'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 (62.7%) in the period of the last 5 years, the total return of 53.5% of ProShares UltraShort Euro is lower, thus worse.
- Compared with SPY (34.7%) in the period of the last 3 years, the total return, or increase in value of 21.6% is smaller, thus worse.

'Compound annual growth rate (CAGR) is a business and investing specific term for the geometric progression ratio that provides a constant rate of return over the time period. CAGR is not an accounting term, but it is often used to describe some element of the business, for example revenue, units delivered, registered users, etc. CAGR dampens the effect of volatility of periodic returns that can render arithmetic means irrelevant. It is particularly useful to compare growth rates from various data sets of common domain such as revenue growth of companies in the same industry.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (10.2%) in the period of the last 5 years, the compounded annual growth rate (CAGR) of 9% of ProShares UltraShort Euro is lower, thus worse.
- Compared with SPY (10.5%) in the period of the last 3 years, the annual return (CAGR) of 6.8% is smaller, thus worse.

'Volatility is a statistical measure of the dispersion of returns for a given security or market index. Volatility can either be measured by using the standard deviation or variance between returns from that same security or market index. Commonly, the higher the volatility, the riskier the security. In the securities markets, volatility is often associated with big swings in either direction. For example, when the stock market rises and falls more than one percent over a sustained period of time, it is called a 'volatile' market.'

Which means for our asset as example:- Compared with the benchmark SPY (20.9%) in the period of the last 5 years, the historical 30 days volatility of 14.4% of ProShares UltraShort Euro is smaller, thus better.
- Compared with SPY (24.1%) in the period of the last 3 years, the historical 30 days volatility of 15.3% is lower, thus better.

'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:- Looking at the downside volatility of 9.7% in the last 5 years of ProShares UltraShort Euro, we see it is relatively lower, thus better in comparison to the benchmark SPY (15.3%)
- Looking at downside deviation in of 10.3% in the period of the last 3 years, we see it is relatively smaller, thus better in comparison to SPY (17.6%).

'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (0.37) in the period of the last 5 years, the ratio of return and volatility (Sharpe) of 0.45 of ProShares UltraShort Euro is greater, thus better.
- During the last 3 years, the ratio of return and volatility (Sharpe) is 0.28, which is smaller, thus worse than the value of 0.33 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.'

Applying this definition to our asset in some examples:- The ratio of annual return and downside deviation over 5 years of ProShares UltraShort Euro is 0.67, which is greater, thus better compared to the benchmark SPY (0.51) in the same period.
- Compared with SPY (0.45) in the period of the last 3 years, the excess return divided by the downside deviation of 0.41 is lower, thus worse.

'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:- Looking at the Ulcer Index of 12 in the last 5 years of ProShares UltraShort Euro, we see it is relatively greater, thus worse in comparison to the benchmark SPY (7.71 )
- During the last 3 years, the Downside risk index is 14 , which is higher, thus worse than the value of 9.08 from the benchmark.

'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:- Compared with the benchmark SPY (-33.7 days) in the period of the last 5 years, the maximum DrawDown of -25.7 days of ProShares UltraShort Euro is greater, thus better.
- Looking at maximum reduction from previous high in of -25.7 days in the period of the last 3 years, we see it is relatively larger, thus better in comparison to SPY (-33.7 days).

'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:- The maximum days under water over 5 years of ProShares UltraShort Euro is 529 days, which is larger, thus worse compared to the benchmark SPY (189 days) in the same period.
- Compared with SPY (189 days) in the period of the last 3 years, the maximum time in days below previous high water mark of 529 days is greater, thus worse.

'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.'

Applying this definition to our asset in some examples:- The average days under water over 5 years of ProShares UltraShort Euro is 135 days, which is greater, thus worse compared to the benchmark SPY (46 days) in the same period.
- Compared with SPY (45 days) in the period of the last 3 years, the average time in days below previous high water mark of 200 days is greater, 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 ProShares UltraShort Euro are hypothetical, do not account for slippage, fees or taxes, and are based on backtesting, which has many inherent limitations, some of which are described in our Terms of Use.