Hedging bitcoin with other financial assets

Finance Research Letters 30 (2019) 30–36

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Finance Research Letters journal homepage: www.elsevier.com/locate/frl

Hedging bitcoin with other financial assets Debdatta Pala, , Subrata K. Mitrab ⁎

a b

T

Indian Institute of Management Lucknow, Uttar Pradesh, India Indian Institute of Management Raipur, Chhattisgarh, India

ARTICLE INFO

ABSTRACT

Keywords: Hedging Bitcoin GARCH

We compute optimal hedge ratios between bitcoin and other financial assets by using conditional volatility estimates of different GARCH models for a period over January 03, 2011 to February 19, 2018. Gold is found to provide a better hedge against bitcoin. Following generalized orthogonal GARCH, which offers maximum hedging effectiveness, U.S.$1 long of bitcoin could to be hedged with 70 cents short of gold. Our findings are fairly robust to alternate specifications.

JEL classification: C32 G15

1. Introduction Until recently, literature on cryptocurrency has mostly dealt with market efficiency (e.g., Urquhart, 2016; Bariviera, 2017; Nadarajah and Chu, 2017; Brauneis and Mestel, 2018; Cheah et al., 2018; Sensoy, 2019; Tiwari et al., 2018; Vidal-Tomas and Ibanez, 2018), volatility analysis (e.g., Katsiampa, 2017), speculation (e.g., Cheah and Fry, 2015) and returns-transaction relationship (e.g., Balciar et al., 2017; Koutmos, 2018). In response to the spiraling price rise of bitcoin, since its inception in 2009, scholars have also investigated risk mitigating capacity of bitcoin. For example, Dyhrberg (2016a) found that bitcoin could be utilized as hedge for U.S. currency and stocks included in the Financial Times Stock Exchange Index. In parallel, Bouri et al. (2017a) showed that bitcoin acted as hedge against commodities and specifically, energy commodities till 2013. Bouri et al. (2017b) extended the literature on the hedging capabilities of bitcoin against multiple assets spreading over commodities, currencies, bonds as well as stocks. With the use of bivariate dynamic conditional correlation (DCC) model of Engel (2002), they showed that bitcoin acted as strong hedge against commodities, Asia Pacific and Japanese stock indices. We distinguish from Bouri et al. (2017b) in the following ways: First, unlike previous investigations that explored the hedging capabilities of bitcoin for other assets, we set to examine hedging bitcoin with other assets. This may be of interest to the investors as weighted average bitcoin price across different exchanges has crashed to U.S.$ 6937 in the first week of February 2018 from the historical peak at U.S.$ 18,972 in December 2017. Second, on the methodological front, studies till date had mostly used DCC. However, the limitations of DCC model are: (a) it does not cover asymmetric relationship between the underlying assets; and (b) its estimation is bounded by model-specificity. To capture the possible asymmetric relation between the underlying assets we employ asymmetric dynamic conditional correlation - generalized autoregressive conditional heteroscedasticity (ADCC-GARCH) model of Cappiollo et al. (2006). Along with, we use the generalized orthogonal GARCH (GO-GARCH) approach, of van der Weide (2002), that besides relaxing the model-specificity addresses the estimation challenge of multiple variables in large data set. Third, following Kroner and Sultan (1993), we compute optimal hedge ratios between bitcoin and other financial assets by using the conditional

⁎

Corresponding author. E-mail address: [email protected] (D. Pal).

https://doi.org/10.1016/j.frl.2019.03.034 Received 5 June 2018; Received in revised form 18 December 2018; Accepted 26 March 2019 Available online 29 March 2019 1544-6123/ © 2019 Elsevier Inc. All rights reserved.

Finance Research Letters 30 (2019) 30–36

D. Pal and S.K. Mitra

Table 1 Summary statistics of daily return in percentage.

