Estimating the Beta of Bitcoin

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Estimating the Beta of Bitcoin

Abstract

This paper seeks to estimate the beta of bitcoin against five different portfolios. Two of

the portfolios are to see if any insight can be made into bitcoin pricing through a Capital

Asset Pricing Model analysis. Three of the portfolios are to see if any empirical data can

be used to develop insight into the classification debate surrounding bitcoin. The paper

begins with a discussion of bitcoin, bitcoin price history, and the bitcoin classification

debate, then discusses beta, how beta is calculated, and beta adjustments for asynchronous

data, followed by a discussion on purpose and methodology, then the results in detail, and

finally a summary of the results and their implications.

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Bitcoin

Bitcoin is a peer to peer payment system which was proposed in 2008 and introduced January 3rd

2009.1 An important distinction is necessary for clarity between bitcoin the payment system and bitcoin

the token of the payment system, for the purposes of this paper “bitcoin” refers to the token. Bitcoin

prices have been incredibly volatile, undergoing several bubbles and collapses in its short life. From

January to October of 2011, the price went from $0.90 to almost $30 then back down to approximately

$3. From January to July of 2013 the price went from $13.50 to over $230 then back down to around

$100. The largest bubble to date occurred in late 2013 and early 2014 which saw the price skyrocket to a

peak of more than $1100 and fall back down dramatically. Charts graphing these dramatic price

movements are included in the appendix to this paper. With these incredible price movements it would

seem that all risk of bitcoin returns would be idiosyncratic, with little to no market influence observable.

This seems to be a decent hypothesis, however to the best of my knowledge empirical evidence

supporting this remains unpublished.

Much debate surrounds the classification of bitcoin; it might be a currency, commodity, or even

perhaps some new asset class. For many, the bitcoin token would be most aptly classified as a currency,

indeed it is often called a “cryptocurrency”. The US Financial Crimes Enforcement Network agrees with

this, and has ruled that virtual currencies are no different than traditional currencies when it comes to

compliance with money transmission regulations.2 However, there are others that disagree with this

classification. For example, the US Commodities Futures Trading Commission has publicly stated that it

believes bitcoin to be a “commodity covered by the Commodity Exchange Act”.3 Bergstra and Weijland

(2014) have proposed that bitcoin is a new asset class which they have termed Money-like Information

Commodity.4 The debate surrounding bitcoin’s classification is far from being resolved, and

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commentators have largely taken a conceptual approach. Thus far no one has searched for empirical

indications that could shed light on this debate.

Beta (β)

Beta (β) measures the systemic risk of an individual asset when compared to a benchmark

portfolio. The benchmark portfolio can be any portfolio, although the meaning of beta changes

depending on which benchmark it is calculated against. There are three equivalent ways to calculate

beta, perhaps the simplest calculation to understand would be from correlation and volatility, which is

𝛽𝑎 = 𝜌𝑎𝑝(�̃�𝑎, �̃�𝑝)𝜎𝑎𝜎𝑝

𝜎𝑝2

Where 𝛽𝑎 is the beta of the asset 𝑎 against portfolio 𝑝,

𝜌𝑎𝑝 is the correlation of asset 𝑎 against portfolio 𝑝,

�̃�𝑎 is the sample return of the asset, �̃�𝑝 is the sample return of the portfolio,

𝜎𝑎 is the standard deviation of the asset, and 𝜎𝑝 is the standard deviation of the portfolio.

This calculation is identical to the calculation from covariance and variance, which is

𝛽𝑎 = 𝑐𝑜𝑣(�̃�𝑎,�̃�𝑝)

𝜎𝑝2

Where 𝛽𝑎 is the beta of the asset 𝑎 against portfolio 𝑝,

𝑐𝑜𝑣(�̃�𝑎, �̃�𝑝) is the covariance of the returns of asset 𝑎 against the returns of portfolio 𝑝,

and 𝜎𝑝2 is the variance of the portfolio.

For the purposes of the Capital Asset Pricing Model (CAPM), the benchmark portfolio is taken to be the

Market Portfolio, a weighted sum of every investable asset. The CAPM analysis attempts to calculate

the assets appropriate return when its beta is known. Roll (1977) critiqued the CAPM showing that there

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are many problems inherent in creating or even observing a Market Portfolio.5 Because of this difficulty

practitioners often substitute a market tracking index for the purposes of calculating beta. When viewed

in the light of the CAPM, the definition of beta is a regression of asset returns against portfolio returns.

