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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

Type Metric Comment
Excess Inflation Adjusted Return \(\dfrac{1 + R_{P_{t_1, t_2}}}{1+\pi_{t_1, t_2}} - 1\)

\(\pi_{t_1, t_2} = \dfrac{\text{CPI}_{t_2} - \text{CPI}_{t_1}}{\text{CPI}_{t_1}}\)
Return corrected for inflation Corrects for past, not necessarily indicative of future
Jensen \(\alpha\) \(R_p - R_\min\) Excess return more than required
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 \(\beta\)
Calmar \(\dfrac{R_p}{\text{Max Drawdown}}\)
Sterling \(\dfrac{R_p}{\text{Max Drawdown} - 10 \%}\)
Omega \(\dfrac{P(\text{gain}) \times \mu_\text{gain}}{P(\text{loss}) \times \mu_\text{loss}}\)

\(\dfrac{R_p - R_f}{\sum \min \{ w R_{pt} - R_f, 0 \}}\)

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

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

image-20240312125247782

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

image-20240312124816425

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

Last Updated: 2025-07-26 ; Contributors: AhmedThahir, web-flow

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