Comparing Sharpe-Optimized Portfolios with Risk and Stability Measures
Summary
The discussion outlines ways to compare portfolios produced by Sharpe ratio optimization before investing. When portfolios were built using the same objective, their Sharpe ratios can be compared directly, but an in-sample ratio is only an estimate and offers limited evidence about future performance. Adjusted Sharpe ratios that account for out-of-sample performance can provide a more relevant comparison.
It also recommends resampling the construction data, through bootstrap methods or cross-validation, to see whether estimated portfolio weights are stable. The information ratio offers a benchmark-relative comparison using active returns and their variability; other possible measures include the Sortino and Omega ratios. The discussion gives no empirical results or detailed procedures, so these measures should be treated as complementary diagnostics rather than proof that a portfolio will perform well in live markets.
Key ideas
- Compare portfolios optimized under the same criterion using their Sharpe ratios.
- In-sample Sharpe ratios provide limited evidence about future performance.
- Adjusted Sharpe ratios can emphasize performance beyond the data used to construct a portfolio.
- Bootstrap resampling or cross-validation can reveal how stable estimated portfolio weights are.
- The information ratio compares active returns against a benchmark, while Sortino and Omega ratios are other possible measures.
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# Is there any way to compare portfolios created using sharpe optimization model?
# Is there any way to compare portfolios created using sharpe optimization model?
I created different portfolios using sharpe portfolio optimization model and I want to know is there any way to compare those portfolios before actually investing in them?
## Answer by develarist (score 1)
https://quant.stackexchange.com/a/49693
If they were computed with the same criterion, the Sharpe ratio, you can simply compare the different portfolios' Sharpe ratios with one another: $\frac{\mu_{1}-r_f}{\sigma(r_{1})}$ vs $\frac{\mu_{2}-r_f}{\sigma(r_{2})} \dots$ vs $\frac{\mu_{P}-r_f}{\sigma(r_{P})}$, where $r_p\in\mathbb{R}^{T\times 1}$ is the weighted return time series (vector) for portfolios $p=1,2,\dots,P$.
Adjusted Sharpe ratios that give attention to out-of-sample performance are a good indicator to see how they will perform on future, unseen data. In-sample Sharpe ratios, on the other hand, which are probably what you computed, don't imply much about future performance other than being expected values.
Resampling the data used for constructing portfolios, possibly with bootstrap replacement or K-fold cross-validation, so that you have several estimates for the portfolio weights rather than only a one-off solution, will also help establish how stable or consistent your estimates are in-sample for out-of-sample use.
The information ratio, $\frac{\mu_p-\mu_b}{\sigma(r_p-r_b)}$, compares portfolio $p$ against some benchmark portfolio $b$ based on the active return, or difference between the expected returns of the two portfolios, and the standard deviation of the difference between the running return time series (vectors) of each, $r_p\in\mathbb{R}^{T\times 1}$ and $r_b\in\mathbb{R}^{T\times 1}$. For example, portfolio $p=1$ can be compared individually to all other $P$ portfolios by letting the others take turns being the benchmark.
Other performance measures used in portfolio management are the Sortino ratio and Omega ratio.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.