This is especially useful for illustrating the idea of beta as the amount of systemic risk from a portfolio

in an asset. The regression definition is

�̃�𝑎 = 𝛼𝑎,𝑝 + 𝛽𝑎 ∙ �̃�𝑝 + 𝜖�̃�

Where �̃�𝑎 is the sample returns of asset 𝑎,

𝛼𝑎,𝑝 is the alpha (excess returns) of asset 𝑎 against portfolio 𝑝,

𝛽𝑎 is the beta of the asset 𝑎 against portfolio 𝑝,

�̃�𝑝 is the sample returns of portfolio 𝑝,

and 𝜖�̃� is the idiosyncratic risk of asset 𝑎.

Although for the purposes of the CAPM the benchmark portfolio should attempt to include the weighted

sum of as many assets as possible, beta can also be calculated against other portfolios. For example, beta

calculated against an individual investor’s portfolio would show that investor the rate at which risk is

added to the portfolio by adding the asset.

There exists a problem in estimating betas from real world trading information which is caused

by asynchronous price observations. For example, if we have price observations for the benchmark

portfolio occurring regularly (frequent trading) while price observations for the asset occur infrequently,

a specific periods last price information might have occurred at different times and therefore have

different information impounded in it. This informational asymmetry can lead to an imperfect estimation

of beta. To tackle this issue, Scholes and Williams (1977) proposed estimating leading and lagging

betas, betas calculated on next and previous period returns, and then summing all calculated betas and

adjusting for autocorrelation.6 This produces a fairly good estimation of beta, but has the problem of

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producing high error rates. To further improve on this theory Dimson (1979) proposed a trade-to-trade

beta which adjusts the regression to account for time differences between price observations instead of

the entire period.7

Purpose and Methodology

I am interested in estimating the beta of bitcoin for many reasons. First and foremost this inquiry

has not to my knowledge been rigorously performed yet, and is a very interesting topic which I think

deserves to be researched, especially in relation to the two CAPM analyses. In addition to this, if

noteworthy results are obtained from the other analyses, it could potentially shed light onto the debate

surrounding the classification of bitcoin. To attempt the CAPM analysis, I ran beta, Sholes-Williams

beta, and Dimson beta calculations of bitcoin against both the S&P 500 and the FTSE Global All Cap

Index (tracked by ETF VT). I have made the same calculations against three other “portfolios” to see if

there is potentially any empirical insight to be had in relation to the classification debate surrounding

bitcoin. The three other portfolios chosen are the Bloomberg Dollar Spot Index which tracks a basket of

10 currencies against the US dollar (BBDXY),8 the historical spot price of gold (XAU), and the

Bloomberg Commodity Index (BCOM).9 All analyses were performed across a variety of time series

and data resolutions, namely five years of monthly data, approximately five years of daily data, one year

of daily data, and three months of ten minute data. All data was retrieved from the Bloomberg

Professional service on October 20th 2015. All dollars are US Dollars. A beta of near 1 or greater than 1

would indicate that bitcoin prices contain systemic risk related to the benchmark portfolio. Because

bitcoin is very volatile, a result near 0 would indicate that bitcoin prices are uncorrelated with the

benchmark portfolio and do not share systemic risk. A result of negative 1 or less than that would

indicate that bitcoin could function as a hedge against systemic risk from the benchmark portfolio.

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S&P 500 (SPX)

The S&P 500 is an index of 500 large cap companies from the United States.10 The beta of

bitcoin calculated on five years of monthly data against the S&P 500 was performed by calculating the

covariance of bitcoin and S&P 500 returns and dividing by the variance of S&P 500 returns. The

resulting beta of 5.05 is a rather interesting result as it would indicate a high level of shared risk,

however as we see below the scatterplot of returns does not produce much confidence in this result.

There are many extreme outliers, the most notable example of this being November of 2013, when

bitcoin had a return of 451% while the S&P 500 returned 2.8%. This result comes with a very low 𝑅2,

indicating that the regression is a poor descriptor of the data.

