'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.'

Using this definition on our asset we see for example:- Looking at the total return of 30.5% in the last 5 years of ProShares Ultra 20+ Year Treasury, we see it is relatively lower, thus worse in comparison to the benchmark SPY (133.2%)
- Compared with SPY (80.4%) in the period of the last 3 years, the total return, or increase in value of 62.5% is lower, 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.'

Which means for our asset as example:- Compared with the benchmark SPY (18.5%) in the period of the last 5 years, the annual performance (CAGR) of 5.5% of ProShares Ultra 20+ Year Treasury is smaller, thus worse.
- Looking at compounded annual growth rate (CAGR) in of 17.6% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (21.8%).

'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 (18.7%) in the period of the last 5 years, the 30 days standard deviation of 27.3% of ProShares Ultra 20+ Year Treasury is higher, thus worse.
- Compared with SPY (22.4%) in the period of the last 3 years, the 30 days standard deviation of 31% is greater, thus worse.

'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.'

Which means for our asset as example:- The downside deviation over 5 years of ProShares Ultra 20+ Year Treasury is 19%, which is higher, thus worse compared to the benchmark SPY (13.6%) in the same period.
- Compared with SPY (16.2%) in the period of the last 3 years, the downside volatility of 21% is greater, thus worse.

'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:- The risk / return profile (Sharpe) over 5 years of ProShares Ultra 20+ Year Treasury is 0.11, which is lower, thus worse compared to the benchmark SPY (0.85) in the same period.
- Compared with SPY (0.86) in the period of the last 3 years, the ratio of return and volatility (Sharpe) of 0.49 is lower, thus worse.

'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:- Compared with the benchmark SPY (1.18) in the period of the last 5 years, the downside risk / excess return profile of 0.16 of ProShares Ultra 20+ Year Treasury is lower, thus worse.
- Compared with SPY (1.19) in the period of the last 3 years, the downside risk / excess return profile of 0.72 is smaller, thus worse.

'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:- Compared with the benchmark SPY (5.59 ) in the period of the last 5 years, the Ulcer Index of 18 of ProShares Ultra 20+ Year Treasury is greater, thus worse.
- During the last 3 years, the Downside risk index is 20 , which is greater, thus worse than the value of 6.36 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 reduction from previous high of -42.5 days of ProShares Ultra 20+ Year Treasury is smaller, thus worse.
- Looking at maximum DrawDown in of -42.5 days in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (-33.7 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 under water over 5 years of ProShares Ultra 20+ Year Treasury is 641 days, which is higher, thus worse compared to the benchmark SPY (139 days) in the same period.
- During the last 3 years, the maximum days below previous high is 414 days, which is larger, thus worse than the value of 119 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:- Compared with the benchmark SPY (32 days) in the period of the last 5 years, the average days under water of 244 days of ProShares Ultra 20+ Year Treasury is higher, thus worse.
- During the last 3 years, the average days under water is 136 days, which is greater, thus worse than the value of 25 days from the benchmark.

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 Ultra 20+ Year Treasury 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.