The financial market has throughout been subjected to a lot of volatility which has made it an area of speculative investment for investors. Of all the other concerns that investors have with regards to risk minimisation, the two concerns that this paper focuses on are : (a) Volatility in Prices of their stocks and (b) Financial Fraud Crimes. The same concerns also apply when investors decide to invest in Cryptocurrency. Thus this paper tries to draw a competitive analysis between Cryptocurrencies and Traditional Stocks based on parameters (a) and (b) stated above, taking Bitcoins and S&P 500 Index Portfolio as representatives of cryptocurrencies and traditional stocks in the US Stock Market, respectively. Using instruments like Value at Risk analysis, forensic accounting index and an econometric model, the conclusion that has been reached is that the S&P 500 Index Portfolio is a less risky prospect for investment, as compared to Bitcoins, in terms of the aforementioned parameters, in the US Stock Market.


​Bitcoins, Cryptocurrency, Cryptohacks, Financial-Fraud-Crime, Forensic Accounting, S&P 500 Index, Value-at-Risk Analysis.


In today’s date, given a financial world with so much volatility and dynamicity, an investor seems to stand invariably at an inflection point, when faced with a choice of investment. Managing investment capital and liquidity of assets, strategically, has come to be recognised as a virtue.

Historically, it has been observed, in the case of traditional stocks, the announcement of fraud has had an adverse impact on their prices and consequently also on an investor’s portfolio-holding and wealth. The factors except for financial frauds that are taken into consideration in an investor’s decisions to hold stocks are ​volatility in commodity prices of the companies he is about to invest in, volatility of foreign exchange market, equity price risk​, etc, to name a few. In certain situations, hence, investors also like to explore new avenues of investment, diversifying their portfolios by investment in digital currencies.

Figure 1​​ : Y- axis depicting the rise and drop in S&P 500 index portfolio (in USD) over years 2012-2019.

With the coming of age cryptocurrency, especially Bitcoin, which is slowly moving towards a receiving end of peoples’ trust and acceptance globally, more people are looking forward to investing into it and holding it as a part of their portfolio. However, Bitcoin’s volatility still continues to be a question of concern for some investors and so does it’s utility as a store of value, hence.

For sake of a competitive analysis, in an attempt to look for courses of investment with the objective of risk minimisation between traditional stocks and cryptocurrency two representative alternatives: ​S&P 500 ​and ​Bitcoins ​have been taken into account. The reasons have been listed as follows:

  1. The S&P 500 takes under its wings 500 large companies’ stocks in the United States. It is thus considered the best representation of the U.S stock market.
  2. Bitcoin, similarly, has had an all-time record of being the most widely invested in cryptocurrency. As also remarked by Alex Mashinsky, CEO at Celsius Network when reporting to FOX Business, ​​”the most popular crypto is Bitcoin because it was the first one to be widely used and is generally considered the safest to own.”

The idea of this paper is to conduct a case study on the US Stock Market under the influence of Crypto-Hacks and Price-Volatility, implementing concepts of simple financial tools, concepts of forensic accounting and simple econometrics, on statistical software (STATA and Python), to determine safer avenues of investment, by drawing a competitive analysis between cryptocurrencies and traditional stock index portfolio.

Figure 2​ ​: Y- axis depicting rise and drop in Bitcoin Prices (in USD) – y axis over the year 2013 -2014.


To analyze the impact of price-volatility and financial-fraud-crimes on cryptocurrency and the traditional stock market, with an objective of investigating which of the two is a less-risky avenue of investment for a probationary investor.


The ​paper construction​ has been done in two parts:

Part A​:

Sub-part Objective​: Analysis of portfolio investment in Bitcoin ​versus​ S&P 500 Index Portfolio, gauging for ​price volatility of the assets​.

The instrument used: For this ​comparison of risk involved​ in initial investment in Bitcoin and S&P 500 Portfolio (over a period of two months), the instrument used is ​Value at Risk​ (mean-variance analysis), with​ normality assumption​ imposed on our conjured portfolios.

Part B:

Sub-part Objective​: Analysis of portfolio investment in Bitcoin ​versus​ S&P Index Portfolio, gauging for ​financial fraud crimes. The instruments used:

● ​for Part B(i)​​ the use of ​a pre-conducted analysis of the forensic accounting report prepared by V&M Breakouts​ (on the overall US Stock market by V&M Breakouts) has been made in order to analytically come to conclusion as to ​how reliable the S​&P 500 portfolio​ is in terms of being an investment with low risk of financial fraud.​

● ​For Part B(ii)​​ ​a simple econometric model ​with variables – Bitcoin Monthly Prices regressed over Reported Bitcoin Monthly Hacks (in USD) of the preceding two periods, has been constructed to determine​ how reliable​ Bitcoin​ investments are in face of fraudulent activities and crypto hackers.​


The ​exhaustive list of assumptions ​for this analysis, to better facilitate drawing a competitive analysis between cryptocurrencies and traditional stocks include​ :

  1. The investor has ​no dearth of resources for investment​.
  2. His decision for investment in Cryptocurrencies and Traditional Stock is ​a mutually exclusive decision.
  3. The investor is essentially ​risk-averse​ and hence chooses to diversify his share in a huge portfolio​ when investing in traditional stocks. Thus he chooses to invest in S&P index share, ​which has shares of about 500 companies and covers​ ​80 % of the US- equity market​​, which in turn minimises his risk from the investment when one single company in the ​S&P 500 Index Portfolio​ performs poorly. When investing in cryptocurrency chooses ​BITCOINS​ which is observed to have the highest returns in the cryptocurrency market.
  4. Prices of stocks and bitcoins are ​normally distributed.​ This serves as a basic touchstone for easy calculation.
  5. Market conditions are normal.