To capture a higher resolution, the same calculation was done on daily data for approximately 5

years. In order to compensate for asynchronous data, both the Sholes-Williams and Dimson betas were

calculated on this data set. The beta without adjustment was 0.35, and after Scholes-Williams

adjustment rose to 0.52. The scatterplot of returns is as follows:

y = 5.0469x + 0.2407

R² = 0.042

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S&P 500 Returns

Bitcoin vs S&P 500 Monthly Returns 5 Years

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As can be seen from the data, no real regression can be honestly performed as there is no relationship in

the data. Dimson adjusted returns heavily impact data points which are temporally close to each other, as

asset returns are adjusted by dividing by the square of the time difference from the previous data point,

and portfolio returns are adjusted by dividing by the inverse of the squared time differences. The

Dimson beta of this data set is 0.24, however as we can see from the scatterplot found in Figure 5 in the

appendix this result also does not carry much weight.

To see previous results with less noise but still a significant amount of data, identical calculations

were performed on one year of daily data. The beta of this data set was found to be 0.37, and after

Sholes-Williams adjustment rose to 1.07, however as seen in the scatterplot below the regression is a

poor descriptor of the data with an 𝑅2 of only 0.0089.

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S&P 500 Returns

Bitcoin vs S&P 500 Daily Returns 2010-2015

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After the Dimson adjustment the beta was calculated to be 0.28, but again the low 𝑅2 of 0.009 indicates

a poor regression. This scatterplot can be seen in Figure 6 in the appendix.

To capture an even higher level of resolution identical calculations were performed on three

months of ten minute data. The beta of this data set was calculated to be 0.29, and after Scholes-

Williams adjustment rose to 0.32. Again, the regression is not significant.

y = 0.369x - 5E-05

R² = 0.0089

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S&P 500 Returns

Bitcoin vs S&P 500 Daily Returns 2014-2015

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S&P 500 Returns

Bitcoin vs S&P 500 10 Minute Returns 3 Months

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After the Dimson adjustment the beta was calculated to be 0.32, but the 𝑅2 is too low for significance.

The scatterplot is included here to illustrate how Dimson adjustments heavily impact temporally close

data points; it is rather remarkable how many of the S&P 500 returns approximate 0%.

FTSE Global All Cap Index (VT)

The FTSE Global All Cap Index is a global index that covers approximately 7,400 securities.11 It

is tracked by the ETF VT, which was used for this analysis. The beta of bitcoin calculated on five years

of monthly data against VT was performed by calculating the covariance of bitcoin and VT returns and

dividing by the variance of VT returns. The calculated beta of 3.88 is rather high, but the 𝑅2 is low

indicating the regression is not a good descriptor of the underlying data.

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S&P500 Adjusted Returns

Bitcoin vs S&P 500 Dimson

10 Minute Returns 3 Months

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Again the outliers are rather dramatic, and in November of 2013 bitcoin returned 451% while VT

returned 1.5%. Perhaps without the handful of data points that are outliers the result would be

significant, but removing inconvenient data points to achieve significance would not be advisable.




adjustment rose to 0.47. As seen in the scatterplot the actual returns seem to be randomly distributed,

and the low 𝑅2 of 0.002 indicates that the results are not significant.

y = 3.8805x + 0.2708

R² = 0.034

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VT Returns

Bitcoin vs VT Monthly Returns 5 Years

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After Dimson adjustment, the beta was calculated to be 0.22, however again the low 𝑅2 indicates that

the results are not significant. The scatterplot of Dimson adjusted returns for this data set can be found in

Figure 7 in the appendix.



Scholes-Williams adjustment rose to 0.83. Again the scatterplot of returns indicates that the results are

not significant; this scatterplot can be seen in Figure 8 in the appendix. After Dimson adjustment the

beta was calculated to be 0.26, again with a low 𝑅2 of 0.008 indicating the results are not significant; the

scatterplot of these results can be found in Figure 9 in the appendix.



Williams adjustment rose to 0.34. The low 𝑅2 indicates that these results are not significant; the

scatterplot of returns can be found in Figure 10 in the appendix. After Dimson adjustment the beta was

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VT Returns

Bitcoin vs VT Daily Returns 2010-2015

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calculated to be 0.28, with a low 𝑅2 of 0.002 indicating the results are not significant; the scatterplot of

these results can be found in Figure 11 in the appendix.