Minimum Maximum Median Mean Standard deviation Jarque–Bera test p-value

BTC

S&P500

Gold

Wheat

−84.88 147.44 0.22 0.572 7.988 440,000 0.00

−6.896 4.632 0.035 0.042 0.893 2700 0.00

−8.897 4.845 0.009 −0.003 1.036 4100 0.00

−25.74 23.761 0.000 −0.024 2.597 29,000 0.00

volatility estimates of DCC-GARCH, ADCC-GARCH and GO-GARCH specifications. Finally, by using the hedging effectiveness, we compare the models to show how hedge ratios differ across GARCH models. To the best of our knowledge, this may be one of the earliest studies in the field financial research on cryptocurrency to offer comparison among alternative models based on their hedging effectiveness. In this study, to investigate the possibility of hedging bitcoin prices with other assets we include S&P500 composite price index, gold and wheat as representatives of stocks, precious metal and commodity, respectively. Among various stock indices, namely S&P500, FTSE100, DAX30, following Bouri et al. (2017b), we include S&P500 composite price index as it is market-capitalizationweighted index of the 500 largest U.S. publicly traded firms and is widely considered as a proxy of world stock market. We include gold in our analysis as both bitcoin and gold is valued for their scarcity and both the assets are international in nature as hardly controlled by any sovereign government (Dyhrberg, 2016b). Wheat, a non-energy commodity, has been included as it is uncorrelated with bitcoin, however, has experienced significant price movements since 2008 (Pal and Mitra, 2017, 2018). We show that bitcoin/gold offers the maximum hedging effectiveness. 2. Data We use daily spot closing price of bitcoin, S&P500 composite price index, gold (London bullion market), and wheat (Minneapolis and Duluth U.S. No 1 Dark Northern Spring) spanning from 03 January, 2011 to 19 February, 2018 and each series contains 1839 observations. Bitcoin price is sourced from https://finance.yahoo.com/cryptocurrencies that offers a weighted average bitcoin price across different exchanges and rest of time series data is availed from Data Stream International. Prices of bitcoin (BTC), gold (GOLD), and wheat (WHEAT) are denoted by U.S.$ per bitcoin, U.S.$ per troy ounce, and U.S.$ per bushel. While BTC trades 24/ 7, S&P 500 index data is available only for weekdays, hence, we have taken only weekdays data to maintain similarity. Table 1 presents the summary statistics of the underlying return series. Jarque-Bera test indicates that series are not following normal distribution. Pearson correlations between daily returns of the underlying variables are given in Table 2. Bitcoin return exhibits weak positive correlation with S&P500, gold, and wheat. 3. Methodology Following Kroner and Sultan (1993, the risk minimizing hedge ratio between asset m and asset n can be represented as m, n, t

(1)

= hmn, t / hnn, t

where hmn,t denotes the conditional covariance between asset m and asset n and hnn,t represents conditional variance of asset n at time t. One-dollar long position in asset m is possible to be hedged by a short position in Φm,n, t dollars asset n. A negative hedge ratio indicates that pairs are negatively correlated. In such cases hedging can be done taking long position with both the assets or taking short position with both the underlying assets. We compute optimal hedge ratios following DCC-GARCH, ADCC-GARCH and GO-GARCH approaches (see Appendix I for formal description). Performance of optimal hedge ratios originated from various GARCH estimations is assessed by hedging effectiveness (HE) index (Arouri et al., 2012; Basher and Sadorsky, 2016), Table 2 Pearson correlations (of daily returns).

BTC S&P500 GOLD WHEAT

BTC

S&P500

Gold

Wheat

1.000 0.012 0.064 0.015

1.000 −0.009 0.030

1.000 0.024

1.000

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Finance Research Letters 30 (2019) 30–36

D. Pal and S.K. Mitra

Fig. 1. Optimal hedge ratios of bitcoin with S&P500, gold, and wheat.

HE =

varunhedged

varhedged (2)

varunhedged

where varhedged denotes the variance of the returns of the bitcoin-other asset portfolio and varunhedged refers to the variance of returns of portfolio of bitcoin. A high HE index would indicate an improved hedging effectiveness. 4. Results Fig. 1 portrays one-period-ahead optimal hedge ratios of bitcoin with S&P500 composite price index, gold, and wheat. Table 3 outlays the correlations between hedge ratios. Pairwise correlations across the GARCH models are positive. Furthermore, the correlation between hedge ratios of DCC- as well as ADCC-GARCH models are comparatively high. Based on Basher and Sadorsky (2016), rolling window method is employed for forecasting conditional volatility (one-periodahead) which is used to generate one-day-ahead hedge ratio. Fixed width rolling window with daily observations is used to generate 25, 50 and 100 one-day-ahead hedge ratios forecasts and models are refitted for every 10 observations (Table 4). We have also carried out the analysis with weekly observations and model is estimated for one-week-ahead hedge ratios forecast length of 25 and 50 weekly observations and with model refit after every 10 observations (Table 5). With reference to the middle panel of Table 4 (forecast length of 50 days), the mean value of hedge ratio of bitcoin with S&P500 is Table 3 Correlations between hedge ratios.

