Portfolio Evaluation¶
Evaluation of portfolio as whole, without examining the individual securities.
However, for portfolio revision, you need to examine the individual securities.
Metrics¶
| Ratio | ||
|---|---|---|
| Sharpe | \(\dfrac{R_P - R_f}{\sigma_p}\) | Price premium per unit risk |
| Treynor | \(\dfrac{R_P-R_f}{\beta_P}\) | Price premium per unit \(\beta\) |
| Jensen \(\alpha\) | \(R_p - R_\min\) | Excess return more than required |
| Calmar | \(\dfrac{R_p}{\text{Max Drawdown}}\) | |
| Sterling | \(\dfrac{R_p}{\text{Max Drawdown} - 10 \%}\) |
Drawdown¶
Percentage peak-to-trough decline during a specific time period
Measured once a new high is reached, because a minimum cannot be measured yet since the value could decrease further
Sharpe Ratio¶
Limitations¶
Selection bias of strategies results in false-positives regarding the success of a strategy
Deflated Sharpe Ratio¶
Probability that SR is statistically-significant, after controlling for inflationary effect of
- No of independent trials with the strategy \(k\)
- List all the returns of all strategies
-
Find the independent series
-
Data Dredging \(V \left[ \widehat{\text{SR}}_k \right]\)
- Non-normality of returns: \(\hat y_3, \hat y_4\)
- Length of time series \(T\)
Can help identify if the benefits is due to chance