The objective of this study is to evaluate assets' performance by considering the exit time within the risk measurement framework alongside Shannon entropy and, alternatively, excluding these factors, which can be used to create a portfolio aligned with short- or long-term objectives. This portfolio effectively balances the potential risks and returns, guiding investors to make decisions that are in line with their financial goals. To assess the performance, we used data envelopment analysis (DEA), whereby we utilized the risk measure as an input and the mean return as an output. The stop point probability-CVaR (SPP-CVaR) was the risk measurement used when considering the exit time. We calculated the SPP-CVaR by converting the risk-neutral density to the real-world density, calibrating the parameters, running simulations for price paths, setting the stop-profit points, determining the exit times, and calculating the SPP-CVaR for each stop-profit point. To account for negative data and to incorporate the exit time, we have proposed a model that integrates the mean return and SPP-CVaR, utilizing DEA. The resulting inefficiency scores of this model were compared with those of the mean-CVaR model, which calculates the risk across the entire time horizon and does not take the exit time and Shannon entropy into account. To accomplish this, an analysis was conducted on a portfolio that included a variety of stocks, cryptocurrencies, commodities, and precious metals. The empirical application demonstrated the enhancement of asset selection for both short-term and long-term investments through the combined use of Shannon entropy and the exit time.
Keywords: CVaR; SPP-CVaR; Shannon entropy; data envelopment analysis; portfolio performance evaluation; risk management; stop strategy.