Part A​​:

For analysis of portfolio investment in Bitcoin ​versus​ in S&P Index, gauging for ​price volatility of the assets​, we have constructed a Value at Risk (VaR) Model. This VaR Model constructed only takes into account one of the few investment’s risk aspect, ie. risk attributed by Volatility in Price.​

The value-at-risk approach has been used to derive a quantitative measure for the investor’s portfolio risks under normal market conditions. For a given portfolio, ​value-at-risk measures the maximum future loss from a portfolio incurred in terms of market value, that, under normal market conditions, will not be exceeded (under a defined confidence level over a predetermined decision period- 60 days in this case).

Under the Variance-Covariance Method, the VaR calculation is carried out using the following steps :

  1. Calculating ​periodic returns of the S&P Index and Bitcoin, calculating each of these returns as a percentage change in ​daily adjusted prices​ with respect to the previous day, for a term of three years (2017-2019). (Observation: The percentage change is positive when price-index is rising in the following period, negative when it is falling in the following period.)
  2. The individual is taken to initially invest $ 15294.27 either in BITCOIN ​or​ S&P 500 Index, in tandem with assumption 2. For simplicity, here, initial_investment taken to be the highest recorded price of Bitcoin in the period 2017-2019. This implies that this maximum the investor is willing to invest if he wants to minimise his riskS.
  3. Calculating the mean and standard deviation of the total investment for each of the two portfolios, as (initial_investment + mean of returns) and (initial_investment * standard deviation of returns) respectively.
  4. Fitting each of the two portfolios to a normal distribution with a confidence interval of 95%.
  5. Estimating the value at risk (VaR) for each of the investments by subtracting the initial investment, over a period of 60 days.

Figure 3 :​ ​Returns from Portfolios : Left : Portfolio for Bitcoin; Right : Portfolio for S&P 500 Index

Figure 4:​​ Maximum Portfolio loss ($) over 2-month-period : Left : Bitcoin portfolio; Right : S&P 500 Index portfolio.

Inference from the above analysis​ : Figure-4 depicts that for the same level of investment (​​$ 15294.27)​ ​over the same period of time, Value At Risk for an investor at 95% confidence interval is higher for investment in Bitcoin as compared to an investment in S&P 500 Index. Over a decision period of 60 days, the maximum loss in the portfolio was calculated as $1511.6 for S&P 500 index and $8109.6 for Bitcoin (nearly 8 times the maximum loss incurred by investment in S&P 500 Index).

Thus under normal market conditions, a risk-averse individual, making a mutually exclusive decision should choose to invest in the S&P 500 to minimise his risk. The inference drawn from the VaR analysis thus is, investment in Bitcoin could be a more risky affair if the individual’s concern is the volatility of commodity prices of his assets.

Part B:

Part B(I)

Forensic accounting is a combination of accounting and investigative techniques used to detect the discrepancies and irregularities in financial data.

V&M Breakouts is a consultancy company that had first divided the whole of the US Stock market into various sectors, namely – Healthcare, financials, industrials, Services, utilities, real-estates, technology, consumer goods, Basic materials, energy and then devised an index to identify the sectors of the US Stock market that tended to be more vulnerable to financial fraud crimes by using means of forensic accounting. They had enlisted companies susceptible to fraud, under each of these sectors accordingly, as Forensic Negative stocks.

Companies with strong financial statements, low risk of bankruptcy and earnings manipulation were considered Forensic Positive by V&M, whereas the ones with weak financial statements, high risk of bankruptcy and earnings manipulation (all directly/ indirectly indicative of fraud) were taken to be Forensic Negative. Their reports have been directly incorporated in column-B of the table constructed below.

For illustration, it was observed that 32% of all stocks in the US Stock market that fall under the Healthcare sector were Forensic Negative, and only 11% of all the stocks in S&P 500 were under the Healthcare sector. A similar interpretation applies to all the sectors. The following table has been constructed by computation of column A and compilation of data for column B from sources enlisted below the table.

For analysis, ​correlation​ analysis has been carried out between percentage share of these sectors in Forensic Negative Portfolio against percentage share each of these sectors in S&P 500 portfolio (in terms of number of companies in S&P 500 falling under each sector).

