'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.'

Applying this definition to our asset in some examples:- Looking at the total return, or increase in value of -12.6% in the last 5 years of ProShares UltraShort Euro, we see it is relatively lower, thus worse in comparison to the benchmark SPY (91.7%)
- Looking at total return, or increase in value in of 9.8% in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (47.9%).

'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.'

Which means for our asset as example:- The annual return (CAGR) over 5 years of ProShares UltraShort Euro is -2.7%, which is lower, thus worse compared to the benchmark SPY (13.9%) in the same period.
- Compared with SPY (13.9%) in the period of the last 3 years, the annual performance (CAGR) of 3.2% is lower, thus worse.

'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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (19%) in the period of the last 5 years, the volatility of 14.9% of ProShares UltraShort Euro is smaller, thus better.
- Looking at 30 days standard deviation in of 13.7% in the period of the last 3 years, we see it is relatively lower, thus better in comparison to SPY (22.8%).

'The downside volatility is similar to the volatility, or standard deviation, but only takes losing/negative periods into account.'

Which means for our asset as example:- Looking at the downside volatility of 10.7% in the last 5 years of ProShares UltraShort Euro, we see it is relatively lower, thus better in comparison to the benchmark SPY (13.8%)
- Looking at downside volatility in of 9.4% in the period of the last 3 years, we see it is relatively lower, thus better in comparison to SPY (16.7%).

'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 risk / return profile (Sharpe) of -0.35 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 risk / return profile (Sharpe) is 0.05, which is lower, thus worse than the value of 0.5 from the benchmark.

'The Sortino ratio improves upon the Sharpe ratio by isolating downside volatility from total volatility by dividing excess return by the downside deviation. The Sortino ratio is a variation of the Sharpe ratio that differentiates harmful volatility from total overall volatility by using the asset's standard deviation of negative asset returns, called downside deviation. The Sortino ratio takes the asset's return and subtracts the risk-free rate, and then divides that amount by the asset's downside deviation. The ratio was named after Frank A. Sortino.'

Using this definition on our asset we see for example:- Looking at the excess return divided by the downside deviation of -0.48 in the last 5 years of ProShares UltraShort Euro, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.82)
- Looking at excess return divided by the downside deviation in of 0.07 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.68).

'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.'

Which means for our asset as example:- The Ulcer Index over 5 years of ProShares UltraShort Euro is 14 , which is greater, thus worse compared to the benchmark SPY (5.82 ) in the same period.
- During the last 3 years, the Ulcer Index is 7.73 , which is higher, thus worse than the value of 7.14 from the benchmark.

'Maximum drawdown measures the loss in any losing period during a fund’s investment record. It is defined as the percent retrenchment from a fund’s peak value to the fund’s valley value. The drawdown is in effect from the time the fund’s retrenchment begins until a new fund high is reached. The maximum drawdown encompasses both the period from the fund’s peak to the fund’s valley (length), and the time from the fund’s valley to a new fund high (recovery). It measures the largest percentage drawdown that has occurred in any fund’s data record.'

Using this definition on our asset we see for example:- The maximum reduction from previous high over 5 years of ProShares UltraShort Euro is -29.6 days, which is greater, thus better compared to the benchmark SPY (-33.7 days) in the same period.
- Looking at maximum drop from peak to valley in of -21 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.'

Applying this definition to our asset in some examples:- Looking at the maximum days below previous high of 694 days in the last 5 years of ProShares UltraShort Euro, we see it is relatively greater, thus worse in comparison to the benchmark SPY (139 days)
- During the last 3 years, the maximum days below previous high is 175 days, which is larger, thus worse than the value of 139 days from the benchmark.

'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:- Looking at the average time in days below previous high water mark of 238 days in the last 5 years of ProShares UltraShort Euro, we see it is relatively greater, thus worse in comparison to the benchmark SPY (36 days)
- Compared with SPY (45 days) in the period of the last 3 years, the average time in days below previous high water mark of 43 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 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.