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Tara Iyer

doi:10.5089/9781616358068.065.A999

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Back Matter

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Tara Iyer

0000000404811396

https://isni.org/isni/0000000404811396 International Monetary Fund

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Publication Date:: 11 Jan 2022

eISBN:: 9781616358099

ISBN:: 9781616358099

Language:: English

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References

Adrian, T., and R. Weeks-Brown. 2021. “Crypto Assets as National Currency? A Step Too Far.” IMF Blog. International Monetary Fund, Washington, DC.
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Adrian, T., D. He, and A. Narain. 2021. “Global Crypto Regulation Should be Comprehensive, Consistent, and Coordinated.” IMF Blog. International Monetary Fund, Washington, DC.
- Search Google Scholar
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Bank for International Settlements (BIS). 2021. “Prudential Treatment of Cryptoasset Exposures.” In Basel Committee on Banking Supervision Consultative Document, September, Basel, Switzerland.
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Briere, M., K. Oosterlinck, and A. Szafarz. 2015. “Virtual Currency, Tangible Return: Portfolio Diversification with Bitcoin.” Journal of Asset Management 16 (6): 365–373.
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Chainanalysis. 2021. “The 2021 Global Crypto Adoption Index.” In Geography of Cryptocurrency Report.
- Search Google Scholar
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Cryptohead. 2021. “The 2021 Crypto-Ready Index.” In Cryptohead Research Report.
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Charfeddine, L. Benlagha, N., and Y. Maouchi. 2020. “Investigating the Dynamic Relationship Between Cryptocurrencies and Conventional Assets: Implications for Financial Investors.” Economic Modelling 85: 198–217.
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Conlon, T., and R. McGee. 2020. “Safe Haven or Risky Hazard? Bitcoin during the COVID-19 Bear Market.” Finance Research Letters 101607.
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Diebold, F. X., and K. Yilmaz. 2012. “Better to Give Than to Receive: Predictive Directional Measurement of Volatility Spillovers.” International Journal of Forecasting 28(1): 57–66.
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Diebold, F. X., and K. Yilmaz. 2014. “On the Network Topology of Variance Decompositions: Measuring the Connectedness of Financial Firms.” Journal of Econometrics 182(1): 119–134.
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Dyhrberg, A. 2016. “Hedging Capabilities of Bitcoin. Is It the Virtual Gold?” Finance Research Letters 16: 139–144.
- Search Google Scholar
- Export Citation
Financial Stability Board (FSB). 2018. “Crypto-Asset Markets. Potential Channels for Future Financial Stability Implications.” Basel, Switzerland.
- Search Google Scholar
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Griffin, J., and A. Shams. 2020. “Is Bitcoin Really Un-Tethered?” The Journal of Finance 75: 1913–64.
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Guesmi, K., S. Saadi, I. Abid, and Z. Ftiti. 2019. “Portfolio Diversification with Virtual Currency: Evidence from Bitcoin.” International Review of Financial Analysis 63 431–37.
- Search Google Scholar
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International Monetary Fund (IMF). 2018. “A Bumpy Road Ahead.” In Global Financial Stability Report. Washington, DC, April.
- Search Google Scholar
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International Monetary Fund (IMF). 2021. “The Crypto Ecosystem: Financial Stability Risks and Implications for Emerging Markets.” In Global Financial Stability Report. Washington, DC, October.
- Search Google Scholar
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Misrach, Bruce. 2021. “Stablecoins: Survivorship, Transactions Costs, and Exchange Microstructure.” Rutgers University Working Paper, April 2021.
- Search Google Scholar
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Maniff, J., S. Minhas, D. Rodziewicz, and R. Ruiz. 2020. “Safe Haven Performance in the Age of Bitcoin.” Economic Bulletin, Federal Reserve Bank of Kansas City.
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- Export Citation
Shahzad, S.J.H., E. Bouri, D. Roubaud, L. Kristoufek, and B. Lucey. 2019. “Is Bitcoin a Better Safe-Haven Investment than Gold and Commodities?” International Review of Financial Analysis.
- Search Google Scholar
- Export Citation
Symitsi, E., and K. Chalvatzis. 2018. “Return, Volatility and Shock Spillovers of Bitcoin with Energy and Technology Companies.” Econ. Lett. 170: 127–130.
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Umar, Z., N. Trabelsi, and F. Alqahtani. 2021. “Connectedness Between Cryptocurrency and Technology Sectors: International Evidence.” International Review of Economics and Finance 72 910–922.
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- Export Citation
Zeng, T., M. Yang, and Y. Shen. 2020. “Fancy Bitcoin and Conventional Financial Assets: Measuring Market Integration Based on Connectedness Networks”. Economic Modelling 90: 209–220.
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Appendix

I. Crypto-Equity Spillover Model

The Diebold-Yilmaz (2012 and 2014) interconnectedness and spillover model used in the empirical analysis is outlined below, with further details available in the original papers.

