Alternative measures of risk

Introduction to Portfolio Analysis in Python

Charlotte Werger

Data Scientist

Looking at downside risk

Graph of upside and downside risk

A good risk measure should focus on potential losses i.e. downside risk

Sortino ratio

Similar to the Sharpe ratio, just with a different standard deviation
$ Sortino \; Ratio = \frac{R_p - R_f}{\sigma_d}$
$\sigma_d$ is the standard deviation of the downside.

Downside risk calculation

Sortino ratio in python

# Define risk free rate and target return of 0
rfr = 0
target_return = 0

# Calcualte the daily returns from price data
apple_returns=pd.DataFrame(apple_price.pct_change())

# Select the negative returns only 
negative_returns = apple_returns.loc[apple_returns['AAPL'] < target]

# Calculate expected return and std dev of downside returns
expected_return = apple_returns['AAPL'].mean()
down_stdev = negative_returns.std()

# Calculate the sortino ratio
sortino_ratio = (expected_return - rfr)/down_stdev
print(sortino_ratio)

0.07887683763760528

Maximum draw-down

The largest percentage loss from a market peak to trough
Dependent on the chosen time window
The recovery time: time it takes to get back to break-even

Draw-downs of the S&P500 over time

Maximum daily draw-down in Python

# Calculate the maximum value of returns using rolling().max()
roll_max = apple_price.rolling(min_periods=1,window=250).max()

# Calculate daily draw-down from rolling max
daily_drawdown = apple_price/roll_max - 1.0

# Calculate maximum daily draw-down
max_daily_drawdown = daily_drawdown.rolling(min_periods=1,window=250).min()

# Plot the results
daily_drawdown.plot()
max_daily_drawdown.plot()
plt.show()

Maximum draw-down of Apple

Maximum draw-down plot of Apple prices

Let's practice!

Introduction to Portfolio Analysis in Python