October 17, 2016

Team Hullabaloo

Jon-Paul Navarro

Alex Moore

Jake Tremblay

Quieting the Chaos Kraken Investment Case Study: An Analysis and Investment Strategy for

Bitcoin and Ether

Introduction

Bitcoin (BTX) and Ether (ETH) are two of the highest profile members of crypto-currencies—a new,

exciting asset class that has come into being within the past decade. These assets run on decentralized

networks that produce a ledger of transactions using the computing power of all machines on the

network. This running account of historical transactions, with each step having its own unique

cryptographic signature, creates a record that is nearly impossible to alter without detection. This

technology, popularly referred to as Blockchain, has been referenced by many as having the potential to

revolutionize a wide range of transactions inside and outside of the financial industry.

Unlike traditional fiat currencies, no government or central body guarantees the value of these assets.

Market sentiment regarding the future utility and value of these assets can therefore produce large

swings in value. Further compounding this issue, there are dozens of crypto-currencies vying for market

dominance. Despite these enduring questions, the market performances of Ether and Bitcoin, the two

crypto-currencies with the highest market capitalization, as of the publishing date of this analysis, have

been objectively impressive. In evaluating how to invest one million dollars in Bitcoin, Ether, or some

combination of both for the next five years, balancing the large potential upside of these assets with

their volatility played a large role in our deliberations.

Current State of the Crypto-Currency Market

At present, Bitcoin has the largest market capitalization of any cryptocurrency, equivalent to

approximately $9.8 billion USD as of October 2016. This market capitalization eclipses that of the next

most prominent cryptocurrency, Ether (which we will refer to interchangeably as Ethereum) by nearly

an order of magnitude. In turn, Ethereum’s market capitalization is approximately four times greater

than the next closest competitor (Table 1).

Table 1. Snapshot of Crypto-Currency Market October 9, 2016

Asset Market Capitalization (USD)

Price (USD) Trading Volume (24hr)

Bitcoin $9,829,675,887 $617.72 $35591448

Ethereum $1,044,348,129 $12.32 $9,981,326

Ripple $261,532,818 $0.007372 $2464,481

Litecoin $183,515,682 $3.83 $1,038,614 Source: coinmarketcap.com

As the oldest crypto-currency, Bitcoin obtained first mover advantage in this space and spawned a

plethora of imitators. There is no central bank regulating Bitcoin, and total supply is capped at 21 million

Bitcoins. Generation of new Bitcoin is determined by a process called mining. In essence, network users

supply computational power to verify transactions on the Bitcoin network; this computational work is

rewarded with Bitcoin according to predetermined mining rates. Mining rates decline each year, and

current projections estimate that Bitcoin mining will halt in approximately the year 2140. After this

point, no new Bitcoins will enter into circulation. Given a small amount of Bitcoin lost yearly due to

various causes, Bitcoin circulation will almost certainly contract slightly after mining halts. This eventual

monetary contraction reinforces Bitcoin’s central purpose to act as a relatively stable, easily

transferrable store of value.

Ether is a relatively new entrant into the crypto-currency market. Announced in January 2014 and

initially traded in late July 2015, Ether has quickly attained the second largest market capitalization of

any crypto-currency. Ether serves as the “fuel” for the broader Ethereum, a Blockchain platform that

enables smart contracts based on Turing complete architecture. In lay terms, Ethereum allows

developers impressive flexibility in using the network to facilitate a variety of smart contracts. In theory,

Ethereum’s large community of developers will expand Blockchain technology to a variety of everyday

uses. This ideally creates and encourages a network effect in which the more users adopt Ether and use

it as a currency to execute smart contracts, the more valuable Ether becomes. Based on the velocity of

the price increase of Ether, there are a number of people who believe in this optimistic view of Ether’s

future.

In contrast to the declining mining rates of Bitcoin, Ethereum’s developers have projected a constant

rate of Ether issuance of 18,000,000 ETH per year in perpetuity. As the monetary base of Ether

increases, a small yearly percentage loss of Ether from circulation will eventually equilibrate with Ether

issuance, leading to a relatively constant amount of Ether in circulation. Per the Ethereum consortium,

this equilibration is projected to occur approximately 64 years after Ether is initially issued,

corresponding to 2079. A projected change from a proof of work system to proof of stake for Ethereum

may slightly alter this issuance model; per Ethereum literature, however, the change will not materially

affect the monetary base of Ether.