Consider an N variable covariance-stationary data-generating process x_t = Θ(L)u_t, where Θ(L) = Θ₀ + Θ₁L + Θ₂L² + ... and $E [u_{t} u_{t}^{'}] = I$ , which is estimated using a vector autoregression (VAR) model. Taking the variance decomposition of this process yields the following forecast error variance decomposition (FEVD) matrix, with each element d_ij indicating the spillover from the j^th variable to the i i^th variable:

The diagonal elements in the matrix (d_ii) contain the spillovers to self, while the off-diagonal elements capture the spillovers from other variables. For the purpose of the analysis here, only the cross-variance decompositions are counted, and self-spillovers are excluded. The last column of the table above provides the total spillovers to variable i from all other variables in the model, while the last row contains the total spillovers from variable j to all other variables in the system. Thus, the total spillover to each variable i in the VAR is derived as the sum of the off-diagonal elements in the row for that particular variable i, so that the total directional connectedness from others to $C_{i \leftarrow \cdot}^{H}$ , is

\begin{matrix} C_{i \leftarrow \cdot}^{H} = \underset{j \neq i}{Σ_{j = 1}^{N} d_{i j}^{H}} & (1) \end{matrix}

Similarly, total spillovers to other variables in the system from each variable j, or $C_{\cdot \leftarrow j}^{H}$ , is the column sum associated with j, excluding self-spillovers, that is,

\begin{matrix} C_{\cdot \leftarrow j}^{H} = \underset{i \neq j}{Σ_{i = 1}^{N} d_{i j}^{H}} & (2) \end{matrix}

Net spillovers are defined as the difference between (1) and (2). Total interconnectedness, C^H, among the variables in the system is defined as the sum of all the off-diagonal entries of the FEVD, so that

\begin{matrix} C^{H} = \frac{1}{N} \underset{i \neq j}{Σ_{i, j = 1}^{N} d_{i j}^{H}} & (3) \end{matrix}

Diebold and Yilmaz use the generalized forecast error variance decomposition (GVD) method derived in Pesaran and Shin (1998) to identify the VAR. GVDs have the advantage of being order-invariant unlike Cholesky ordering schemes, which can potentially be arbitrary.^²⁰ GVDs allow for correlated shocks, implying that the H-step ahead variance decomposition matrix $D^{g H} = [d_{i j}^{g H}]$ has entries

\begin{matrix} d_{i j}^{g H} = \frac{σ_{j j}^{- 1} Σ_{h = 0}^{H - 1} (e_{i}^{'} Θ_{h} Σ e_{j})^{2}}{Σ_{h = 0}^{H - 1} e_{i}^{'} Θ_{h} Σ Θ_{h}^{'} e_{i}} & (4) \end{matrix}

As inputs to the VAR model to estimate the sequence of FEVDs, we use two transformations of the relevant variables: returns and volatility. Returns are defined as the percentage daily change in the closing price of crypto assets and equity indices, excluding trading holidays, while volatility is computed as the standard deviation of absolute percentage changes in intra-day prices (see Table A1). The VAR is estimated over a rolling window of 100 days over two different sample periods: Jan 2017-Dec 2019 and Jan 2020-Nov 2021.

II. Data

The variables used in the VAR analysis and the data sources are described in Table A1. All variables are in daily frequency, unless otherwise noted.

^{Table A1.}

Variable Description and Data Sources

^{Table A1.}

Variable Description and Data Sources

Variable	Description	Source
Bitcoin-USD	Daily closing price of Bitcoin in US dollars based on direct quote prices and CryptoCompare’s volume-weighted index calculation methodology for digital assets	CryptoCompare
Tether-USD	Daily closing price of Tether in US dollars based on direct quote prices and CryptoCompare’s volume-weighted index calculation methodology for digital assets	CryptoCompare
Ether-USD	Daily closing price of Ether in US dollars based on direct quote prices and CryptoCompare’s volume-weighted index calculation methodology for digital assets	CryptoCompare
S&P 500 Index	Equity index comprised of 500 large-capitalization companies in the United States	Yahoo Finance
Nasdaq Index	Tech-heavy equity index comprised of more than 2,500 common equities in the United States	Yahoo Finance
Russell 2000 Index	Equity index comprised of 2,000 small-capitalization companies in the United States	Yahoo Finance
10-Year Yield	US 10-year sovereign bond yield	Yahoo Finance
VIX Index	30-day expected volatility of the US stock market, based on S&P 500 options	Yahoo Finance
Oil Price Index	Brent crude oil price index	Yahoo Finance
MSCI Emerging Market Index	Equity index with large and mid-cap representation for 27 emerging markets	Yahoo Finance

