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.'

Applying this definition to our asset in some examples:- Looking at the total return, or increase in value of 562.2% in the last 5 years of Bitcoin, we see it is relatively greater, thus better in comparison to the benchmark SPY (102.4%)
- Looking at total return in of 103.7% in the period of the last 3 years, we see it is relatively larger, thus better in comparison to SPY (35%).

'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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (15.2%) in the period of the last 5 years, the compounded annual growth rate (CAGR) of 46% of Bitcoin is larger, thus better.
- Compared with SPY (10.5%) in the period of the last 3 years, the annual return (CAGR) of 26.8% is higher, thus better.

'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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (20.9%) in the period of the last 5 years, the historical 30 days volatility of 65.5% of Bitcoin is larger, thus worse.
- During the last 3 years, the 30 days standard deviation is 57.8%, which is greater, thus worse than the value of 17.3% from the benchmark.

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

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (15%) in the period of the last 5 years, the downside risk of 44.5% of Bitcoin is larger, thus worse.
- Looking at downside volatility in of 38.8% in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (12.1%).

'The Sharpe ratio was developed by Nobel laureate William F. Sharpe, and is used to help investors understand the return of an investment compared to its risk. The ratio is the average return earned in excess of the risk-free rate per unit of volatility or total risk. Subtracting the risk-free rate from the mean return allows an investor to better isolate the profits associated with risk-taking activities. One intuition of this calculation is that a portfolio engaging in 'zero risk' investments, such as the purchase of U.S. Treasury bills (for which the expected return is the risk-free rate), has a Sharpe ratio of exactly zero. Generally, the greater the value of the Sharpe ratio, the more attractive the risk-adjusted return.'

Which means for our asset as example:- The ratio of return and volatility (Sharpe) over 5 years of Bitcoin is 0.66, which is greater, thus better compared to the benchmark SPY (0.61) in the same period.
- Looking at Sharpe Ratio in of 0.42 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.47).

'The Sortino ratio improves upon the Sharpe ratio by isolating downside volatility from total volatility by dividing excess return by the downside deviation. The Sortino ratio is a variation of the Sharpe ratio that differentiates harmful volatility from total overall volatility by using the asset's standard deviation of negative asset returns, called downside deviation. The Sortino ratio takes the asset's return and subtracts the risk-free rate, and then divides that amount by the asset's downside deviation. The ratio was named after Frank A. Sortino.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (0.85) in the period of the last 5 years, the downside risk / excess return profile of 0.98 of Bitcoin is larger, thus better.
- During the last 3 years, the ratio of annual return and downside deviation is 0.63, which is smaller, thus worse than the value of 0.67 from the benchmark.

'The Ulcer Index is a technical indicator that measures downside risk, in terms of both the depth and duration of price declines. The index increases in value as the price moves farther away from a recent high and falls as the price rises to new highs. The indicator is usually calculated over a 14-day period, with the Ulcer Index showing the percentage drawdown a trader can expect from the high over that period. The greater the value of the Ulcer Index, the longer it takes for a stock to get back to the former high.'

Applying this definition to our asset in some examples:- The Ulcer Ratio over 5 years of Bitcoin is 42 , which is greater, thus worse compared to the benchmark SPY (9.32 ) in the same period.
- Looking at Ulcer Index in of 49 in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (10 ).

'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.'

Using this definition on our asset we see for example:- The maximum DrawDown 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.
- During the last 3 years, the maximum reduction from previous high is -76.6 days, which is smaller, thus worse than the value of -24.5 days from the benchmark.

'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.'

Which means for our asset as example:- Looking at the maximum time in days below previous high water mark of 580 days in the last 5 years of Bitcoin, we see it is relatively larger, thus worse in comparison to the benchmark SPY (488 days)
- Looking at maximum time in days below previous high water mark in of 580 days in the period of the last 3 years, we see it is relatively larger, 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:- The average time in days below previous high water mark over 5 years of Bitcoin is 179 days, which is greater, thus worse compared to the benchmark SPY (124 days) in the same period.
- Compared with SPY (181 days) in the period of the last 3 years, the average days under water of 237 days is higher, thus worse.

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.