Skip to main content

Market risk and Bitcoin returns

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.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3

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.

References

  • Ang, A., & Chen, J. (2007). CAPM over the long run: 1926–2001. Journal of Empirical Finance, 14(1), 1–40.

    Google Scholar 

  • Bali, T. G., Cakici, N., Yan, X. S., & Zhang, Z. (2005). Does idiosyncratic risk really matter? Journal of Finance, 60(2), 905–929.

    Google Scholar 

  • Bali, T. G., & Engle, R. F. (2010). The intertemporal capital asset pricing model with dynamic conditional correlations. Journal of Monetary Economics, 57(4), 377–390.

    Google Scholar 

  • BBC. (2017). ECB cuts interest rates to record low. November 7, 2013.

  • Bekaert, G., & Hoerova, M. (2014). The VIX, the variance premium and stock market volatility. Journal of Econometrics, 183(2), 181–192.

    Google Scholar 

  • Bessembinder, H. (1992). Systematic risk, hedging pressure, and risk premiums in futures markets. Review of Financial Studies, 5(4), 637–667.

    Google Scholar 

  • Bouoiyour, J., & Selmi, R. (2015). What does Bitcoin look like? Annals of Economics and Finance, 16(2), 449–492.

    Google Scholar 

  • Bouri, E., Jalkh, N., Molnár, P., & Roubaud, D. (2017). Bitcoin for energy commodities before and after the December 2013 crash: Diversifier, hedge or safe haven? Applied Economics, 49, 1–11.

    Google Scholar 

  • Brière, M., Oosterlinck, K., & Szafarz, A. (2015). Virtual currency, tangible return: Portfolio diversification with Bitcoin. Journal of Asset Management, 16(6), 365–373.

    Google Scholar 

  • Campbell, J. Y., & Hentschel, L. (1992). No news is good news: An asymmetric model of changing volatility in stock returns. Journal of Financial Economics, 31(3), 281–318.

    Google Scholar 

  • Ciaian, P., Rajcaniova, M., & Kancs, D. A. (2016). The economics of BitCoin price formation. Applied Economics, 48(19), 1799–1815.

    Google Scholar 

  • CoinMarketCap. (2017). Cryptocurrency market capitalizations. Publicly available online: https://coinmarketcap.com/. Accessed on October 1, 2017.

  • Da, Z., Guo, R. J., & Jagannathan, R. (2012). CAPM for estimating the cost of equity capital: Interpreting the empirical evidence. Journal of Financial Economics, 103(1), 204–220.

    Google Scholar 

  • Dickey, D. A., & Fuller, W. A. (1979). Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association, 74, 427–431.

    Google Scholar 

  • Dickey, D. A., & Fuller, W. A. (1981). Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica, 49, 1057–1072.

    Google Scholar 

  • Elliott, G., Rothenberg, T. J., & Stock, J. H. (1996). Efficient tests for an autoregressive unit root. Econometrica, 64(4), 813–836.

    Google Scholar 

  • Goyal, A., & Santa-Clara, P. (2003). Idiosyncratic risk matters! Journal of Finance, 58(3), 975–1007.

    Google Scholar 

  • Gregoriou, G. N., & Gueyie, J. P. (2003). Risk-adjusted performance of funds of hedge funds using a modified Sharpe ratio. Journal of Wealth management, 6(3), 77–83.

    Google Scholar 

  • Grinberg, R. (2012). Bitcoin: An innovative alternative digital currency. Hastings Science and Technology Law Journal, 4, 159.

    Google Scholar 

  • Hall, A. (1994). Testing for a unit root in time series with pretest data-based model selection. Journal of Business and Economic Statistics, 12(4), 461–470.

    Google Scholar 

  • Hamilton, J. D. (1988). Rational-expectations econometric analysis of changes in regime: An investigation of the term structure of interest rates. Journal of Economic Dynamics and Control, 12(2–3), 385–423.

    Google Scholar 

  • Hamilton, J. D. (1989). A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica, 57(2), 357–384.

