Journal of Investment Strategies

Ali Hirsa
Managing Partner, Sauma Capital LLC & Professor, Columbia University

Welcome to the fourth issue of the ninth volume of The Journal of Investment Strategies. In this issue, you will find three papers: “The price of Bitcoin: GARCH evidence from high-frequency data”, “Portfolio allocation based on expected profit and loss measures” and, finally, “Quant investing in cluster portfolios”.

For around a decade, both theoretical models and empirical studies have been trying to understand the phenomenon that is virtual currencies. Many previous studies have looked at factors related to blockchain technology and its implications for financial markets and virtual currency price formation.

In our first paper, “The price of Bitcoin: GARCH evidence from high-frequency data”, Pavel Ciaian, d’Artis Kancs and Miroslava Rajcaniova attempt to shed light on the highly complex dynamics of Bitcoin price formation by making use of high-frequency data. They estimate the price determinants of Bitcoin with a generalized autoregressive conditional heteroscedasticity (GARCH) framework using high-frequency data. First, they derive a conceptual model of Bitcoin price formation. Second, building on previous empirical studies regarding Bitcoin price formation, they apply a GARCH model to estimate factors affecting Bitcoin’s price using hourly data for the period 2013–21 using more than four million observations.

Their empirical results confirm that Bitcoin transaction demand and speculative demand have a statistically significant impact on Bitcoin price formation. This responds negatively to Bitcoin velocity, whereas positive shocks to the Bitcoin stock, interest rate and the size of the Bitcoin economy exercise an upward pressure on the Bitcoin price. The high-frequency data analyzed in this study provides additional insights that would have remained masked had the authors used averaged daily or weekly prices.

In our second paper, “Portfolio allocation based on expected profit and loss measures”,  J. H. Venter and P. J. de Jongh formulate the portfolio allocation problem by allowing both long and short positions and by taking trading and interest rate costs into account. Expressions are derived for the portfolio profit or loss (PL) that may result over a holding period. The expected profit (EP) and the expected loss (EL) are taken as measures of reward and risk. Optimal portfolios are considered to be allocations that maximize EP subject to EL being below a specified fraction of EP. Simple expressions are shown for the reward and risk contributions of individual stocks to the portfolio expected PL. This optimal portfolio approach is referred to as the EP–EL method, and it is compared with a method based on maximal expected PL subject to controlled volatility measured by expected absolute PL deviation. The calculations required for these optimal portfolios are formulated as linear programming problems.

The authors illustrate properties of the EP–EL method through extensive results based on the market trading of 12 stocks. This leads to allocations that – among others – simultaneously maximize EP and EL while keeping the latter below an acceptable fraction of the former. This paper is written for a single-period trading decision problem. However, trading is a repetitive process, and it is challenging to extend the formulation and results to take this into account. The authors assume the trader will close their positions at the end of the holding period. However, if a subsequent period requires the trader to take a position in the same stock in the portfolio of the prior period, unnecessary closing and reopening costs may occur. Hence, the basic expressions for PL should be changed to take such issues into account. The authors leave these questions to future research.

In the issue’s third paper, “Quant investing in cluster portfolios”, Ali N. Akansu, Marco Avellaneda and Anqi Xiong discuss portfolio construction for investing in a given number of assets based on partitioning the investment universe into clusters. The clusters are determined from the trailing correlation matrix via an information-theoretic algorithm that uses thresholding of high-correlation pairs. The authors calculate the principal eigenvector of each cluster from its correlation matrix and the corresponding eigenportfolio. The cluster portfolios are combined into a single N-asset portfolio based on a weighting scheme for the clusters.

Various tests conducted on components of the DJIA and a 30-stock basket of large-cap stocks indicate that the new portfolios are superior to the DJIA and other mean–variance portfolios in terms of their risk-adjusted returns from 2009 to 2019. The authors also tested the cluster portfolios for a larger basket of 373 Standard & Poor’s 500 components from 2001 to 2019. The test results provide convincing evidence that a cluster-based portfolio can outperform passive investing. The universe of stocks discussed in this paper is limited to 30 stocks. A discussion on the scalability of the proposed approach would be very useful.

On behalf of the editorial board, we hope you are doing well during the Covid-19 pandemic. We would like to thank our readers for their continued support of, and keen interest in, The Journal of Investment Strategies. We look forward to sharing with you the growing list of practical papers on a broad variety of topics related to modern investment strategies that we continue to receive from both academics and practitioners.