DCC-GARCH /ADCC-GARCH DCC-GARCH /GO-GARCH ADCC-GARCH /GO-GARCH

BTC/S&P500

BTC/Gold

BTC/Wheat

0.9136 0.4157 0.3562

0.994 0.544 0.547

0.996 0.689 0.725

32

33

0.0808 0.1611 −0.0528

0.2740 0.2925 0.4137

0.1089 0.1353 −0.0072

0.7147 0.7820 0.6859

0.2427 0.2858 0.1705

Minimum

0.3591 0.4827 0.0380

25 10 Mean

0.4459 0.5276 0.5965

1.5497 1.7204 1.2787

0.6598 1.0366 0.3169

Maximum

0.0272 0.0299 0.0278

0.0428 0.0443 0.0457

0.0409 0.0438 0.0128

Hedging effectiveness

0.1494 0.1756 0.1700

0.5740 0.5973 0.7005

0.2287 0.3972 0.0909

50 10 Mean

−0.0133 0.0216 −0.0069

0.2728 0.2792 0.4026

−0.2047 0.0367 −0.0630

Minimum

0.4123 0.4362 0.6314

1.5096 1.4768 1.2723

0.6210 1.0175 0.3226

Maximum

0.0220 0.0243 0.0261

0.0318 0.0321 0.0376

0.0262 0.0287 0.0070

Hedging effectiveness

0.0660 0.0851 0.1014

0.5236 0.5409 0.5852

0.0611 0.1607 0.0689

100 10 Mean

−0.0328 −0.0142 −0.0561

0.1975 0.2240 0.3323

−0.2722 −0.1803 −0.0389

Minimum

0.4037 0.4824 0.6891

1.4276 1.4059 1.4064

0.6340 0.8757 0.4277

Maximum

0.0139 0.0143 0.0135

0.0165 0.0161 0.0193

0.0194 0.0190 0.0103

Hedging effectiveness

Note: Fixed width rolling window with daily observations is used to generate 25, 50 and 100 one-day-ahead hedge ratios forecasts. Models are refitted for every 10 observations.

BTC/S&P500 DCC-GARCH ADCC-GARCH GO-GARCH BTC/GOLD DCC-GARCH ADCC-GARCH GO-GARCH BTC/WHEAT DCC-GARCH ADCC-GARCH GO-GARCH

Forecast length (days) Model refit (days)

Table 4 Hedge ratio and hedging effectiveness using daily observations.

D. Pal and S.K. Mitra

Finance Research Letters 30 (2019) 30–36

Finance Research Letters 30 (2019) 30–36

D. Pal and S.K. Mitra

Table 5 Hedge ratio and hedging effectiveness (HE) using weekly observations. Forecast length (weeks) Model refit (weeks) BTC/S&P500 DCC-GARCH ADCC-GARCH GO-GARCH BTC/GOLD DCC-GARCH ADCC-GARCH GO-GARCH BTC/WHEAT DCC-GARCH ADCC-GARCH GO-GARCH

25 10 Mean

Hedging effectiveness

50 10 Mean

Minimum

Maximum

Minimum

Maximum

Hedging effectiveness

0.3591 0.4827 0.0380

0.0808 0.1611 −0.0528

0.6598 1.0366 0.3169

0.0409 0.0438 0.0072

0.3591 0.4827 0.0380

0.0808 0.1611 −0.0528

0.6598 1.0366 0.3169

0.0355 0.0392 0.0087

0.7147 0.7820 0.6859

0.2740 0.2925 0.4137

1.5497 1.7204 1.2787

0.0428 0.0443 0.0457

0.7147 0.7820 0.6859

0.2740 0.2925 0.4137

1.5497 1.7204 1.2787

0.0412 0.0435 0.0419

0.2427 0.2858 0.1705

0.1089 0.1353 −0.0072

0.4459 0.5276 0.5965

0.0418 0.0441 0.0264

0.2427 0.2858 0.1705

0.1089 0.1353 −0.0072

0.4459 0.5276 0.5965

0.0384 0.0414 0.0253

Note: Fixed width rolling window with weekly observations is used to generate 25 and 50 one-period-ahead hedge ratios forecasts. Models are refitted for every 10 observations.