Bloomberg Dollar Spot Index (BBDXY)

The Bloomberg Dollar Spot Index tracks a basket of ten global currencies against the US

Dollar.8 The beta of bitcoin calculated on five years of monthly data against BBDXY was performed by

calculating the covariance of bitcoin and BBDXY returns and dividing by the variance of BBDXY

returns. The calculated beta of -7.01 is very low, but the 𝑅2 of 0.029 is low indicating the regression is

not a good descriptor of the underlying data.



calculated on this data set. The beta without adjustment was -0.51, and after Scholes-Williams

adjustment fell to -0.89. As seen in the scatterplot the actual returns seem to be randomly distributed,


y = -7.0051x + 0.3132

R² = 0.0291

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Bitcoin vs BBDXY Monthly Returns 5 Years

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After Dimson adjustment, the beta was calculated to be -0.43, however again the low 𝑅2 of 0.006

indicates that the results are not significant. The scatterplot of Dimson adjusted returns for this data set

can be found in Figure 12 in the appendix.





beta was calculated to be 0.14, again with a low 𝑅2 of 0.0008 indicating the results are not significant;

the scatterplot of these results can be found in Figure 14 in the appendix.



Williams adjustment remained approximately the same at to 0.29. The low 𝑅2 indicates that these results

are not significant; the scatterplot of returns can be found in Figure 15 in the appendix. After Dimson

adjustment the beta was calculated to be 32.43, an extraordinary amount, but the low 𝑅2 of 0.0009

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BBDXY Returns

Bitcoin vs BBDXY Daily Returns 2010-2015

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indicates the results are not significant. The scatterplot is included below to further highlight how

Dimson adjustment impacts temporally close data points, especially with a volatile asset like bitcoin. A

return of below 100% seems impossible, but remember that the Dimson adjustment amplifies returns on

assets with large returns that have temporally close data points.

Gold (XAU)

Gold is a commodity which historically has served as money. The beta of bitcoin calculated on

five years of monthly data against gold was performed by calculating the covariance of bitcoin and gold

returns and dividing by the variance of gold returns. The calculated beta of -0.04 is low, but the 𝑅2 of

approximately 0 is low indicating the regression is not a good descriptor of the underlying data.

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BBDXY Adjusted Returns

Bitcoin vs BBDXY Dimson 10 Minute Returns 3 Months

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calculated on this data set. The beta without adjustment was -0.08, and after Scholes-Williams



y = -0.0382x + 0.2873

R² = 6E-06

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Gold Returns

Bitcoin vs Gold Monthly Returns 5 Years

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Gold Returns

Bitcoin vs Gold Daily Returns 2010-2015

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After Dimson adjustment, the beta was calculated to be -0.06, however again the low 𝑅2 of 0.006





Scholes-Williams adjustment fell to 0.31. Again the scatterplot of returns indicates that the results are


beta was calculated to be -0.17, again with a low 𝑅2 of 0.004 indicating the results are not significant;



months of ten minute data. The beta of this data set was calculated to be -0.12, and after Scholes-

Williams adjustment fell slightly to -0.15. The low 𝑅2 indicates that these results are not significant; the


calculated to be -6.04, but the low 𝑅2 of 0.0003 indicates the results are not significant. The scatterplot

of Dimson adjusted returns for this data set can be found in Figure 20 in the appendix.

Bloomberg Commodity Index (BCOM)

The Bloomberg Commodity Index is a weighted average of twenty two exchange-traded futures

on physical commodities.9 The beta of bitcoin calculated on five years of monthly data against gold was

performed by calculating the covariance of bitcoin and gold returns and dividing by the variance of gold

returns. The calculated beta of 2.13 is high, but the 𝑅2 of 0.0134 is low indicating the regression is not a

good descriptor of the underlying data.

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y = 2.1239x + 0.3018

R² = 0.0134

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BCOM Returns

Bitcoin vs BCOM Monthly Returns 5 Years

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BCOM Returns

Bitcion vs BCOM Daily Returns 2010-2015

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After Dimson adjustment, the beta was calculated to be 0.19, however again the low 𝑅2 of 0.007







beta was calculated to be 0.05, again with a low 𝑅2 of 0.0006 indicating the results are not significant;




Williams adjustment rose slightly to 0.17. The low 𝑅2 indicates that these results are not significant; the


calculated to be 0.49, but the low 𝑅2 of 0.0007 indicates the results are not significant. The scatterplot

of Dimson adjusted returns for this data set can be found in Figure 25 in the appendix.

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Summary of Results

Data Set and Calculation XBT vs.

