Portfolio Evaluation¶
- Evaluation of portfolio as whole, without examining the individual securities.
- However, for portfolio revision, you need to examine the individual securities.
- Always perform evaluation using synthetic dataset (Gaussian Copula, Cholesky decomposition) to ensure portfolio will perform well in different possible scenarios
Metrics¶
| Ratio | ||
|---|---|---|
| Sharpe | \(\dfrac{R_P - R_f}{\sigma_p}\) | Price premium per unit risk |
| Sortino | \(\dfrac{R_P - R_f}{{\sigma_\text{semi}}_p}\) | Price premium per unit of downside 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¶
Non-normality leads to under-estimating the variance in sharpe ratio estimate
Selection bias of strategies results in false-positives regarding the success of a strategy
Non-Normality Adjusted Sharpe Ratio¶
\[ \hat \sigma^2 (\widehat {\text{SR}}) = \dfrac{1}{n-1} \left( 1 - \hat \gamma_3 \widehat {\text{SR}} + \dfrac{\hat \gamma_4 - 1}{4} \widehat {\text{SR}}^2 \right) \]
Deflated Sharpe Ratio¶
\[ \begin{aligned} \text{DSR} &= P(\text{SR}^* \le \widehat {\text{SR}} ) \\ &= \Phi \left( \dfrac{ \text{SR}^* - \widehat {\text{SR}} }{\hat \sigma(\widehat {\text{SR}})} \right) \end{aligned} \]
- \(\text{SR}^* =\) benchmark sharpe ratio
- \(\widehat{\text{SR}} =\) estimated sharpe ratio of portfolio
- \(\phi=\) cdf of normal distribution
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