0.2287 under the DCC-GARCH model, denoting that hedging of U.S.$1 long position in bitcoin is possible for 22 cents short position in the stock market. The corresponding mean values under the ADCC- and GO-GARCH models are 0.3972 and 0.0909, respectively. Among the three GARCH models, ADCC-GARCH offers the most effective hedge. The average hedge ratio of bitcoin with gold is 0.5740 under DCC-GARCH, indicating that U.S.$1 long of bitcoin could be hedged by 57 cents short of gold. The corresponding hedge ratios under the ADCC-GARCH and GO-GARCH models are 0.5973 and 0.7005, respectively. Therefore, following the ADCC-GARCH and GO-GARCH specification, U.S.$1 long position in bitcoin is possible to be hedged by short positions in the gold market for 59 cents and 70 cents, respectively. Bitcoin/gold had shown maximum hedging effectiveness under GO-GARCH. The average hedge ratios between bitcoin and wheat are 0.1494, 0.1756, and 0.1700 under DCC-, ADCC-, and GO-GARCH, respectively, and GO-GARCH model has attained the highest hedging effectiveness. In Table 5, we outlay values of mean hedge ratios and hedging effectiveness using weekly data with model refit for 10 weeks. For forecast length of 50 weeks, average hedge ratios for hedge between bitcoin and S&P500 index under DCC, ADCC and GO-GARCH specifications are 0.3591, 0.4827, and 0.0380, respectively, and ADCC-GARCH offers the highest hedging effectiveness. Similarly, average hedge ratios for bitcoin/gold hedge under DCC, ADCC and GO-GARCH specifications are 0.7147, 0.7820, and 0.6859, respectively, and the highest hedging effectiveness is offered by ADCC-GARCH. Also, for bitcoin/wheat hedge, ADCC-GARCH offers the highest hedging effectiveness. Overall, bitcoin/gold has offered the highest hedging effectiveness across GARCH specifications over various forecast lengths, that is, gold is the preferred hedge, over stock and commodity, against bitcoin. 5. Conclusion Our results suggest that bitcoin can be hedged with S&P500 composite price index, gold, and wheat. GO-GARCH specification offers greater hedging effectiveness over DCC-GARCH and ADCC-GARCH. Among the underlying assets, gold is found to provide a better hedge against bitcoin. Following GO-GARCH specification, U.S.$1 long of bitcoin could be hedged with 70 cents short of gold. Our findings are reasonably robust to the choice of model refits. Future research may explore hedging other cryptocurrencies with stocks, precious metals, and commodities. Acknowledgements We thank the Editor and both the reviewers for their valuable comments that had added substantial value to the paper. Appendix I Description of GARCH approaches Let xt is a r × 1 vector of returns of underlying assets. AR(1) representation of xt is conditional on the information set Wt − 1 and xt is represented as:

x t = µ + bxt t

1

+

(1)

t

(2)

= Kt1/2 ut

where Kt is a r × r conditional covariance matrix of xt and ut is r × 1 i.i.d random vector of errors.DCC-GARCH of Engel (2002) first estimates GARCH parameters followed by conditional correlations. 34

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D. Pal and S.K. Mitra

(3)

Kt = Bt Xt Bt where Xt denotes a matrix of conditional correlation and Bt is a diagonal matrix as follows: 1/2 1/2 Xt = diag (g1, t1/2 , ... gm,1/2 t ) Gt diag (g1, t , ... gr , t )

(4)

1/2 Bt = diag (k1,1/2 t , ... k r , t )

(5)

The representations for k for GARCH (1,1) is represented as:

ki, t = vi +

i

2 i, t 1

+

(6)

i ki, t 1

Gt indicates a symmetric positive definite matrix as:

Gt = (1

¯ +

2) G

1

1ut 1 ut 1

+

(7)

2 Gt 1

where G¯ refers to a r × r unconditional correlation matrix of ui,t. Both Ω1 and Ω2 are non-negative The correlation estimator is represented as: i, j , t

gi, j, t

=

gi, i, t gj, j, t

(8)

Cappiello et al. (2006) added an asymmetric term on the DCC-GARCH model and suggested the ADCC-GARCH as follows:

ki, t = vi +

i

2 i, t 1

+

i ki, t 1

+

i

2 i, t 1 L( i, t 1)

(9)

where L(ωi,t − 1) denotes an indicator function equals to 1 if ωi,t − 1 < 0 or else 0. Under ADCC-GARCH model, Gt is represented as:

Gt = (G¯

¯ P GP

¯ Q GQ

R G¯ R ) + P ut 1 ut 1 P + Q Gt 1 Q + R ut ut R

(10)

where P, Q, and R are of the r × r matrices while ut denotes standardized errors with a zero-threshold equal to ut if less than 0 (and 0 otherwise). G¯ and G¯ denote the unconditional matrices of ut and ut , respectively. Under GO-GARCH model, van der Weide (2002) suggested the returns of underlying assets (xt) as:

x t = at +

(11)

t

where at indicates conditional mean, and ut is an error term. The GO-GARCH model incorporates xt − at on a set of unobserved exogenous factors as follows: t

(12)

= Aft

A=

(13)