Time Resolution Beta SPX VT BBDXY XAU BCOM

Five Years Monthly Data Beta 5.05 3.88 -7.01 -0.04 2.13

Five Years Daily Data Scholes-Williams Beta 0.52 0.47 -0.89 1.03 1.18

Five Years Daily Data Dimson Beta 0.24 0.22 -0.43 -0.06 0.19

One Year Daily Data Scholes-Williams Beta 1.07 0.83 0.42 0.31 0.42

One Year Daily Data Dimson Beta 0.28 0.26 0.14 -0.17 0.05 Three Months

Ten Minute Data Scholes-Williams Beta 0.32 0.34 0.29 -0.15 0.17

Three Months

Ten Minute Data Dimson Beta 0.32 0.28 32.43 -6.04 0.49

As we can see, all results were not statistically significant and no real consistent estimation of

beta can be made. For the purposes of the CAPM analysis, it seems that all bitcoin risk is idiosyncratic,

and it shares no systemic risk from the market portfolio. This is an interesting result because it means

that bitcoin offers new diversification for the investor trying to create a market portfolio. For the

purposes of contributing to the classification debate, it appears that bitcoin does not share significant

amounts of systemic risk with currencies, gold, or commodities more broadly. This perhaps slightly

supports the assertion that bitcoin represents a new class of asset, but that is up to the reader to decide

for themselves.

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Appendix.

Figures 1 through 4 demonstrate the volatile nature of the price of bitcoin over time.

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Bitcoin Price July 2010 to October 2015

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Figure 5 shows the scatterplot of five years of Dimson adjusted bitcoin returns against S&P 500 returns.

A trend line illustrating the regression is not shown as it is obvious both visually and from the low 𝑅2

that the data does not have a significant regression.

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Bitcoin Price August 2013 to April 2014

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S&P 500 Returns

Bitcoin vs S&P 500 Daily

Dimson Returns 2010-2015

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Figure 6 shows the scatterplot of one year of Dimson adjusted bitcoin returns against S&P 500 returns.

A trend line illustrating the regression is not shown as it is obvious both visually and from the low 𝑅2

that the data does not have a significant regression.

Figure 7 shows the scatterplot of five years of Dimson adjusted bitcoin returns against VT returns. A

trend line illustrating the regression is not shown as it is obvious both visually and from the low 𝑅2 that

the data does not have a significant regression.

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S&P 500 Adjusted Returns

Bitcoin vs S&P 500 Daily

Dimson Returns 2014-2015

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VT Adjusted Returns

Bitcoin vs VT Dimson Returns

by Day 2010-2015

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Figure 8 shows the scatterplot of one year of daily returns of bitcoin against VT. A trend line illustrating

the regression is not shown as it is obvious both visually and from the low 𝑅2 that the data does not have

a significant regression.

Figure 9 shows the scatterplot of one year of Dimson adjusted daily returns of bitcoin against VT. A

trend line illustrating the regression is not shown as it is obvious both visually and from the low 𝑅2 that

the data does not have a significant regression.

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VT Returns

Bitcoin vs VT Daily Returns 2014-2015

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VT Adjusted Returns

Bitcoin vs VT Dimson

Daily Returns 2014-2015

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Figure 10 shows the scatterplot of three months of ten minute returns of bitcoin against VT. A trend line

illustrating the regression is not shown as it is obvious both visually and from the low 𝑅2 that the data

does not have a significant regression.

Figure 11 shows the scatterplot of three months of Dimson adjusted ten minute returns of bitcoin against

VT. A trend line illustrating the regression is not shown as it is obvious both visually and from the low

𝑅2 that the data does not have a significant regression. Note again how the Dimson adjustment impacts

temporally close data points.

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-6.0% -5.0% -4.0% -3.0% -2.0% -1.0% 0.0% 1.0% 2.0% 3.0% 4.0%

Bit

coin

Ret

urn

s

VT Returns

Bitcoin vs VT 10 Minute Returns 3 Months

-30.00%

-20.00%

-10.00%

0.00%

10.00%

20.00%

30.00%

40.00%

-10.00% -8.00% -6.00% -4.00% -2.00% 0.00% 2.00% 4.00% 6.00%

Bit

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VT Adjusted Returns

Bitcoin vs VT Dimson 10 Minute Returns 3 Months

25

Figure 12 shows the scatterplot of five years of daily returns of bitcoin against BBDXY. A trend line