The differing issuance models of Ether and Bitcoin also speak to the broader point that the two assets

were designed for different purposes. Bitcoin was designed primarily as an asset. It was designed as a

digital currency to serve as a relatively stable source of value. Ether, in contrast, was designed with a

broader purpose. It was designed to enable a whole system of smart contracts. While the distinction

may be subtle, we believe it is critical to address. Whether the two assets serve distinct purposes

determines whether the two can coexist for a significant time in the future.

Ultimately, however, the subtle differences between Bitcoin and Ether distract from the broader issue

that a great deal of uncertainty remains around the future of crypto-currencies. Whereas some

countries have moved to embrace crypto-currencies, a number still do not recognize them as legal

tender (see Exhibit 1 for an example in Kenya). This uncertainty is reflected in significant fluctuations in

the price of both Bitcoin and Ethereum. Weekly volatility in bitcoin prices, for instance, has exceeded

the volatility in US equities, US real estate, oil prices, and emerging market equities for the past five

years. Over the past year, volatility in Ether has surpassed the volatility of bitcoin (see Figure 1 for price

comparison of Bitcoin and Ether over the past fourteen months). Any reasonable investment strategy in

these two assets must, therefore, address and at least partially mitigate this volatility.

Figure 1: Price Comparison- Ether vs Bitcoin Over Lifespan of Ether

Data Courtesy of Bloomberg, October 2016

Investment Thesis

The fact that crypto-currencies are being evaluated in the framework of an investment case competition

highlights that these securities do not act like traditional fiat currencies. No investor looks to park a

million dollars worth of Japanese yen or British pounds or some combination thereof in a vault for five

years. The reason for this is relatively simple – most currencies are expected to decline in value. Some

expectation of inflation is built in. Five years from now, one million dollars will not have the same

purchasing power it does today.

We do not conceptualize crypto-currencies in the same fashion. There is an expectation of return on

investment. We argue therefore that a more constructive framework for evaluating investment in these

entities is to treat them as assets. For the sake of simplicity, we will continue to refer to Ether and

Bitcoin as crypto-currencies, but a more accurate term is likely crypto-assets. Like any assets, the value

of Ether and Bitcoin are determined by supply and demand. Advantageously, the developers of Bitcoin

and Ethereum have defined the supply schedule for both currencies, as has been described above.

The second determinant of cryptocurrency value (demand) is much harder to project. This difficulty is

compounded by the fact that the purposes of these two currencies differ. Bitcoin is designed to be a

stable source of value. A valuable analogy is gold. The price of gold increases and decreases with supply

and consumer sentiment, but the primary determinant of its value is that financial actors believe it will

continue to have value in the future. They do not expect to use gold for any kind of application; they

expect to exchange it for goods or services in the future.

Alternately, Ether is probably more analogous to oil. Demand is not dependent solely on an expectation

of future value; it is also a function of utility. Oil prices historically have increased when the potential

uses of oil have increased. Ether’s value will be determined in a similar fashion; it depends on the

number of applications created on the Ethereum framework that will use Ether as a fuel. Prices have

risen recently in large part because investors are bullish on the possibility that Ethereum’s Blockchain

technology will be used in an increasing variety of transactions. With prominent firms like Microsoft and

Thomson Reuters already beginning to build projects on the application development platform, it is a

reasonable expectation that Ethereum will continue to expand, increasing the demand for Ether.

Further evidence of the promising nature of this Blockchain technology is the fact that major financial

institutions including JP Morgan, Credit Suisse, Goldman Sachs, and RBS are all exploring potential

Blockchain applications within their internal operations.

In summary, therefore, we have two fundamentally different assets. One is designed to be a vehicle for

value storage and transfer; the other is designed to act as fuel for a platform utilized in a wide variety of

applications. There is no question that Bitcoin has the more prominent market position at present.

Bitcoin’s market capitalization exceeds that of Ethereum by almost an order of magnitude. It has been

present for a longer period of time and has experienced significantly less volatility than Ethereum over

the short period that the two currencies can be compared head to head. Ethereum, however, offers

significantly higher upside and more impressive recent financial performance. By extending Blockchain

technology to a variety of transactions, Ethereum may serve to make Blockchain technology and crypto-

currencies mainstream. If Ethereum can achieve this goal, the value of Ether will increase accordingly.