Sectors% share of the sector in S&P Portfolio in terms of Number of companies (A)*  % share of the sector in the overall portfolio of Forensic Negative Stocks (based on overall US stock data)​* (B)  
Real Estate5.45
Consumer Goods252
Basic Materials5.66
Source: Compiled from Wikipedia, Seekingalpha.com

Table 1:​ ​Shows the percentage share of different sectors in S&P 500 Portfolio and percentage share of the same sectors of red-flagged stocks calculated with forensic accounting

Inference from the above correlation: ​A​ ​negative correlation implies that a sector with a higher risk of forensic fraudulence occupies a smaller share of the S&P 500 Portfolio. This implies that an individual who invests in S&P 500 minimises his risks of incurring a loss in a market circumstanced with fraud crimes. Even if few companies in the portfolio are held to be risky, the overall spread of risk is minimised with a higher share of the portfolio being filled with less risky companies in terms of a financial fraud crime. Thus S&P 500 is a fairly risk-free avenue for investment.

Part B(II)

For analysis of portfolio investment in Bitcoin gauging for ​financial fraud crimes​, an Econometric Model has been constructed ​with variables – Monthly Bitcoin prices and Reported Monthly Bitcoin Hacks​. Regression of Bitcoin prices (monthly) on the Reported Bitcoin Hacks ​of the previous time periods (rather than regression of Bitcoin prices (monthly) on Reported Bitcoin Hacks of the same period) has been performed, as it is obvious that financial frauds occurring on the current period will most likely affect the prices of stocks in the following periods (if at all they have an impact).

Here it is observed that there is a significant effect of Bitcoin Hacks on Bitcoin prices for two consecutive periods. The estimated equation for the model can be written as:

Y​t​ ​​= 4489.848 + 0.0000724 ​X​​t-1​+​​ ​0.0000519 ​X​​t-2

where, ​Y​​t =​ M​ onthly Bitcoin prices in dollars of (t) ​​th​ ​period

X​t​​ -​ 1​​= Reported Bitcoin Hacks of the (t-1) ​​th​ ​period
X​t​​ -​ 2​=​​ ​Reported Bitcoin Hacks of the (t-2) ​​th ​​period

ANOVA table for the model, obtained under the usual Ordinary Least Square assumptions is given as-

It goes on to show that if there is a decrease of hacks by 100,000 dollars in period t-1 then, keeping other things constant, there is an average fall of 7.24 dollars in the price of Bitcoin in period t. If there is a decrease of hacks by 100,000 dollars in period t-2 then keeping other things constant there is an average fall of 5.19 dollars in the price of Bitcoin in period t. Coefficient of X​​t-1 ​and X​​t-2 ​is significant at 5% level of significance as the p-value for the coefficient is 0.003 and 0.02 respectively (i.e. less than 0.05). R​2​​ or goodness of fit of this estimated model is 0.3969 (​fairly high​). 40% of the variation in Prices of Bitcoin can be explained by the Hacks of the previous two periods.

Inference from the above model​: ​This model shows that any measure by an authority to ebb the level of crypto hackers will have a higher impact (on stopping the prices of bitcoins from falling) after a lag of two periods. Hence, any measure to minimise the risk of crypto-hack will not have any significant impact, immediately ​(in the directly following period). And, thus it may be a risky affair for a probationary investor expecting immediate returns, in a market faced with crypto hackers, to invest in Bitcoins.

Compiling the inferences from above two analysis in Part b (i) and Part b (ii) : ​From Part B analysis, ​S&P clearly stands out to be a less risky avenue of investment if the investor’s main concern is to minimise his portfolio risk in face of financial fraud crimes​, while choosing to invest between Bitcoin (correspondingly Cryptocurrency) or S&P 500 index (correspondingly also traditional stocks).

Compiling the inferences from Part A and Part B analysis: ​​Thus under normal market conditions, a risk-averse individual, making a mutually exclusive decision should choose to invest in the S&P 500 to minimise his risk. The inference drawn from the VaR analysis, forensic analysis and the econometric model thus is, investment in Bitcoin could be a more risky affair, if (a) the individual’s concern is the volatility of commodity prices of his assets, and, if (b) the individual’s concern is the risk that is entailed by financial fraud crimes.


The paper presented is limited in its scope in the sense that leaving aside the underlying assumptions, for instance, normality in the stock market and cryptocurrency market, it makes ​use of historical data to come to analytical conclusions​, and thus, in the process, fails to capture other market contingencies that the traditional stock market and cryptocurrency market are faced with. Given the existing state of affairs, with the massive pandemic attack – COVID-19 and the global economy going down the slope, the above analysis may not hold true.

In this paper, after use of financial tools like Value-at-Risk Analysis, analysis of Forensic Accounting data and finally construction and interpretation of an econometric model, it can be claimed with a certain degree of conviction that under an imposed condition of normalcy in the traditional stock and cryptocurrency market, S&P 500 Portfolio (which has been taken to be a representative of the traditional stocks) outperforms the Bitcoins (taken to be a representative of cryptocurrency), in terms of being a better risk minimising portfolio in the face of (a) Volatility of Prices and (b) Financial Fraud Crimes, in the US Stock Market. Hence, it can be concluded that under normal market conditions, ​S & P 500 Index Portfolio stands at a competitive advantage over Bitcoins​ in the US Stock Market.


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