Figure 13 shows the scatterplot of one year of daily returns of bitcoin against BBDXY. A trend line



-80.0%

-60.0%

-40.0%

-20.0%

0.0%

20.0%

40.0%

60.0%

-3.0% -2.0% -1.0% 0.0% 1.0% 2.0% 3.0% 4.0%

Bit

coin

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eturn

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Bitcoin vs BBDXY Dimson


-25.0%

-20.0%

-15.0%

-10.0%

-5.0%

0.0%

5.0%

10.0%

15.0%

20.0%

-6.0% -5.0% -4.0% -3.0% -2.0% -1.0% 0.0% 1.0% 2.0%

Bit

coin

Ret

urn

s

BBDXY Returns

Bitcion vs BBDXY Daily Returns 2014-2015

26

Figure 14 shows the scatterplot of one year of Dimson adjusted returns of bitcoin against BBDXY

returns. A trend line illustrating the regression is not shown as it is obvious both visually and from the

low 𝑅2 that the data does not have a significant regression.

Figure 15 shows the scatterplot of three months of bitcoin returns against BBDXY returns. A trend line



-30.0%

-25.0%

-20.0%

-15.0%

-10.0%

-5.0%

0.0%

5.0%

10.0%

15.0%

20.0%

-2.0% -1.5% -1.0% -0.5% 0.0% 0.5% 1.0% 1.5% 2.0%

Bit

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Bitcoin vs BBDXY Dimson


-10.0%

-8.0%

-6.0%

-4.0%

-2.0%

0.0%

2.0%

4.0%

6.0%

8.0%

-0.8% -0.6% -0.4% -0.2% 0.0% 0.2% 0.4% 0.6%

Bit

coin

Ret

urn

s

BBDXY Returns

Bitcoin vs BBDXY 10 Minute Returns 3 Months

27

Figure 16 shows the scatterplot of five years of Dimson adjusted returns of bitcoin against gold. A trend

line illustrating the regression is not shown as it is obvious both visually and from the low 𝑅2 that the

data does not have a significant regression.

Figure 17 shows the scatterplot of one year of daily returns of bitcoin against gold. A trend line



-80.0%

-60.0%

-40.0%

-20.0%

0.0%

20.0%

40.0%

60.0%

-20.0% -15.0% -10.0% -5.0% 0.0% 5.0% 10.0%

Bit

coin

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Gold Adjusted Returns

Bitcoin vs Gold Dimson


-25.0%

-20.0%

-15.0%

-10.0%

-5.0%

0.0%

5.0%

10.0%

15.0%

20.0%

-4.0% -3.0% -2.0% -1.0% 0.0% 1.0% 2.0% 3.0% 4.0% 5.0%

Bit

coin

Ret

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Gold Returns

Bitcoin vs Gold Daily Returns 2014-2015

28

Figure 18 shows the scatterplot of one year of Dimson adjusted returns of bitcoin against gold. A trend


data does not have a significant regression.

Figure 19 shows three months of ten minute returns of bitcoin against gold. A trend line illustrating the

regression is not shown as it is obvious both visually and from the low 𝑅2 that the data does not have a

significant regression.

-30.0%

-25.0%

-20.0%

-15.0%

-10.0%

-5.0%

0.0%

5.0%

10.0%

15.0%

20.0%

-8.0% -6.0% -4.0% -2.0% 0.0% 2.0% 4.0% 6.0% 8.0%

Bit

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Bitcoin vs Gold Dimson


-10.0%

-8.0%

-6.0%

-4.0%

-2.0%

0.0%

2.0%

4.0%

6.0%

8.0%

-0.6% -0.4% -0.2% 0.0% 0.2% 0.4% 0.6% 0.8% 1.0%

Bit

coin

Ret

urn

s

Gold Returns

Bitcoin vs Gold 10 Minute Returns 3 Months

29

Figure 20 shows three months of Dimson adjusted ten minute returns. A trend line illustrating the


significant regression. Note again how the Dimson adjustment impacts temporally close data points.

