Portfolio and Statistics¶
What is a Portfolio?¶
Put simply a portfolio is just a set of allocations in a variety of securities. For example:
- 20 % in APPL
- 30 % in FB
- 50% in GOOG
These percentages should add up to 100% (or if defined as weights they should add up to 1).
Key Statistics for a Portfolio¶
- Daily Returns - The percent returned from 1 day to the next for a stock.
- Cumulative Return - The amount returned after an entire time period.
- Avg. Daily Return - Mean of Daily Returns
- Std. Daily Return - Std. Dev of Daily Returns
Sharpe Ratio¶
For each case, which portfolio is better?
The Sharpe Ratio is a measure for calculating risk-adjusted return, and this ratio has become the industry standard for such calculations.
It was developed by Nobel laureate William F. Sharpe.
The formula for the Sharpe Ratio (SR):
$SR = \frac{R_p - R_f}{\sigma_p}$
- $R_p$ is Expected Portfolio return
- $R_f$ is Risk-Free Return
- $\sigma_p$ is Portfolio Standard Deviation
What is risk free return? The return you would receive if you put your money in an investment such as a bank savings account, LIBOR, Treasury Bonds that are essentially “risk-free”.
Currently in the United States (early 2017), these returns are very close to 0%, so its just easier to approximate Rf as 0.
Keep in mind though, the Federal Reserve may continue to raise interest rates in the future, effecting this result!
For now, assuming $R_f$ is 0, we get:
SR = Mean Return / Std. Dev.
Keep in mind that Sharpe originally thought of this as a yearly metric (as in mean yearly return vs. mean daily return)
This is easy to fix for us though!
Annualized Sharpe Ratio¶
The annualized Sharpe Ratio (ASR) can be obtained by multiplying against a K-Factor (K) based on your Sampling Rate:
| Frequency | K-Factor |
|---|---|
| Daily | sqrt(252) |
| Weekly | sqrt(52) |
| Monthly | sqrt (12) |
So that you just calculate ASR = K * SR