^{Table A1.}

Variable Description and Data Sources

Variable	Description	Source
Bitcoin-USD	Daily closing price of Bitcoin in US dollars based on direct quote prices and CryptoCompare’s volume-weighted index calculation methodology for digital assets	CryptoCompare
Tether-USD	Daily closing price of Tether in US dollars based on direct quote prices and CryptoCompare’s volume-weighted index calculation methodology for digital assets	CryptoCompare
Ether-USD	Daily closing price of Ether in US dollars based on direct quote prices and CryptoCompare’s volume-weighted index calculation methodology for digital assets	CryptoCompare
S&P 500 Index	Equity index comprised of 500 large-capitalization companies in the United States	Yahoo Finance
Nasdaq Index	Tech-heavy equity index comprised of more than 2,500 common equities in the United States	Yahoo Finance
Russell 2000 Index	Equity index comprised of 2,000 small-capitalization companies in the United States	Yahoo Finance
10-Year Yield	US 10-year sovereign bond yield	Yahoo Finance
VIX Index	30-day expected volatility of the US stock market, based on S&P 500 options	Yahoo Finance
Oil Price Index	Brent crude oil price index	Yahoo Finance
MSCI Emerging Market Index	Equity index with large and mid-cap representation for 27 emerging markets	Yahoo Finance

III. Additional Results

^{Table A2.}

Crypto-Equity Volatility Spillovers in Emerging Markets

Sources: CryptoCompare; Yahoo Finance; author’s calculations. Notes: The spillovers are based on model estimation using daily volatility data for the time periods January 2017–December 2019 and January 2020– November 2021. In tables a and b, for the i-th row and j-th column in the matrix, the ij-th entry represents the spillover from asset j to asset i or the percent of forecast error variance of asset i due to shocks from asset j Rows add up to 100 percent. EM = emerging market.

^{Table A3.}

Crypto-Equity Return Spillovers in Emerging Markets

Sources: CryptoCompare; Yahoo Finance; author’s calculations. Notes: The spillovers are based on model estimation using daily returns data for the time periods January 2017–December 2019 and January 2020– November 2021. In tables a and b, for the i-th row and j-th column in the matrix, the ij-th entry represents the spillover from asset j to asset i or the percent of forecast error variance of asset i due to shocks from asset j Rows add up to 100 percent. EM = emerging market.

The author would like to thank Tobias Adrian, Fabio Natalucci, Mahvash Qureshi, Jerome Vandenbussche, Evan Papageorgiou, and Tomohiro Tsuruga for many helpful suggestions, and reviewers at the IMF Monetary and Capital Markets Department, Research Department, Strategy, Policy, and Review Department, and Communications Department for useful comments.

Adrian and Weeks-Brown (2021) discuss the risks associated with adopting crypto assets as a national currency, and Adrian, He, and Narain (2021) write about the risks associated with an unregulated crypto ecosystem. For a detailed discussion of the trends of crypto adoption (“cryptoization”) in emerging market economies and the risks and opportunities, see IMF (2021).

In November 2021, Bitcoin and Ether accounted for about 40 and 20 percentof total crypto market cap, respectively, while Tether, the largest stablecoin and in the top five crypto assets by market cap, accounted for about three percent of total crypto market cap.

The increase in crypto asset market capitalization is quite stark even when compared to the total US stock market capitalization, which itself has increased significantly since the pandemic. In early 2019, crypto asset market cap was about 0.4 percent of total US stock market capitalization, but this has increased to close to 5 percent in September 2021.

Several studies report limited interconnectedness between crypto and conventional assets such as equities and currencies in the pre-pandemic period (for example, Briere and others 2015; Dyhrberg 2016; Shahzad and others 2019; Guesmi and others 2019; Charfeddine and others 2020; Symitsi and others 2018; and Umar and others 2021), but note that spillovers increase during market stress episodes and may have been rising (Zeng and others 2020; Conlon and McGee 2020; and Maniff and others 2020).