1/2O

where O is an orthogonal matrix and Ψ represents an unconditional covariance matrix.

ft = Kt1/2 ut

(14)

= 1. where ut is identified as K(uit) = 0 and K Subsequently, the combined Eqs. (11), (12) and (14) offers the following: (uit2 )

(15)

x t = at + AKt1/2 ut

References Arouri, M., Jouini, J., Nguyen, D.K., 2012. On the impacts of oil price fluctuations on European equity markets: volatility spillover and hedging effectiveness. Energy Econ. 34, 611–617. Basher, S.A., Sadorsky, P., 2016. Hedging emerging market stock prices with oil, gold, VIX, and bonds: a comparison between DCC, ADCC and GO-GARCH. Energy Econ. 54, 235–247. Balciar, M., Bouri, E., Gupta, R., Roubaud, D., 2017. Can volume predict bitcoin returns and volatility? A quantiles-based approach. Econ. Model. 64, 74–81. Bariviera, A.F., 2017. The inefficiency of Bitcoin revisited: a dynamic approach. Econ. Lett. 161, 1–4. Bouri, E., Jalkh, N., Molnár, P., Roubaud, D., 2017a. Bitcoin for energy commodities before and after the December 2013 crash: diversifier, hedge or safe haven. Appl. Econ. 49, 5063–5073. Bouri, E., Molnár, P., Azzi, G., Roubaudd, D., Hagfors, L.I., 2017b. On the hedge and safe haven properties of Bitcoin: is it really more than a diversifier. Finance Res. Lett. 20, 192–198. Brauneis, A., Mestel, R., 2018. Price discovery of cryptocurrencies: bitcoin and beyond. Econ. Lett. 165, 58–61. Cappiello, L., Engle, R.F., Sheppard, K., 2006. Asymmetric correlations in the dynamics of global equity and bond returns. J. Finan. Econometr. 4, 537–572. Cheah, E.T., Fry, J., 2015. Speculative bubbles in bitcoin markets? An empirical investigation into the fundamental value of Bitcoin. Econ. Lett. 130, 32–36. Cheah, E.T., Mishra, T., Parhi, M., Zhang, Z., 2018. Long memory interdependency and inefficiency in bitcoin markets. Econ. Lett. 167, 18–25. Dyhrberg, A.H., 2016a. Hedging capabilities of bitcoin. Is it the virtual gold. Finance Res. Lett. 16, 139–144. Dyhrberg, A.H., 2016b. Bitcoin, gold and the dollar – A GARCH volatility analysis. Finance Res. Lett. 16, 85–92. Engle, R.F., 2002. Dynamic conditional correlation: a simple class of multivariate generalized autoregressive conditional heteroskedasticity models. J. Busi. Econ. Stat. 20, 339–350.

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Finance Research Letters 30 (2019) 30–36

D. Pal and S.K. Mitra

Katsiampa, P., 2017. Volatility estimation for Bitcoin: a comparison of GARCH models. Econ. Lett. 158, 3–6. Koutmos, D., 2018. Bitcoin returns and transaction activity. Econ. Lett. 167, 81–85. Pal, D., Mitra, S.K., 2017. Time-frequency contained co-movement of crude oil and world food prices: a wavelet-based analysis. Energy Econ. 62 (2), 230–239. Pal, D., Mitra, S.K., 2018. Interdependence between crude oil and world food prices: a detrended cross correlation analysis. Physica A 492, 1032–1044. Vidal-Tomas, D., Ibanez, A., 2018. Semi-strong efficiency of bitcoin. Finance Res. Lett. 27, 259–265. http://dx.doi.org/10.1016/j.frl.2018.03.013. Kroner, K.F., Sultan, J., 1993. Time dynamic varying distributions and dynamic hedging with foreign currency futures. J. Finan. Quant. Anal. 28, 535–551. Nadarajah, S., Chu, J., 2017. On the inefficiency of Bitcoin. Econ. Lett. 150, 6–9. Sensoy, A., 2019. The inefficiency of bitcoin revisited: a high-frequency analysis with alternative currencies. Finance Res. Lett. 28, 68–73. https://doi.org/10.1016/j. frl.2018.04.002. Tiwari, A.K., Jana, R.K., Das, D., Roubaud, D., 2018. Informational efficiency of bitcoin—an extension. Econ. Lett. 163, 106–109. Urquhart, A., 2016. The inefficiency of bitcoin. Econ. Lett. 148, 80–82. van der Weide, R., 2002. GO-GARCH: a multivariate generalized orthogonal GARCH model. J. Appl. Econometr. 17, 549–564.

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