This outcome, however, is far from certain, and this uncertainty is reflected in the marked volatility of

both Ether and Bitcoin.

Investment Strategy

An ideal investment strategy in these two cryptocurrencies would expose an investor to the positive

upside potential of Ether while using the comparative stability of Bitcoin and diversification effects to

reduce portfolio variance. Based on historical data of these two currencies, we determined that the

returns of the two currencies are essentially uncorrelated (Figure 2). Holding a portfolio of these two

assets therefore offers the potential for diversification. Using the past six months of data to minimize

any pricing aberrations surrounding the first months of the release of Ether, we used a nonlinear

optimization model in Microsoft Excel to construct a minimum variance portfolio of these two assets

that consists of 67% Bitcoin and 33% Ether.

Figure 2: Ether Return (Y axis) vs Bitcoin Return (X axis)

Data courtesy of Bloomberg, October 2016

Investment Strategy Verification

In order to verify that the Minimum Variance Portfolio (MVP) was the optimal portfolio strategy, three

approaches were used for the quantitative analysis: a 5-year regression forecast, a back-test of six

months of weekly historical prices , and a 52-week Monte Carlo simulation. These tests included three

alternative portfolio strategies in addition to the MVP: 100% Bitcoin, 100% Ether, and a 50% Bitcoin/50%

Ether portfolio.

Regression Model Forecasting

The first step for this forecast method was to analyze the correlation between Bitcoin and Ether along

with more traditional assets. All selected assets were categorized into three “superclasses”: capital

assets, consumable/transformable assets, and store of value assets. Then the correlations were

computed to determine the sensitivity of the crypto-currencies to these comparable assets

For capital assets, we measured the correlation between Bitcoin and Ether to the S&P 500 Index (SPX).

It is difficult to select an individual equity or fixed income security that would best relate to the crypto-

currencies, and it is highly unlikely that a single asset of this nature has such an influential relationship

with the crypto-currencies. Therefore we thought it prudent to use a widely-accepted and diverse index

to replicate the capital market.

For consumable/transformable assets, we analyzed the relationship between Bitcoin and Ether with

several commodities and valuable minerals. We looked at commodities with varying supplies but with

high and stable intrinsic values. The assets that were analyzed were: Gold, Palladium, Neodymium,

Copper, Crude Oil, and Platinum.

Finally for store of value assets, we measured the relationship between the two crypto-currencies and

several fiat currencies. We chose five major currencies: the Japanese Yen, New Zealand Dollar,

Norwegian Krone, British Pound, and the Euro. We also chose five emerging market currencies: Czech

Koruna, Romanian Leu, Argentinian Peso, Hungarian Forint, and the Chinese Renminbi. The emerging

market currencies provided interesting feedback in terms of their correlation to each other and their

significance in the regression forecast models (see Exhibit 2). This could suggest that as some of these

nations face inflation, or even devaluation, pressures perhaps there is a flight to alternative assets, like

crypto-currencies, to protect investor worth.

Table 2: Correlation Results

After analyzing the correlation of each superclass asset with Bitcoin and Ether (see above Table 2), we

chose the most significant commodity from the transformable asset category and the most significant

fiat currency from the store of value asset by finding the individual assets with the lowest p-values (see

Exhibit 3). We accomplished this by running several multivariate regressions against five years of

historical Bitcoin prices (October 7, 2011 to October 6, 2016) and then against all historical weekly prices

of Ether (August 6, 2015 to October 6, 2016). Assets were eliminated until only three variables remained

for each regression: the S&P 500 index, one statistically significant commodity, and one statistically

significant fiat currency.

Using this three-variable regression formula for each crypto-currency, we proceeded to forecast the end

of year prices for five years. The growth rate of the S&P 500 was calculated using the 10-year U.S.

treasury rate plus a 5.7% market risk premium. Growth rates for commodities and fiat currencies were

derived from prevailing prices quoted on futures markets. Values were then entered into our regression

model to calculate yearly prices of Bitcoin and Ether, which can be seen in Table 3. At the end of Year 5,

the MVP is the second most valuable (see Table 4).