    Google Scholar 

  • Hamilton, J. D. (1990). Analysis of time series subject to changes in regime. Journal of Econometrics, 45(1–2), 39–70.

    Google Scholar 

  • Haubrich, J., Pennacchi, G., & Ritchken, P. (2012). Inflation expectations, real rates, and risk premia: Evidence from inflation swaps. Review of Financial Studies, 25(5), 1588–1629.

    Google Scholar 

  • Jagannathan, R., & McGrattan, E. R. (1995). The CAPM debate. Federal Reserve Bank of Minneapolis Quarterly Review, 19(4), 2–17.

    Google Scholar 

  • Kirchler, M., & Huber, J. (2007). Fat tails and volatility clustering in experimental asset markets. Journal of Economic Dynamics and Control, 31(6), 1844–1874.

    Google Scholar 

  • Krishnamurthy, A., & Vissing-Jorgensen, A. (2012). The aggregate demand for treasury debt. Journal of Political Economy, 120(2), 233–267.

    Google Scholar 

  • Li, X., & Wang, C. A. (2017). The technology and economic determinants of cryptocurrency exchange rates: The case of Bitcoin. Decision Support Systems, 95, 49–60.

    Google Scholar 

  • Lo, S., & Wang, J. C. (2014). Bitcoin as money? Current policy perspectives no. 14-4, Federal Reserve Bank of Boston.

  • MacKinnon, J. G. (1996). Numerical distribution functions for unit root and cointegration tests. Journal of Applied Econometrics, 11, 601–618.

    Google Scholar 

  • Mandelbrot, B. (1963). The variation of certain speculative prices. Journal of Business, 36(4), 394–419.

    Google Scholar 

  • Maurer, B., Nelms, T. C., & Swartz, L. (2013). When perhaps the real problem is money itself! The practical materiality of Bitcoin. Social Semiotics, 23(2), 261–277.

    Google Scholar 

  • Mills, D., Wang, K., Malone, B., Ravi, A., Marquardt, J., Chen, C., et al. (2016). Distributed ledger technology in payments, clearing, and settlement. Staff working paper no. 2016-095, Board of Governors of the Federal Reserve System.

  • Nakamoto, S. (2009). Bitcoin: A peer-to-peer electronic cash system. Publicly available online: www.bitcoin.org.

  • NewsBitcoin. (2017). Bitcoin whales and how they make market waves. Publicly available online: https://news.bitcoin.com/bitcoin-whales-and-how-they-make-market-waves/. Accessed on October 1, 2017.

  • Phillips, K. L. (1991). A two-country model of stochastic output with changes in regime. Journal of International Economics, 31(1), 121–142.

    Google Scholar 

  • Phillips, P. C. B., & Perron, P. (1988). Testing for a unit root in time series regression. Biometrika, 75(2), 335–346.

    Google Scholar 

  • Pieters, G., & Vivanco, S. (2017). Financial regulations and price inconsistencies across Bitcoin markets. Information Economics and Policy, 39, 1–14.

    Google Scholar 

  • Shen, C. H. (1994). Testing efficiency of the Taiwan–US forward exchange market—A Markov switching model. Asian Economic Journal, 8(2), 205–216.

    Google Scholar 

  • Signer, A., & Favre, L. (2002). The difficulties of measuring the benefits of hedge funds. Journal of Alternative Investments, 5(1), 31–41.

    Google Scholar 

  • Wall Street Journal. (2014). Yellen on Bitcoin: Fed doesn’t have authority to regulate it in any way. February 27, 2014.

  • Whaley, R. E. (2009). Understanding the VIX. Journal of Portfolio Management, 35(3), 98–105.

    Google Scholar 

  • Wheelock, D. C., & Wohar, M. E. (2009). Can the term spread predict output growth and recessions? A survey of the literature. Federal Reserve Bank of St. Louis Review, 91(51), 419–440.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Dimitrios Koutmos.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-019-03255-6

Keywords

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

JEL Classification

  • G12
  • G17
  • G23