'The total return on a portfolio of investments takes into account not only the capital appreciation on the portfolio, but also the income received on the portfolio. The income typically consists of interest, dividends, and securities lending fees. This contrasts with the price return, which takes into account only the capital gain on an investment.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (100.7%) in the period of the last 5 years, the total return, or increase in value of 17.6% of ProShares UltraShort Euro is lower, thus worse.
- During the last 3 years, the total return, or increase in value is 35.4%, which is higher, thus better than the value of 33.2% 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.'

Using this definition on our asset we see for example:- Looking at the annual performance (CAGR) of 3.3% in the last 5 years of ProShares UltraShort Euro, we see it is relatively lower, thus worse in comparison to the benchmark SPY (15%)
- During the last 3 years, the annual performance (CAGR) is 10.6%, which is greater, thus better than the value of 10% 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:- Compared with the benchmark SPY (20.9%) in the period of the last 5 years, the historical 30 days volatility of 15.2% of ProShares UltraShort Euro is lower, thus better.
- During the last 3 years, the historical 30 days volatility is 16%, which is lower, thus better than the value of 17.3% from the benchmark.

'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:- Looking at the downside risk of 10.6% in the last 5 years of ProShares UltraShort Euro, we see it is relatively smaller, thus better in comparison to the benchmark SPY (15%)
- During the last 3 years, the downside deviation is 11.1%, which is lower, thus better than the value of 12% from the benchmark.

'The Sharpe ratio is the measure of risk-adjusted return of a financial portfolio. Sharpe ratio is a measure of excess portfolio return over the risk-free rate relative to its standard deviation. Normally, the 90-day Treasury bill rate is taken as the proxy for risk-free rate. A portfolio with a higher Sharpe ratio is considered superior relative to its peers. The measure was named after William F Sharpe, a Nobel laureate and professor of finance, emeritus at Stanford University.'

Using this definition on our asset we see for example:- Looking at the ratio of return and volatility (Sharpe) of 0.05 in the last 5 years of ProShares UltraShort Euro, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.6)
- During the last 3 years, the Sharpe Ratio is 0.51, which is larger, thus better than the value of 0.44 from the benchmark.

'The Sortino ratio measures the risk-adjusted return of an investment asset, portfolio, or strategy. It is a modification of the Sharpe ratio but penalizes only those returns falling below a user-specified target or required rate of return, while the Sharpe ratio penalizes both upside and downside volatility equally. Though both ratios measure an investment's risk-adjusted return, they do so in significantly different ways that will frequently lead to differing conclusions as to the true nature of the investment's return-generating efficiency. The Sortino ratio is used as a way to compare the risk-adjusted performance of programs with differing risk and return profiles. In general, risk-adjusted returns seek to normalize the risk across programs and then see which has the higher return unit per risk.'

Using this definition on our asset we see for example:- The downside risk / excess return profile over 5 years of ProShares UltraShort Euro is 0.07, which is lower, thus worse compared to the benchmark SPY (0.83) in the same period.
- Looking at excess return divided by the downside deviation in of 0.73 in the period of the last 3 years, we see it is relatively larger, thus better in comparison to SPY (0.62).

'The ulcer index is a stock market risk measure or technical analysis indicator devised by Peter Martin in 1987, and published by him and Byron McCann in their 1989 book The Investors Guide to Fidelity Funds. It's designed as a measure of volatility, but only volatility in the downward direction, i.e. the amount of drawdown or retracement occurring over a period. Other volatility measures like standard deviation treat up and down movement equally, but a trader doesn't mind upward movement, it's the downside that causes stress and stomach ulcers that the index's name suggests.'

Which means for our asset as example:- Compared with the benchmark SPY (9.32 ) in the period of the last 5 years, the Downside risk index of 15 of ProShares UltraShort Euro is larger, thus worse.
- Looking at Downside risk index in of 13 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:- The maximum drop from peak to valley over 5 years of ProShares UltraShort Euro is -25.7 days, which is higher, thus better 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 reduction from previous high of -24.4 days is greater, thus better.

'The Drawdown Duration is the length of any peak to peak period, or the time between new equity highs. The Max Drawdown Duration is the worst (the maximum/longest) amount of time an investment has seen between peaks (equity highs). Many assume Max DD Duration is the length of time between new highs during which the Max DD (magnitude) occurred. But that isn’t always the case. The Max DD duration is the longest time between peaks, period. So it could be the time when the program also had its biggest peak to valley loss (and usually is, because the program needs a long time to recover from the largest loss), but it doesn’t have to be'

Using this definition on our asset we see for example:- The maximum days under water over 5 years of ProShares UltraShort Euro is 529 days, which is higher, thus worse compared to the benchmark SPY (488 days) in the same period.
- Compared with SPY (488 days) in the period of the last 3 years, the maximum time in days below previous high water mark of 412 days is lower, thus better.

'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:- Looking at the average time in days below previous high water mark of 191 days in the last 5 years of ProShares UltraShort Euro, we see it is relatively higher, thus worse in comparison to the benchmark SPY (123 days)
- Looking at average time in days below previous high water mark in of 127 days in the period of the last 3 years, we see it is relatively lower, thus better in comparison to SPY (180 days).

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 Euro are hypothetical and do not account for slippage, fees or taxes.