Interconnectedness in this note is measured in terms of correlations, which provide a sense of the strength of the overall association between two variables, as well as spillovers, which indicate the impact of one variable on the other.

There might, however, be other potential risks associated with Tether, including a high observed failure rate of stablecoins, and the fact that Tether may not be fully backed by reserves at all times (Mizrach 2021 and Griffin and Shams 2020).

The S&P 500 index is considered among the best gauges of large-cap equity market movements in the United States, while the Nasdaq is a tech-heavy market-cap-weighted index of more than 2500 stocks, including some of the largest companies in the United States. The Russell 2000 index is a weighted index of 2000 small-cap companies in the United States and is a measure of the investment opportunities afforded by small cap stocks.

While stablecoins are usually pegged to the US dollar and other fiat currencies, small deviations from the market reference are common and rapidly reversed through arbitrage, generating the observed variations in prices.

Looking at the various sub-components of the S&P 500 index (such as consumer discretionary and staples, industry, healthcare, technology, and financials), the return (volatility) correlation of Bitcoin and Tether have increased significantly for all sectors and range between 0.27 to 0.38 (0.28 to 0.65) and –0.06 to –0.15 (0.19 to 0.35), respectively.

The MSCI index is a widely quoted equity market index that tracks the performance of mid- and large-cap equities across 27 emerging market economies.

The underlying premise of the approach is that the variance decomposition matrix associated with an N variable data generating process forms a weighted and directed network that can be used to estimate the direction and magnitude of spillovers among the variables, based on the share of the forecast error variation attributable to other variables. See appendix for further details.

The baseline model includes Bitcoin and Tether which have had the highest trading volumes for most of the pandemic (October 2021 Global Financial Stability Report, Chapter 2). Including Ether in the model does not significantly alter the results for the other assets in the VAR system, while its volatility and returns spillovers are estimated to be generally quite small. The Nasdaq index is also excluded from the model given its high correlation with the S&P 500 index, but the results are qualitatively robust to including it instead.

Considering the T-bill rate in first differences rather than in levels does not affect the results. Moreover, while the VIX is excluded from the baseline specification for the volatility VAR model as it tracks S&P volatility closely, the results remain qualitatively robust when including it as an additional exogenous variable. The VIX is included in the VAR model for returns.

Returns are defined as one-day log differences, whereas volatility is based on intra-day spreads with volatility = 0.361*[Ln (High Price) – Ln(Low Price)^2] following the formula used in Diebold-Yilmaz (2012). See the appendix for further details.

As in Diebold-Yilmaz (2012), the length of the forecast horizon and rolling window is considered to be 10 days and 100 days, respectively, but the results are robust when considering longer durations (20 days and 150 days, respectively).

While Bitcoin and Tether price movements are also highly correlated (the correlation is about 0.5 for price volatility and –0.25 for returns in 2020–21), the spillovers for Tether to equity prices are obtained controlling for Bitcoin prices in the VAR.

This note considers emerging market economies as countries that are included in the MSCI emerging market index.

The baseline specification of the VAR was checked against various alternative specifications for robustness, including using the VIX as an exogenous variable and replacing the S&P 500 index with the Nasdaq index. The core set of findings remain qualitatively similar.

Pesaran, H., and Y. Shin. 1998. “Generalized Impulse Response Analysis in Linear Multivariate Models.” Economic Letters 58, 17–29.

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Cryptic Connections: Spillovers between Crypto and Equity Markets

Author:

Tara Iyer

Volume/Issue:: Volume 2022: Issue 001

Publisher:: International Monetary Fund

ISBN:: 9781616358099

Pages:: 13

DOI:: https://doi.org/10.5089/9781616358068.065

References
Appendix
- I. Crypto-Equity Spillover Model
II. Data
III. Additional Results

	x₁	x₂	...	x_j=N	Total spillover to i
x₁	$d_{11}^{H}$	$d_{12}^{H}$	...	$d_{1N}^{H}$	$Σ_{j = 1}^{N} d_{1 j}^{H}, j \neq 1$
x₂	$d_{21}^{H}$	$d_{22}^{H}$		$d_{2N}^{H}$	$Σ_{j = 1}^{N} d_{2 j}^{H}, j \neq 2$
.	.	.	.	.	.
x_i=N	$d_{N1}^{H}$	$d_{N2}^{H}$	...	$d_{NN}^{H}$	$Σ_{j = 1}^{N} d_{N j}^{H}, j \neq N$
Total spillover by j	$\underset{i \neq 1}{Σ_{i = 1}^{N} d_{i 1}^{H}}$	$\underset{i \neq 2}{Σ_{i = 1}^{N} d_{i 2}^{H}}$	...	$\underset{i \neq N}{Σ_{i = 1}^{N} d_{i N}^{H}}$	$\frac{1}{N} Σ_{i j = 1}^{N} d_{i j}^{H}, i \neq j$

