'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (64.1%) in the period of the last 5 years, the total return, or increase in value of 41.6% of ProShares UltraShort Euro is lower, thus worse.
- Looking at total return in of 14.2% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (48.1%).

'The compound annual growth rate isn't a true return rate, but rather a representational figure. It is essentially a number that describes the rate at which an investment would have grown if it had grown the same rate every year and the profits were reinvested at the end of each year. In reality, this sort of performance is unlikely. However, CAGR can be used to smooth returns so that they may be more easily understood when compared to alternative investments.'

Applying this definition to our asset in some examples:- Looking at the annual return (CAGR) of 7.2% in the last 5 years of ProShares UltraShort Euro, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (10.4%)
- Looking at compounded annual growth rate (CAGR) in of 4.5% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (14%).

'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.'

Applying this definition to our asset in some examples:- Looking at the 30 days standard deviation of 17.1% in the last 5 years of ProShares UltraShort Euro, we see it is relatively higher, thus worse in comparison to the benchmark SPY (13.6%)
- Looking at historical 30 days volatility in of 13.8% in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (12.8%).

'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:- Looking at the downside deviation of 17.6% in the last 5 years of ProShares UltraShort Euro, we see it is relatively greater, thus worse in comparison to the benchmark SPY (14.9%)
- Looking at downside risk in of 14.2% in the period of the last 3 years, we see it is relatively smaller, thus better in comparison to SPY (14.5%).

'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:- Looking at the Sharpe Ratio of 0.28 in the last 5 years of ProShares UltraShort Euro, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.58)
- Compared with SPY (0.9) in the period of the last 3 years, the ratio of return and volatility (Sharpe) of 0.15 is lower, thus worse.

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (0.53) in the period of the last 5 years, the ratio of annual return and downside deviation of 0.27 of ProShares UltraShort Euro is smaller, thus worse.
- Looking at ratio of annual return and downside deviation in of 0.14 in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (0.79).

'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 Downside risk index of 16 in the last 5 years of ProShares UltraShort Euro, we see it is relatively greater, thus worse in comparison to the benchmark SPY (4.02 )
- Looking at Ulcer Index in of 15 in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (4.09 ).

'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:- Compared with the benchmark SPY (-19.3 days) in the period of the last 5 years, the maximum drop from peak to valley of -31.5 days of ProShares UltraShort Euro is lower, thus worse.
- Looking at maximum DrawDown in of -29.6 days in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (-19.3 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). 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'

Which means for our asset as example:- The maximum days below previous high over 5 years of ProShares UltraShort Euro is 1139 days, which is larger, thus worse compared to the benchmark SPY (187 days) in the same period.
- Compared with SPY (139 days) in the period of the last 3 years, the maximum days under water of 691 days is larger, thus worse.

'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:- Compared with the benchmark SPY (41 days) in the period of the last 5 years, the average days under water of 530 days of ProShares UltraShort Euro is greater, thus worse.
- Compared with SPY (35 days) in the period of the last 3 years, the average time in days below previous high water mark of 326 days is greater, thus worse.

Historical returns have been extended using synthetic data.
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- "Year" returns in the table above are not equal to 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.