'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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (110.3%) in the period of the last 5 years, the total return of 11.5% of ProShares UltraShort Euro is smaller, thus worse.
- Compared with SPY (39.7%) in the period of the last 3 years, the total return, or increase in value of 24.1% is smaller, thus worse.

'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 2.2% in the last 5 years of ProShares UltraShort Euro, we see it is relatively lower, thus worse in comparison to the benchmark SPY (16.1%)
- During the last 3 years, the compounded annual growth rate (CAGR) is 7.5%, which is lower, thus worse than the value of 11.8% from the benchmark.

'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.'

Applying this definition to our asset in some examples:- Looking at the historical 30 days volatility of 15.2% in the last 5 years of ProShares UltraShort Euro, we see it is relatively lower, thus better in comparison to the benchmark SPY (20.9%)
- Compared with SPY (17.5%) in the period of the last 3 years, the 30 days standard deviation of 16.1% is lower, thus better.

'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.'

Applying this definition to our asset in some examples:- Looking at the downside volatility of 10.7% in the last 5 years of ProShares UltraShort Euro, we see it is relatively smaller, thus better in comparison to the benchmark SPY (14.9%)
- During the last 3 years, the downside volatility is 11.3%, which is lower, thus better than the value of 12.2% 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.'

Which means for our asset as example:- The ratio of return and volatility (Sharpe) over 5 years of ProShares UltraShort Euro is -0.02, which is smaller, thus worse compared to the benchmark SPY (0.65) in the same period.
- Looking at ratio of return and volatility (Sharpe) in of 0.31 in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (0.53).

'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 downside risk / excess return profile over 5 years of ProShares UltraShort Euro is -0.03, which is lower, thus worse compared to the benchmark SPY (0.91) in the same period.
- During the last 3 years, the ratio of annual return and downside deviation is 0.44, which is lower, thus worse than the value of 0.76 from the benchmark.

'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.'

Applying this definition to our asset in some examples:- Looking at the Downside risk index of 15 in the last 5 years of ProShares UltraShort Euro, we see it is relatively higher, thus worse in comparison to the benchmark SPY (9.32 )
- Compared with SPY (10 ) in the period of the last 3 years, the Ulcer Index of 14 is larger, thus worse.

'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:- Looking at the maximum reduction from previous high of -25.7 days in the last 5 years of ProShares UltraShort Euro, we see it is relatively larger, thus better in comparison to the benchmark SPY (-33.7 days)
- During the last 3 years, the maximum drop from peak to valley is -24.4 days, which is larger, thus better than the value of -24.5 days from the benchmark.

'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:- Looking at the maximum days under water of 529 days in the last 5 years of ProShares UltraShort Euro, we see it is relatively greater, thus worse in comparison to the benchmark SPY (488 days)
- Looking at maximum days below previous high in of 508 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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (124 days) in the period of the last 5 years, the average days under water of 223 days of ProShares UltraShort Euro is greater, thus worse.
- Looking at average days below previous high in of 186 days in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (179 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.