Recent research has demonstrated that many mean-variance and shortfall-based optimal portfolio selection fail to out-perform the Naive (1/n) Portfolio in out-of-sample testing. This paper revisits this line of inquiry by applying the Naive and Sharpe Portfolios to 1100 sector-specific S&P 500 re-sampled data sets from the 2007-2021 time frame. Using April 2020 as the baseline train-test split break point, the Naive Portfolio delivers statistically significantly superior Sharpe Ratios in the test data in ten of the eleven sectors. However, the Sharpe Portfolio delivers statistically significantly superior shortfall values in all eleven sectors in the test data. Using March 2020 and May 2020 as alternative breakpoints gave similar results to the baseline analysis. Interestingly, when the data set was truncated at February 2020 (i.e., before the Covid correction) the Sharpe Portfolio returned statistically significantly better Sharpe Ratios than the Naïve Portfolio in the test data in all but the Energy sector; as in the baseline analysis, the Sharpe Portfolio returned statistically significantly superior shortfall values for all eleven sectors. Thus, the Sharpe Portfolio can deliver acceptable out-of-sample performance, but the conditions for success appear to vary by sector and test data erraticism.

Gold has been traditionally well recognized as a safe heaven for financial markets. Lately, Bitcoin has been gradually considered as a popular alternative. Since the outbreak of COVID-19 in early 2020, it has become even more necessary and critical to examine the diversification capability of them to hedge financial risks associated with an unexpected crisis comparable to the pandemic. This paper hence employs the wavelet analysis, complemented by the multivariate DCC-GARCH approach, to measure the coherence of the gold and Bitcoin prices with six representative stock market indices, three for developed economies and three for emerging economies, all of which are heavily affected by the pandemic. To have a more balanced and comprehensive analysis, two-year data are used, spanning from 12th April 2019 to 15th April 2021, which covers approximately one year before and one year after the announcement of the COVID-19 pandemic. The results suggest that the returns of both gold and Bitcoin are generally not strongly correlated with the market returns of all six indices, particularly for short-term investment horizons. That is, investors in all six indices can benefit through gold, as well as Bitcoin, in terms of hedging. Meanwhile, compared with Bitcoin, gold shows to be less correlated with the indices, particularly for long-term investment horizons. The findings hence suggest that gold and Bitcoin offer diversification benefits to investors in the market indices during a crisis such as the COVID-19 pandemic, especially for short-term investment horizons. The study also reminds policymakers thinking beyond the pandemic about the future of the earth, including air pollution and health, for sustainable development of the whole world.