize both the "good" and "bad" volatility
Upside volatility can skew the ratio downward

Sharpe ratio limitations

Sortino ratio

$$ \text{Sortino Ratio} = (R_p - R_r)/\sigma_d $$

$R_p $: Return of a strategy, portfolio, asset, etc
$R_r $: Risk-free rate
$\sigma_d $: Downside deviation of the excess return ($R_p-R_f$)

Downside vol

Obtain Sortino ratio from bt backtest

resInfo = bt_result.stats

# Get Sortino ratio from backtest stats
print('Sortino ratio daily: %.2f'% resInfo.loc['daily_sortino'])
print('Sortino ratio monthly %.2f'% resInfo.loc['monthly_sortino'])
print('Sortino ratio annually %.2f'% resInfo.loc['yearly_sortino'])

Sortino ratio daily: 0.70
Sortino ratio monthly 0.86
Sortino ratio annually 2.29

Let's practice!

Financial Trading in Python