Table 3: Yearly Price Comparison of Regression Forecast

BTX Correlation ETH Correlation

SPX Index 0.71922 0.5432457

Gold -0.66627 0.8710952

Palladium 0.19623 0.1843996

Neodymium -0.17775 0.7405717

Copper -0.53426 -0.2771128

Crude Oil -0.28977 0.3326146

Platinum -0.46036 0.6019956

Japan (Yen) 0.52740 -0.8788721

New Zealand (Dollar) -0.13500 0.7347087

Norweigan (Krone) 0.42441 -0.3979021

Czech Repubic (Koruna) 0.39868 -0.4836093

Romanian (Leu) 0.20064 -0.2590778

Argentina (Peso) 0.65229 0.8016911

Hungary (Forint) 0.32231 -0.4518543

China (RMB) 0.11155 0.7230970

Great Britain (Pound) -0.09889 -0.7360760

Euro -0.14748 0.4467235

Annual

Return Rate Year 0 Year 1 Year 2 Year 3 Year 4 Year 5

SPX Index 7.43% 2,161.04 2,321.61 2,494.10 2,679.41 2,878.49 3,092.36

Gold 0.14% 1,268.90 1,270.69 1,272.49 1,274.29 1,276.09 1,277.89

Argentina Peso 1.53% 15.19 15.42 15.66 15.90 16.14 16.39

Ether Value 12.98$ 13.77 15.94 18.26 20.74 23.38

SPX Index 7.43% 2,161.04 2,321.61 2,494.10 2,679.41 2,878.49 3,092.36

Palladium -1.74% 668.70 657.04 645.59 634.33 623.27 612.41

Euro 3.45% 1.12 1.16 1.20 1.24 1.28 1.33

BTX Value 610.82$ 737.23 1,015.98 1,311.09 1,623.69 1,954.97

Table 4: Portfolio Value Comparison of Regression Forecast

Back-Testing

The next method applied was a back-test of the four portfolio strategies to weekly historical prices. The

time range for this test was from April 7, 2016 to October 6, 2016. While the MVP finished third in this

test (see table 5), the MVP had the least volatility of the four strategies (see table 6). It is encouraging to

note that the MVP is only 27 basis points short of the return of the all-Ether portfolio and has less than

half its volatility.

Table 5: Portfolio Value Comparison of Back-Test

Table 6: Weekly Return Statistics Comparison of Back-Test

Another piece of evidence supporting the importance of minimizing portfolio variance is the lack of

prevailing movements in the week-to-week price changes from August 6, 2015 to October 6, 2016. Table

7 illustrates the four possible price-changing combinations of Bitcoin and Ether and their respective

probabilities. While the event that both crypto-currencies increase is most likely, there is an even

greater chance that one or both crypto-currency prices decrease (sum of the remaining three events).

Minimizing the exposure to these downturns becomes more important once this evidence is considered.

Table 7: Probability of Weekly Price Changes

Year 0 Year 1 Year 2 Year 3 Year 4 Year 5

MVP Portfolio 1,000,000.00 1,158,217.05 1,518,324.25 1,900,004.17 2,304,758.63 2,734,196.41

100% ETH 1,000,000.00 1,060,755.87 1,228,350.52 1,407,114.65 1,597,862.21 1,801,467.34

100% BTX 1,000,000.00 1,206,947.64 1,663,311.11 2,146,448.93 2,658,206.84 3,200,560.95

50/50 Portfolio 1,000,000.00 1,133,851.75 1,445,830.81 1,776,781.79 2,128,034.52 2,501,014.14

Date Ether Price BTX Price MVP Portfolio 100% Ether 100% BTX 50/50 Portfolio

4/7/2016 8.07 422.00 1,000,000.00 1,000,000.00 1,000,000.00 1,000,000.00

10/6/2016 12.98 610.82 1,501,102.60 1,608,426.27 1,447,440.76 1,527,933.51

MVP Portfolio 100% Ether 100% BTX 50/50 Portfolio

1.56% 1.83% 1.42% 1.63%

6.46% 14.23% 9.04% 7.45%Average Weekly Volatility

Average Weekly Return

P(X)

