'Total return, when measuring performance, is the actual rate of return of an investment or a pool of investments over a given evaluation period. Total return includes interest, capital gains, dividends and distributions realized over a given period of time. Total return accounts for two categories of return: income including interest paid by fixed-income investments, distributions or dividends and capital appreciation, representing the change in the market price of an asset.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (103.4%) in the period of the last 5 years, the total return, or increase in value of -51.9% of ProShares Ultra 20+ Year Treasury is lower, thus worse.
- Looking at total return in of -57.3% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (33.4%).

'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.'

Which means for our asset as example:- The compounded annual growth rate (CAGR) over 5 years of ProShares Ultra 20+ Year Treasury is -13.6%, which is lower, thus worse compared to the benchmark SPY (15.3%) in the same period.
- During the last 3 years, the compounded annual growth rate (CAGR) is -24.7%, which is smaller, thus worse than the value of 10.1% from the benchmark.

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (20.9%) in the period of the last 5 years, the volatility of 35% of ProShares Ultra 20+ Year Treasury is greater, thus worse.
- Looking at volatility in of 35.3% in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (17.3%).

'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 deviation of 24.8% in the last 5 years of ProShares Ultra 20+ Year Treasury, we see it is relatively larger, thus worse in comparison to the benchmark SPY (14.9%)
- Compared with SPY (12.1%) in the period of the last 3 years, the downside volatility of 25.5% is larger, thus worse.

'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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (0.61) in the period of the last 5 years, the Sharpe Ratio of -0.46 of ProShares Ultra 20+ Year Treasury is lower, thus worse.
- Compared with SPY (0.44) in the period of the last 3 years, the Sharpe Ratio of -0.77 is smaller, 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:- Looking at the ratio of annual return and downside deviation of -0.65 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 (0.85)
- Looking at downside risk / excess return profile in of -1.07 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.63).

'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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (9.32 ) in the period of the last 5 years, the Ulcer Ratio of 49 of ProShares Ultra 20+ Year Treasury is larger, thus worse.
- Compared with SPY (10 ) in the period of the last 3 years, the Ulcer Ratio of 50 is higher, 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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (-33.7 days) in the period of the last 5 years, the maximum DrawDown of -78.9 days of ProShares Ultra 20+ Year Treasury is smaller, thus worse.
- Looking at maximum DrawDown in of -72.5 days in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (-24.5 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'

Applying this definition to our asset in some examples:- The maximum days under water over 5 years of ProShares Ultra 20+ Year Treasury is 1075 days, which is higher, thus worse compared to the benchmark SPY (488 days) in the same period.
- Compared with SPY (488 days) in the period of the last 3 years, the maximum days under water of 635 days is greater, 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.'

Applying this definition to our asset in some examples:- The average days below previous high over 5 years of ProShares Ultra 20+ Year Treasury is 476 days, which is higher, thus worse compared to the benchmark SPY (123 days) in the same period.
- During the last 3 years, the average days under water is 274 days, which is higher, thus worse than the value of 180 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 and do not account for slippage, fees or taxes.