'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 performance of -50% 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 (102%)
- Looking at total return, or increase in value in of -57.2% in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (31.5%).

'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.'

Applying this definition to our asset in some examples:- Looking at the compounded annual growth rate (CAGR) of -13% 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 (15.1%)
- Compared with SPY (9.6%) in the period of the last 3 years, the annual return (CAGR) of -24.6% is lower, thus worse.

'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:- 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 30 days standard deviation in of 35.4% in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (17.6%).

'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:- The downside deviation over 5 years of ProShares Ultra 20+ Year Treasury is 24.8%, which is larger, thus worse compared to the benchmark SPY (14.9%) in the same period.
- Compared with SPY (12.4%) in the period of the last 3 years, the downside deviation of 25.6% is greater, thus worse.

'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:- The risk / return profile (Sharpe) over 5 years of ProShares Ultra 20+ Year Treasury is -0.44, which is lower, thus worse compared to the benchmark SPY (0.6) in the same period.
- Compared with SPY (0.4) in the period of the last 3 years, the Sharpe Ratio of -0.77 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.'

Applying this definition to our asset in some examples:- Looking at the downside risk / excess return profile of -0.62 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 (0.84)
- Compared with SPY (0.57) in the period of the last 3 years, the ratio of annual return and downside deviation of -1.06 is lower, thus worse.

'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 Index of 51 of ProShares Ultra 20+ Year Treasury is larger, thus worse.
- Compared with SPY (10 ) in the period of the last 3 years, the Ulcer Index of 54 is larger, thus worse.

'Maximum drawdown is defined as the peak-to-trough decline of an investment during a specific period. It is usually quoted as a percentage of the peak value. The maximum drawdown can be calculated based on absolute returns, in order to identify strategies that suffer less during market downturns, such as low-volatility strategies. However, the maximum drawdown can also be calculated based on returns relative to a benchmark index, for identifying strategies that show steady outperformance over time.'

Which means for our asset as example:- Looking at the maximum DrawDown of -78.9 days 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 (-33.7 days)
- Looking at maximum reduction from previous high 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'

Which means for our asset as example:- The maximum days under water over 5 years of ProShares Ultra 20+ Year Treasury is 1137 days, which is greater, 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 below previous high of 697 days is greater, thus worse.

'The Average 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. 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.'

Which means for our asset as example:- Compared with the benchmark SPY (123 days) in the period of the last 5 years, the average days below previous high of 526 days of ProShares Ultra 20+ Year Treasury is higher, thus worse.
- Looking at average time in days below previous high water mark in of 326 days in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (177 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 Ultra 20+ Year Treasury are hypothetical and do not account for slippage, fees or taxes.