ETH and BTX Up 18 30.00%

ETH and BTX Down 11 18.33%

BTX Down/ ETH Up 14 23.33%

BTX Up/ ETH Down 17 28.33%

Total 60 100.00%

# of Events (X)Type of Event

Monte Carlo Simulation

The final method was to run a 52-week Monte Carlo simulation using Excel’s random number generation

tool simulating a normal distribution of returns (Z). These randomly generated returns were then log-

normally transformed to replicate Bitcoin and Ether prices using the following equation where S is the

price at time t:

( 1) ( )* ZS t S t e

The mean (µ) and sigma (σ) for the above equation were calculated from the weekly returns of both

crypto-currencies from April 7, 2016 to October 6, 2016. Three thousand iterations were run, and the

weekly average was calculated. Table 8 shows average final week prices and portfolio values. Table 9

once again confirms that the MVP has the lowest volatility.

Table 8: Portfolio Value Comparison of Monte Carlo Simulation

Table 9: Weekly Return Statistics Comparison of Monte Carlo Simulation

Conclusion

Ether and Bitcoin are examples of an exciting new asset class that offers significant upside potential.

The potential of Blockchain technology is impressive, and we believe that Ether and Bitcoin, as they are

designed for different purposes, can coexist in the future. Despite the potential of these technologies,

marked volatility remains in the market for these crypto-currencies. To partially offset this projected

volatility, we optimized a portfolio of these two assets to minimize expected variance. This MVP per our

analysis consisted of 67% bitcoin and 33% ether. In addition to the mathematical analysis, we believe

this combination strikes an intuitive balance between the upside potential of Ether and the relative

staying power of Bitcoin. Furthermore, our validation models reinforced the conclusion that this

strategy offers a sound investment approach.

Date ETH Price BTX Price MVP Portfolio 100% ETH 100% BTX 50/50 Portfolio

Week 1 12.98 610.82 1,000,000.00 1,000,000.00 1,000,000.00 1,000,000.00

Week 52 56.25 1,539.85 3,125,181.08 4,333,639.02 2,520,952.10 3,427,295.56

MVP Portfolio 100% Ether 100% BTX 50/50 Portfolio

2.17% 2.88% 1.81% 2.42%

0.15% 0.31% 0.18% 0.19%

Average Weekly Return

Average Weekly Volatility

EXHIBIT 1: Public Notice Issued by Central Bank of Kenya

EXHIBIT 2: Correlation Matrix of Ether and Bitcoin (BTX) to Superclass Assets

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-0.9

5960

-0.9

6028

0.7

7231

-0.8

9490

1.0

0000

Cze

ch R

epub

0.3

9868

0.8

0778

-0.7

4546

-0.2

4453

-0.2

4769

-0.9

0070

-0.9

3525

-0.9

2857

0.8

1118

-0.8

3479

0.9

6479

1.0

0000

Rom

ani

an

0.2

0064

0.6

3288

-0.5

6472

-0.4

5883

-0.1

4910

-0.8

3832

-0.9

4194

-0.8

7717

0.6

4205

-0.8

7753

0.9

3293

0.9

4655

1.0

0000

Arg

ent

ina

0.6

5229

0.8

1087

-0.6

8041

-0.2

4653

-0.2

8336

-0.9

1082

-0.8

0854

-0.8

3462

0.6

5220

-0.6

7343

0.8

6961

0.8

0565

0.7

3509

1.0

0000

Hun

gary

0.3

2231

0.7

3316

-0.6

7065

-0.3

4815

-0.3

0651

-0.9

0680

-0.9

4438

-0.9

2722

0.7

4781

-0.8

9471

0.9

7461

0.9

7528

0.9

4799

0.8

0439

1.0

0000

Chi

nese

Yua

n0.1

1155

0.1

7954

-0.0

1782

-0.6

3648

-0.1

7223

-0.5

8264

-0.6

3245

-0.5

0566

0.0

1753

-0.6

0740

0.6

0071

0.4

8500

0.6

0811

0.6

4942

0.5

8122

1.0

0000

GB

P-0

.09889

-0.3

5250

0.2

2508

0.4

8058

0.2

2344

0.6

5945

0.7

1846

0.5

9886

-0.2

6165

0.6

6727

-0.6

8642

-0.6

2638

-0.7

1528

-0.6

7198

-0.6

8822

-0.7

6391

1.0

0000

Eur

o-0

.14748

-0.6

1442

0.5

4193

0.4

3668

0.1

7112

0.8

2127

0.9

3882

0.8

6636

-0.6

3659

0.8

8674

-0.9

2659

-0.9

4629

-0.9

8990

-0.7

1062

-0.9

5650

-0.6

0654

0.7

3319

1.0

0000

EXHIBIT 3: Summary Output for Ether and Bitcoin Regressions

Ether Regression Results

Regression Statistics

Multiple R 0.913211 R Square 0.833954 Adjusted R Square 0.825366 Standard Error 2.299073 Observations 62

