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?


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.

  • $\begingroup$ Will I be able to compute those ratios prior to investing in them? $\endgroup$ Nov 15 '19 at 1:38
  • $\begingroup$ based on in-sample (training) data, yes. these will merely help form expectations of out-of-sample results, based purely on historical information, were the user to decide to actually commit capital $\endgroup$
    – develarist
    Nov 15 '19 at 1:43

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