Bitcoin was the first cryptocurrency to successfully record transactions on a secure, decentralized blockchain-based network. Launched in early 2009 by its pseudonymous creator Satoshi Nakamoto, Bitcoin is the largest cryptocurrency measured by market capitalization and amount of data stored on its blockchain. The Bitcoin software is free and available online to anyone who wants to run a Bitcoin node and store their own copy of the Bitcoin blockchain. As Bitcoin matures, engineers have designed additional protocols to improve the speed and privacy of Bitcoin transactions, including the Omni Layer, Lightning Network and Liquid Network. Only approximately 21 million bitcoins will ever be created. New coins are minted every 10 minutes by bitcoin miners who help to maintain the network by adding new transaction data to the blockchain.

'Total return is the amount of value an investor earns from a security over a specific period, typically one year, when all distributions are reinvested. Total return is expressed as a percentage of the amount invested. For example, a total return of 20% means the security increased by 20% of its original value due to a price increase, distribution of dividends (if a stock), coupons (if a bond) or capital gains (if a fund). Total return is a strong measure of an investment’s overall performance.'

Which means for our asset as example:- Compared with the benchmark SPY (109.2%) in the period of the last 5 years, the total return, or performance of 769.4% of Bitcoin is larger, thus better.
- Compared with SPY (33.3%) in the period of the last 3 years, the total return, or increase in value of 13.3% is smaller, thus worse.

'The compound annual growth rate isn't a true return rate, but rather a representational figure. It is essentially a number that describes the rate at which an investment would have grown if it had grown the same rate every year and the profits were reinvested at the end of each year. In reality, this sort of performance is unlikely. However, CAGR can be used to smooth returns so that they may be more easily understood when compared to alternative investments.'

Which means for our asset as example:- Looking at the annual return (CAGR) of 54.2% in the last 5 years of Bitcoin, we see it is relatively greater, thus better in comparison to the benchmark SPY (15.9%)
- Looking at annual performance (CAGR) in of 4.3% in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (10.1%).

'Volatility is a rate at which the price of a security increases or decreases for a given set of returns. Volatility is measured by calculating the standard deviation of the annualized returns over a given period of time. It shows the range to which the price of a security may increase or decrease. Volatility measures the risk of a security. It is used in option pricing formula to gauge the fluctuations in the returns of the underlying assets. Volatility indicates the pricing behavior of the security and helps estimate the fluctuations that may happen in a short period of time.'

Applying this definition to our asset in some examples:- The 30 days standard deviation over 5 years of Bitcoin is 64.4%, which is higher, thus worse compared to the benchmark SPY (20.9%) in the same period.
- Compared with SPY (17.6%) in the period of the last 3 years, the 30 days standard deviation of 56% is larger, thus worse.

'The downside volatility is similar to the volatility, or standard deviation, but only takes losing/negative periods into account.'

Which means for our asset as example:- Compared with the benchmark SPY (14.9%) in the period of the last 5 years, the downside risk of 43.8% of Bitcoin is larger, thus worse.
- Compared with SPY (12.3%) in the period of the last 3 years, the downside deviation of 38.4% is larger, thus worse.

'The Sharpe ratio (also known as the Sharpe index, the Sharpe measure, and the reward-to-variability ratio) is a way to examine the performance of an investment by adjusting for its risk. The ratio measures the excess return (or risk premium) per unit of deviation in an investment asset or a trading strategy, typically referred to as risk, named after William F. Sharpe.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (0.64) in the period of the last 5 years, the ratio of return and volatility (Sharpe) of 0.8 of Bitcoin is larger, thus better.
- Compared with SPY (0.43) in the period of the last 3 years, the risk / return profile (Sharpe) of 0.03 is smaller, thus worse.

'The Sortino ratio, a variation of the Sharpe ratio only factors in the downside, or negative volatility, rather than the total volatility used in calculating the Sharpe ratio. The theory behind the Sortino variation is that upside volatility is a plus for the investment, and it, therefore, should not be included in the risk calculation. Therefore, the Sortino ratio takes upside volatility out of the equation and uses only the downside standard deviation in its calculation instead of the total standard deviation that is used in calculating the Sharpe ratio.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (0.9) in the period of the last 5 years, the ratio of annual return and downside deviation of 1.18 of Bitcoin is greater, thus better.
- During the last 3 years, the excess return divided by the downside deviation is 0.05, which is smaller, thus worse than the value of 0.62 from the benchmark.

'Ulcer Index is a method for measuring investment risk that addresses the real concerns of investors, unlike the widely used standard deviation of return. UI is a measure of the depth and duration of drawdowns in prices from earlier highs. Using Ulcer Index instead of standard deviation can lead to very different conclusions about investment risk and risk-adjusted return, especially when evaluating strategies that seek to avoid major declines in portfolio value (market timing, dynamic asset allocation, hedge funds, etc.). The Ulcer Index was originally developed in 1987. Since then, it has been widely recognized and adopted by the investment community. According to Nelson Freeburg, editor of Formula Research, Ulcer Index is “perhaps the most fully realized statistical portrait of risk there is.'

Using this definition on our asset we see for example:- Looking at the Downside risk index of 40 in the last 5 years of Bitcoin, we see it is relatively higher, thus worse in comparison to the benchmark SPY (9.32 )
- Compared with SPY (10 ) in the period of the last 3 years, the Downside risk index of 49 is greater, thus worse.

'A maximum drawdown is the maximum loss from a peak to a trough of a portfolio, before a new peak is attained. Maximum Drawdown is an indicator of downside risk over a specified time period. It can be used both as a stand-alone measure or as an input into other metrics such as 'Return over Maximum Drawdown' and the Calmar Ratio. Maximum Drawdown is expressed in percentage terms.'

Which means for our asset as example:- The maximum drop from peak to valley over 5 years of Bitcoin is -76.6 days, which is lower, thus worse compared to the benchmark SPY (-33.7 days) in the same period.
- Compared with SPY (-24.5 days) in the period of the last 3 years, the maximum DrawDown of -76.6 days is smaller, thus worse.

'The Maximum Drawdown Duration is an extension of the Maximum Drawdown. However, this metric does not explain the drawdown in dollars or percentages, rather in days, weeks, or months. It is the length of time the account was in the Max Drawdown. A Max Drawdown measures a retrenchment from when an equity curve reaches a new high. It’s the maximum an account lost during that retrenchment. This method is applied because a valley can’t be measured until a new high occurs. Once the new high is reached, the percentage change from the old high to the bottom of the largest trough is recorded.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (488 days) in the period of the last 5 years, the maximum days below previous high of 580 days of Bitcoin is higher, thus worse.
- Looking at maximum days under water in of 580 days in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (488 days).

'The Drawdown Duration is the length of any peak to peak period, or the time between new equity highs. The Avg Drawdown Duration is the average amount of time an investment has seen between peaks (equity highs), or in other terms the average of time under water of all drawdowns. So in contrast to the Maximum duration it does not measure only one drawdown event but calculates the average of all.'

Which means for our asset as example:- Looking at the average days under water of 168 days in the last 5 years of Bitcoin, we see it is relatively higher, thus worse in comparison to the benchmark SPY (123 days)
- During the last 3 years, the average days below previous high is 243 days, which is greater, thus worse than the value of 176 days from the benchmark.

Historical returns have been extended using synthetic data.
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- Note that yearly returns do not equal the sum of monthly returns due to compounding.
- Performance results of Bitcoin are hypothetical and do not account for slippage, fees or taxes.