Figure 21 shows five years of daily returns of bitcoin against BCOM. A trend line illustrating the



-150.00%

-100.00%

-50.00%

0.00%

50.00%

100.00%

-0.20% -0.10% 0.00% 0.10% 0.20% 0.30% 0.40% 0.50%

Bit

coin

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Bitcoin vs Gold Dimson 10 Minute Returns 3 Months

-80.0%

-60.0%

-40.0%

-20.0%

0.0%

20.0%

40.0%

60.0%

-10.0% -8.0% -6.0% -4.0% -2.0% 0.0% 2.0% 4.0% 6.0%

Bit

coin

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BCOM Adjusted Returns

Bitcoin vs BCOM Dimson


30

Figure 22 shows one year of daily returns of bitcoin against BCOM. A trend line illustrating the



Figure 23 shows one year of Dimson adjusted returns of bitcoin against BCOM. A trend line illustrating



-25.0%

-20.0%

-15.0%

-10.0%

-5.0%

0.0%

5.0%

10.0%

15.0%

20.0%

-5.0% -4.0% -3.0% -2.0% -1.0% 0.0% 1.0% 2.0% 3.0% 4.0%

Bit

coin

Ret

urn

s

BCOM Returns

Bitcoin vs BCOM Daily Returns 2014-2015

-30.0%

-25.0%

-20.0%

-15.0%

-10.0%

-5.0%

0.0%

5.0%

10.0%

15.0%

20.0%

-6.0% -4.0% -2.0% 0.0% 2.0% 4.0% 6.0%

Bit

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Bitcoin vs BCOM Dimson


31

Figure 24 shows three months of ten minute returns of bitcoin against BCOM. A trend line illustrating



Figure 25 shows three months of Dimson adjusted ten minute returns of bitcoin against BCOM. A trend


data does not have a significant regression. Note again how the Dimson adjustment impacts temporally

close data points.

-8.0%

-6.0%

-4.0%

-2.0%

0.0%

2.0%

4.0%

6.0%

-1.5% -1.0% -0.5% 0.0% 0.5% 1.0%

Bit

coin

Ret

urn

s

BCOM Returns

Bitcoin vs BCOM 10 Minute Returns 3 Months

-40.00%

-30.00%

-20.00%

-10.00%

0.00%

10.00%

20.00%

30.00%

40.00%

-2.00% -1.50% -1.00% -0.50% 0.00% 0.50% 1.00%

Bit

coin

Ad

just

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eturn

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Bitcoin vs BCOM Dimson 10 Minute Returns 3 Months

32

Bibliography

1. https://bitcoin.org/bitcoin.pdf

2. https://www.fincen.gov/statutes_regs/guidance/html/FIN-2013-G001.html

3. http://www.cftc.gov/PressRoom/PressReleases/pr7231-15

4. http://arxiv.org/pdf/1402.4778.pdf

5. Roll, Richard (1977). A critique of the asset pricing theory's tests Part I: On past and

potential testability of the theory. Journal of Financial Economics, 4(2):129–176.

6. Scholes, M. and Williams, J. (1977). Estimating betas from nonsynchronous data. Journal

of Financial Economics, 5:309–327.

7. Dimson, E. (1979). Risk measurement when shares are subject to infrequent trading.

Journal of Financial Economics, 7:197–226.

8. http://www.bloombergindexes.com/content/uploads/sites/3/2013/12/Dollar_Spot_Index_Fact_Sh

eetv2.pdf

9. http://www.bloombergindexes.com/content/uploads/sites/3/content/uploads/sites/3/2015/10/BCO

M-Fact-Sheet.pdf

10. http://ca.spindices.com/indices/equity/sp-500

11. http://www.ftse.com/products/indices/geis-series

https://bitcoin.org/bitcoin.pdf

https://www.fincen.gov/statutes_regs/guidance/html/FIN-2013-G001.html

http://www.cftc.gov/PressRoom/PressReleases/pr7231-15

http://arxiv.org/pdf/1402.4778.pdf

http://www.bloombergindexes.com/content/uploads/sites/3/2013/12/Dollar_Spot_Index_Fact_Sheetv2.pdf

http://www.bloombergindexes.com/content/uploads/sites/3/2013/12/Dollar_Spot_Index_Fact_Sheetv2.pdf

http://www.bloombergindexes.com/content/uploads/sites/3/content/uploads/sites/3/2015/10/BCOM-Fact-Sheet.pdf

http://www.bloombergindexes.com/content/uploads/sites/3/content/uploads/sites/3/2015/10/BCOM-Fact-Sheet.pdf

http://ca.spindices.com/indices/equity/sp-500

http://www.ftse.com/products/indices/geis-series

Documents

Estimating the Beta of Bitcoin