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The volatility of bitcoin (BTC) and time horizon is the center point for investment decisions. However, attention is not often drawn to the relationship between BTC and equity indices. Thus, the purpose of this paper is to investigate the volatility and time frequency domain of BTC with stock markets.

This study investigates the role of cryptocurrencies in enhancing the performance of portfolios constructed from traditional asset classes. Using a long sample period covering not only the large value increases but also the dramatic declines during the beginning of 2018, the purpose of this paper is to provide a more complete analysis of the dynamic nature of cryptocurrencies as individual investment opportunities, and as components of optimal portfolios.

The mean-variance optimization technique of Merton (1990) is applied to develop the risk and return characteristics of the efficient portfolios, along with the optimal weights of the asset class components in the portfolios.

The authors provide evidence that as a single investment, the best cryptocurrency is Ripple, followed by Bitcoin and Litecoin. Furthermore, cryptocurrencies have a useful role in the optimal portfolio construction and in investments, in addition to their original purposes for which they were created. Bitcoin is the best cryptocurrency enhancing the characteristics of the optimal portfolio. Ripple and Litecoin follow in terms of their usefulness in an optimal portfolio as single cryptocurrencies. Including all these cryptocurrencies in a portfolio generates the best (most optimal) results. Contributions of the cryptocurrencies to the optimal portfolio evolve over time. Therefore, the results and conclusions of this study have no guarantee for continuation in an exact manner in the future. However, the increasing popularity and the unique characteristics of cryptocurrencies will assist their future presence in investment portfolios.

This is one of the first studies that examine the role of popular cryptocurrencies in enhancing a portfolio composed of traditional asset classes. The sample period is the largest that has been used in this strand of the literature, and allows to compare optimal portfolios in early/recent subsamples, and during the pre-/post-cryptocurrency crisis periods.

Perhaps the most popular pricing model among Bitcoin enthusiasts is the stock-to-flow (S2F) model. The model gained significant traction after successfully predicting the meteoric rise of Bitcoin prices from late 2020 to early 2021. This paper dissects the S2F model for Bitcoin empirically to determine its viability and investigate whether investors can profit from an S2F-based trading strategy.

This paper, dissects the S2F model for Bitcoin by putting it through a battery of tests to examine its design, characteristics, robustness and appropriateness.

Overall, this paper finds the S2F model to be insensitive to differing assumptions in the early stages of the model, alleviating concerns about data mining. This paper produces a dynamic S2F model with no peek-ahead bias and shows evidence that prediction accuracy increases over time. Finally, this paper shows that a dynamic trading strategy that goes long (short) when Bitcoin is undervalued (overvalued) according to S2F is far less profitable than a classic buy-and-hold strategy.

To the best of the authors’ knowledge, this is the first paper to analyze the S2F model in an academic setting by providing a rigorous assessment of the model's construction. This paper demonstrates how the model can be implemented realistically without the peek-ahead bias, creating a tool that can be used contemporaneously by investors.