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Market risk and Bitcoin returns

Annals of Operations Research volume 294, pages 453–477 (2020)Cite this article

Abstract

Bitcoin is emerging as a distinct asset class among investors given its seemingly detached price behavior relative to market and economic fundamentals. Its incomparably high returns in recent years has further fuelled intense interest and investment into Bitcoin and cryptocurrencies at large. This paper cautions that Bitcoin prices, despite their seemingly attractive independent behavior relative to economic variables, may still be exposed to the same types of market risks which afflict the performance of conventional financial assets. Using a Markov regime-switching model to distinguish between regimes of high and low Bitcoin price volatility, this paper shows that while returns on the aggregate market portfolio cannot explain Bitcoin returns, other asset pricing risk factors, such as interest rates and implied stock market and foreign exchange market volatilities, are important determinants of Bitcoin returns. Distinguishing between periods of high and low Bitcoin price volatility reveals heterogeneity in the explanatory power of market risk factors; in particular, Bitcoin returns are more difficult to explain during periods of high volatility relative to periods with low volatility. This finding can partially explain why extant studies, which neglect to distinguish between exchange rate regimes in Bitcoin, have difficulty linking Bitcoin prices to economic fundamentals.

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Notes

  1. The Federal Reserve Board recently has begun examining blockchain technologies and the distributed public ledger framework which serves as the backbone for validating Bitcoin transactions and tracking the ownership of each Bitcoin (Mills et al. 2016). Federal Reserve Chairwoman Janet Yellen has also publicly spoken about cryptocurrencies and stated that the Federal Reserve does not have the authority to regulate digital currencies (Wall Street Journal 2014). The original 2009 paper on blockchain which started Bitcoin and spurred the development of other cryptocurrencies is authored pseudonymously by "Satoshi Nakamoto" (Nakamoto 2009).

  2. Bitcoin traders often refer to large speculators who sway prices in one direction or another in a short period of time as "Bitcoin whales." These "whale traders" hold a significant quantity of Bitcoins and can sway the market towards their preferential price (NewsBitcoin 2017). One approach they utilize is a technique known among Bitcoin traders as "rinse and repeat." This technique involves selling a large quantity of Bitcoins below their market price and causing a short-run panic and ensuing sell-off by other small traders. This leads to declining Bitcoin prices and a cunning buy opportunity by the whale trader who caused the panic in the first place. This technique is known as "rinse and repeat" because after the whale trader lowers the price (rinse) and repurchases even a larger portion of Bitcoins, they can proceed to replicate (repeat) this strategy indefinitely.

  3. The respective press releases of the FOMC statements detailing QE3 and QE4 can be found here (along with explanations for the target range of 0–1/4 percent for the federal funds rate): https://www.federalreserve.gov/newsevents/pressreleases/monetary20120913a.htm (QE3) and https://www.federalreserve.gov/newsevents/pressreleases/monetary20131218a.htm (QE4).

  4. The press release for this FOMC statement can be found here: https://www.federalreserve.gov/newsevents/pressreleases/monetary20151216a.htm.

  5. See footnote (9) of Bali and Engle (2010), who entertain various volatility estimates and, when taking first-differences, use these estimators as a proxy for volatility shocks. It is important to note that logarithmic first-differences are taken for FXVOL while logarithmic levels are taken for VIX. In rolling unit root tests (not tabulated for brevity), FXVOL is non-stationary at various time windows while VIX appears consistently stationary throughout the sample. Thus, logarithmic first-differences of FXVOL are taken while only logarithmic levels of VIX are taken. Goyal and Santa-Clara (2003) explain why taking logarithmic levels of volatility can help in asset pricing tests.

  6. Various kernel-based sum-of-covariances estimators and autoregressive spectral density estimators are entertained for all the transformed data series to check the robustness of the PP test (they yield qualitatively analogous findings but are not tabulated for brevity). The choice of using a kernel-based estimator versus a spectral density estimator does not systematically affect the aforementioned findings in any substantive way.

  7. The expected duration for the high volatility regime (state 1) is \( \mathop \sum \nolimits_{k = 1}^{\infty } k \times {\text{p}}_{11}^{k - 1} \left( {1 - {\text{p}}_{11} } \right) = 1/\left( {1 - {\text{p}}_{11} } \right) \) while for the low volatility regime (state 2) it is \( 1/\left( {1 - {\text{p}}_{22} } \right) \). More details are provided in Hamilton (1989, p. 374).

  8. The Sharpe ratio for Bitcoin returns, \( R_{t} \) is \( \left( {R_{t} - r_{f} } \right)/\upsigma \) whereby \( r_{f} \) denotes the risk-free rate. This is obtained from Professor Kenneth French's website and it consists of the 1-month Treasury bill return. The denominator for the Sharpe ratio is the standard deviation of Bitcoin returns, \( \sigma \). The VaR for Bitcoin returns is calculated as follows: \( {\text{VaR}} = W\left( {\mu\Delta t - n\sigma \sqrt {\Delta t} } \right) \) whereby \( \mu \) is the mean return for Bitcoin; \( W \) is the value of the portfolio invested in Bitcoin; \( n \) is the number of standard deviations depending on the confidence level; \( \sigma \) is the standard deviation of Bitcoin returns; \( \Delta t \) is the time window. More discussion and derivations of VaR and MVaR can be found in Signer and Favre (2002).

  9. In regression estimates (not tabulated for brevity) of currency futures market returns against \( MKT \) and using the same sample period that is used to examine Bitcoin prices, it can be shown that currency futures generally maintain a stable and statistically significant relation to \( MKT \). This conclusion is reached when examining the returns of the following currency futures markets (Bloomberg code indicated in parentheses): Australian Dollar (AD1), British Pound (BP1), Canadian Dollar (CD1), Euro (EC1), Japanese Yen (JY1), New Zealand Dollar (NV1) and Swiss Franc (SF1), respectively.

  10. Using the same sample period that is used to investigate Bitcoin, and when regressing \( CRSP \) returns against \( DEF \), we can show that rises in \( DEF \) (worsening credit conditions) are associated with declining \( CRSP \) returns (not tabulated for brevity). This type of negative relation between stock market returns and \( DEF \) is commonplace in empirical asset pricing tests yet, given Bitcoin's detached price behavior in relation to stock prices, it is not surprising to see that credit conditions bear a statistically negligible relation to Bitcoin returns.

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  1. Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA, 01609, USA

    Dimitrios Koutmos

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Koutmos, D. Market risk and Bitcoin returns. Ann Oper Res 294, 453–477 (2020). https://doi.org/10.1007/s10479-019-03255-6

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Keywords

  • Asset pricing
  • Bitcoin
  • Markov switching model
  • Risk-return tradeoff

JEL Classification

  • G12
  • G17
  • G23