Risk adjusted returns
Introduction to Portfolio Analysis in Python
Charlotte Werger
Data Scientist
Choose a portfolio
$ $
Portfolio 1
- Annual return of 14%
- Volatility (standard deviation) is 8%
$ $
Portfolio 2
- Annual return of 6%
- Volatility is 3%
Risk adjusted return
$$
- It defines an investment's return by measuring how much risk is involved in producing that return
- It's usually a ratio
- Allows you to objectively compare across different investment options
- Tells you whether the return justifies the underlying risk
Sharpe ratio
- Sharpe ratio is the most commonly used risk adjusted return ratio
- It's calculated as follows:
$ Sharpe \; ratio = \frac{R_p - R_f} {\sigma_p} $
Where: $ R_p$ is the portfolio return, $R_f$ is the risk free rate and ${\sigma_p} $ is the portfolio standard deviation
Remember the formula for the portfolio ${\sigma_p} $?
- $ \sigma_p = \sqrt(Weights \; transposed (Covariance \; matrix \; * \; Weights)$)
Annualizing volatility
$$
- Annualized standard deviation is calculated as follows: $ \sigma_a=\sigma_m * \sqrt{T} $
- $ \sigma_m $ is the measured standard deviation
- $ \sigma_a $ is the annualized standard deviation
- T is the number of data points per year
- Alternatively, when using variance instead of standard deviation; $ \sigma_a^2=\sigma_m^2 * {T} $
Calculating the Sharpe Ratio
# Calculate the annualized standard deviation
annualized_vol = apple_returns.std()*np.sqrt(250)
print (annualized_vol)
0.2286248397870068
# Define the risk free rate
risk_free = 0.01
# Calcuate the sharpe ratio
sharpe_ratio = (annualized_return - risk_free) / annualized_vol
print (sharpe_ratio)
0.6419569149994251
Which portfolio did you choose?
$ $
Portfolio 1
- Annual return of 14%
- Volatility (standard deviation) is 8%
- Sharpe ratio of 1.75
$ $
Portfolio 2
- Annual return of 6%
- Volatility is 3%
- Sharpe ratio of 2
Let's practice!
Introduction to Portfolio Analysis in Python