ANOVA

df SS MS F Significance

F Regression 3 1539.739804 513.2466015 97.1003357 1.3735E-22 Residual 58 306.5726052 5.285734573 Total 61 1846.31241

Coefficients Standard

Error t Stat P-value Lower 95% Upper 95%

Intercept -59.923015 6.972770 -8.593861 0.000000 -73.880531 -45.965500

S&P 500 Index 0.011039 0.004274 2.582875 0.012343 0.002484 0.019594

Gold 0.026324 0.005452 4.828045 0.000010 0.015410 0.037238

Argentina/USD 0.947690 0.189687 4.996074 0.000006 0.567991 1.327390

BitCoin Regression Summary Results

Regression Statistics Multiple R 0.862519 R Square 0.743940 Adjusted R Square 0.743349 Standard Error 122.836655 Observations 1304

ANOVA

df SS MS F Significance

F Regression 3 56989535.96 18996511.99 1258.977311 0 Residual 1300 19615496.93 15088.84379 Total 1303 76605032.89

Coefficients Standard

Error t Stat P-value Lower 95% Upper 95%

Intercept -

3314.862308 79.092466 -41.911227 0.000000 -

3470.025154 -

3159.699463

S&P 500 Index 1.080850 0.018987 56.924579 0.000000 1.043601 1.118099

Palladium -1.146489 0.054429 -21.064064 0.000000 -1.253266 -1.039711

Euro/USD 1982.255847 58.907816 33.650133 0.000000 1866.691055 2097.820640

References

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Coppola, Frances. "Ethereum: The Battle Of The Chains." Forbes. N.p., 28 July 2016. Web. 7 Oct. 2016.

Coy, Peter, and Olga Kharif. "This Is Your Company on Blockchain." Bloomberg News. N.p., 25 Aug. 2016. Web. 07 Oct. 2016.

Ginovsky, John. "Stake Your Financial Life on Blockchain?" Banking Exchange. N.p., n.d. Web.17 Oct. 2016. http://www.bankingexchange.com/news-feed/item/6508-stake-your-financial-life-on-blockchain?Itemid=593.

"JP Morgan Joins Ethereum in Developing Private Blockchain 'Quorum' - CryptoCoinsNews." CryptoCoinsNews. N.p., 2016. Web. 17 Oct. 2016. https://www.cryptocoinsnews.com/jp-morgan-joins-ethereum-developing-private-blockchain-quorum.

Laurent, Lionel, and Elaine He. "Blockchain's Number Just Don't Add Up, Despite the Hpe: Gadfly." Bloomsberg, 8 Sept. 2016. Web. 7 Oct. 2016.

Nakamura, Yuji. "After $65 Million Hack, Questions of Whether Bitcoin Can Be Safe." Bloomberg News. N.p., 17 Aug. 2016. Web. 7 Oct. 2016.

Prableen Bajpai CFA. "Bitcoin Vs Ethereum: Driven by Different Purposes." Investopedia. N.p., 14 Mar. 2016. Web. 17 Oct. 2016. <http://www.investopedia.com/articles/investing/031416/bitcoin-vs-ethereum-driven-different-purposes.asp>.

Shin, Laura. "4 Reasons Why Bitcoin Represents A New Asset Class." Forbes. N.p., 2 June 2016. Web. 7 Oct. 2016.

Stafford, Philip. "Banks Struggle to Make Blockchain Fast and Secure." Financial Times. N.p., 26 Sept. 2016. Web. 07 Oct. 2016.

"What Investors Should Know Before Trading Ether" CoinDesk. N.p., 2016.Web. 17 Oct. 2016. http://www.coindesk.com.

"What Is Ether?" Ethereum.org. N.p., n.d. Web. 10 Oct. 2016. https://www.ethereum.org/ether.