'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:- Compared with the benchmark SPY (101.5%) in the period of the last 5 years, the total return, or increase in value of 136.7% of ProShares UltraShort Yen New is greater, thus better.
- Compared with SPY (29.7%) in the period of the last 3 years, the total return, or performance of 117.7% is larger, thus better.

'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 (15.1%) in the period of the last 5 years, the annual return (CAGR) of 18.8% of ProShares UltraShort Yen New is larger, thus better.
- Compared with SPY (9.1%) in the period of the last 3 years, the compounded annual growth rate (CAGR) of 29.7% is larger, thus better.

'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 19.6% of ProShares UltraShort Yen New is lower, thus better.
- Looking at 30 days standard deviation in of 21.9% in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (17.6%).

'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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (14.9%) in the period of the last 5 years, the downside risk of 14% of ProShares UltraShort Yen New is smaller, thus better.
- During the last 3 years, the downside deviation is 15.9%, which is higher, thus worse than the value of 12.3% 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.'

Applying this definition to our asset in some examples:- Looking at the ratio of return and volatility (Sharpe) of 0.83 in the last 5 years of ProShares UltraShort Yen New, we see it is relatively greater, thus better in comparison to the benchmark SPY (0.6)
- Looking at Sharpe Ratio in of 1.24 in the period of the last 3 years, we see it is relatively larger, thus better in comparison to SPY (0.37).

'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.'

Using this definition on our asset we see for example:- The downside risk / excess return profile over 5 years of ProShares UltraShort Yen New is 1.17, which is larger, thus better compared to the benchmark SPY (0.84) in the same period.
- Compared with SPY (0.53) in the period of the last 3 years, the ratio of annual return and downside deviation of 1.71 is higher, thus better.

'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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (9.32 ) in the period of the last 5 years, the Ulcer Ratio of 9.95 of ProShares UltraShort Yen New is higher, thus worse.
- Compared with SPY (10 ) in the period of the last 3 years, the Ulcer Index of 10 is larger, thus worse.

'Maximum drawdown is defined as the peak-to-trough decline of an investment during a specific period. It is usually quoted as a percentage of the peak value. The maximum drawdown can be calculated based on absolute returns, in order to identify strategies that suffer less during market downturns, such as low-volatility strategies. However, the maximum drawdown can also be calculated based on returns relative to a benchmark index, for identifying strategies that show steady outperformance over time.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (-33.7 days) in the period of the last 5 years, the maximum reduction from previous high of -27.3 days of ProShares UltraShort Yen New is larger, thus better.
- Looking at maximum reduction from previous high in of -27.3 days in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (-24.5 days).

'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) in days.'

Which means for our asset as example:- Compared with the benchmark SPY (488 days) in the period of the last 5 years, the maximum days under water of 417 days of ProShares UltraShort Yen New is smaller, thus better.
- Compared with SPY (488 days) in the period of the last 3 years, the maximum time in days below previous high water mark of 204 days is lower, thus better.

'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.'

Using this definition on our asset we see for example:- The average days below previous high over 5 years of ProShares UltraShort Yen New is 103 days, which is smaller, thus better compared to the benchmark SPY (123 days) in the same period.
- Compared with SPY (177 days) in the period of the last 3 years, the average time in days below previous high water mark of 45 days is smaller, 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 Yen New are hypothetical and do not account for slippage, fees or taxes.