	x₁	x₂	...	x_j=N	Total spillover to i
x₁	$d_{11}^{H}$	$d_{12}^{H}$	...	$d_{1N}^{H}$	$Σ_{j = 1}^{N} d_{1 j}^{H}, j \neq 1$
x₂	$d_{21}^{H}$	$d_{22}^{H}$		$d_{2N}^{H}$	$Σ_{j = 1}^{N} d_{2 j}^{H}, j \neq 2$
.	.	.	.	.	.
x_i=N	$d_{N1}^{H}$	$d_{N2}^{H}$	...	$d_{NN}^{H}$	$Σ_{j = 1}^{N} d_{N j}^{H}, j \neq N$
Total spillover by j	$\underset{i \neq 1}{Σ_{i = 1}^{N} d_{i 1}^{H}}$	$\underset{i \neq 2}{Σ_{i = 1}^{N} d_{i 2}^{H}}$	...	$\underset{i \neq N}{Σ_{i = 1}^{N} d_{i N}^{H}}$	$\frac{1}{N} Σ_{i j = 1}^{N} d_{i j}^{H}, i \neq j$

a. Spillovers Matrix: 2017–19 (percent)						b. Spillovers Matrix: 2020–21 (percent)
	Bitcoin	Tether	S&P 500	Russell 2000	MSCI EM		Bitcoin	Tether	S&P 500	Russell 2000	MSCI EM
Bitcoin	95.3	0.0	1.9	0.8	2.0	Bitcoin	51.0	11.1	14.0	16.0	6.9
Tether	0.1	99.6	0.1	0.2	0.1	Tether	25.0	38.4	14.0	15.0	7.9
S&P 500	1.0	0.0	42.6	27.1	29.3	S&P 500	14.0	5.4	41.0	25.0	15.4
Russell 2000	0.5	0.1	32.0	46.0	21.5	Russell 2000	15.0	4.2	30.0	37.0	13.5
MSCI EM	1.8	0.0	31.8	18.3	48.1	MSCI EM	14.0	4.9	29.0	26.0	25.9

a. Spillovers Matrix: 2017–19 (percent)						b. Spillovers Matrix: 2020–21 (percent)
	Bitcoin	Tether	S&P 500	Russell 2000	MSCI EM		Bitcoin	Tether	S&P 500	Russell 2000	MSCI EM
Bitcoin	95.3	0.0	1.9	0.8	2.0	Bitcoin	51.0	11.1	14.0	16.0	6.9
Tether	0.1	99.6	0.1	0.2	0.1	Tether	25.0	38.4	14.0	15.0	7.9
S&P 500	1.0	0.0	42.6	27.1	29.3	S&P 500	14.0	5.4	41.0	25.0	15.4
Russell 2000	0.5	0.1	32.0	46.0	21.5	Russell 2000	15.0	4.2	30.0	37.0	13.5
MSCI EM	1.8	0.0	31.8	18.3	48.1	MSCI EM	14.0	4.9	29.0	26.0	25.9

a. Spillovers Matrix: 2017–19 (percent)						b. Spillovers Matrix: 2020–21 (percent)
	Bitcoin	Tether	S&P 500	Russell 2000	MSCI EM		Bitcoin	Tether	S&P 500	Russell 2000	MSCI EM
Bitcoin	99.2	0.1	0.1	0.3	0.3	Bitcoin	67.7	5.0	10.0	8.1	8.9
Tether	0.7	98.2	0.2	0.4	0.6	Tether	4.2	73.6	10.0	5.2	6.9
S&P 500	0.3	0.2	44.4	32.0	23.1	S&P 500	8.0	5.0	39.0	25.9	22.3
Russell 2000	0.4	0.5	34.3	46.2	18.6	Russell 2000	8.1	3.7	30.0	37.0	20.8
MSCI EM	0.3	0.4	28.0	21.1	50.3	MSCI EM	7.8	4.6	27.0	21.0	39.5

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Appendix

I. Crypto-Equity Spillover Model

II. Data

III. Additional Results

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