'Total return, when measuring performance, is the actual rate of return of an investment or a pool of investments over a given evaluation period. Total return includes interest, capital gains, dividends and distributions realized over a given period of time. Total return accounts for two categories of return: income including interest paid by fixed-income investments, distributions or dividends and capital appreciation, representing the change in the market price of an asset.'

Applying this definition to our asset in some examples:- The total return over 5 years of ProShares UltraShort Basic Materials is -84.9%, which is smaller, thus worse compared to the benchmark SPY (103.4%) in the same period.
- During the last 3 years, the total return is -38.6%, which is smaller, thus worse than the value of 33.4% from the benchmark.

'The compound annual growth rate (CAGR) is a useful measure of growth over multiple time periods. It can be thought of as the growth rate that gets you from the initial investment value to the ending investment value if you assume that the investment has been compounding over the time period.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (15.3%) in the period of the last 5 years, the annual performance (CAGR) of -31.5% of ProShares UltraShort Basic Materials is lower, thus worse.
- During the last 3 years, the annual performance (CAGR) is -15%, which is lower, thus worse than the value of 10.1% from the benchmark.

'In finance, volatility (symbol σ) is the degree of variation of a trading price series over time as measured by the standard deviation of logarithmic returns. Historic volatility measures a time series of past market prices. Implied volatility looks forward in time, being derived from the market price of a market-traded derivative (in particular, an option). Commonly, the higher the volatility, the riskier the security.'

Using this definition on our asset we see for example:- The volatility over 5 years of ProShares UltraShort Basic Materials is 49.8%, which is larger, thus worse compared to the benchmark SPY (20.9%) in the same period.
- Looking at historical 30 days volatility in of 41.1% in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (17.3%).

'Downside risk is the financial risk associated with losses. That is, it is the risk of the actual return being below the expected return, or the uncertainty about the magnitude of that difference. Risk measures typically quantify the downside risk, whereas the standard deviation (an example of a deviation risk measure) measures both the upside and downside risk. Specifically, downside risk in our definition is the semi-deviation, that is the standard deviation of all negative returns.'

Which means for our asset as example:- The downside risk over 5 years of ProShares UltraShort Basic Materials is 35%, which is greater, thus worse compared to the benchmark SPY (14.9%) in the same period.
- During the last 3 years, the downside deviation is 28.9%, which is greater, thus worse than the value of 12.1% from the benchmark.

'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:- Looking at the Sharpe Ratio of -0.68 in the last 5 years of ProShares UltraShort Basic Materials, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.61)
- Compared with SPY (0.44) in the period of the last 3 years, the Sharpe Ratio of -0.43 is lower, 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:- The ratio of annual return and downside deviation over 5 years of ProShares UltraShort Basic Materials is -0.97, which is lower, thus worse compared to the benchmark SPY (0.85) in the same period.
- Compared with SPY (0.63) in the period of the last 3 years, the excess return divided by the downside deviation of -0.61 is lower, thus worse.

'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:- The Downside risk index over 5 years of ProShares UltraShort Basic Materials is 79 , which is higher, thus worse compared to the benchmark SPY (9.32 ) in the same period.
- Looking at Downside risk index in of 34 in the period of the last 3 years, we see it is relatively greater, 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:- Looking at the maximum DrawDown of -92.8 days in the last 5 years of ProShares UltraShort Basic Materials, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (-33.7 days)
- Compared with SPY (-24.5 days) in the period of the last 3 years, the maximum drop from peak to valley of -53.7 days is lower, 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:- Looking at the maximum time in days below previous high water mark of 1065 days in the last 5 years of ProShares UltraShort Basic Materials, we see it is relatively larger, thus worse in comparison to the benchmark SPY (488 days)
- During the last 3 years, the maximum time in days below previous high water mark is 432 days, which is smaller, thus better than the value of 488 days from the benchmark.

'The Average 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. 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:- Compared with the benchmark SPY (123 days) in the period of the last 5 years, the average time in days below previous high water mark of 463 days of ProShares UltraShort Basic Materials is greater, thus worse.
- Compared with SPY (180 days) in the period of the last 3 years, the average days below previous high of 170 days is lower, thus better.

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 ProShares UltraShort Basic Materials are hypothetical and do not account for slippage, fees or taxes.