'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.'

Which means for our asset as example:- The total return over 5 years of ProShares Ultra 20+ Year Treasury is 116.3%, which is higher, thus better compared to the benchmark SPY (67.6%) in the same period.
- Looking at total return in of 81.3% in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (36.7%).

'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.'

Using this definition on our asset we see for example:- The annual performance (CAGR) over 5 years of ProShares Ultra 20+ Year Treasury is 16.7%, which is greater, thus better compared to the benchmark SPY (10.9%) in the same period.
- Compared with SPY (11%) in the period of the last 3 years, the annual return (CAGR) of 22% is larger, thus better.

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (19%) in the period of the last 5 years, the 30 days standard deviation of 27.4% of ProShares Ultra 20+ Year Treasury is larger, thus worse.
- During the last 3 years, the historical 30 days volatility is 29%, which is higher, thus worse than the value of 22% from the benchmark.

'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:- Compared with the benchmark SPY (13.9%) in the period of the last 5 years, the downside risk of 18.9% of ProShares Ultra 20+ Year Treasury is higher, thus worse.
- Looking at downside volatility in of 19.6% in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (16.2%).

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (0.44) in the period of the last 5 years, the risk / return profile (Sharpe) of 0.52 of ProShares Ultra 20+ Year Treasury is greater, thus better.
- During the last 3 years, the Sharpe Ratio is 0.67, which is larger, thus better than the value of 0.39 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:- Compared with the benchmark SPY (0.6) in the period of the last 5 years, the downside risk / excess return profile of 0.75 of ProShares Ultra 20+ Year Treasury is greater, thus better.
- Compared with SPY (0.53) in the period of the last 3 years, the ratio of annual return and downside deviation of 1 is larger, thus better.

'The ulcer index is a stock market risk measure or technical analysis indicator devised by Peter Martin in 1987, and published by him and Byron McCann in their 1989 book The Investors Guide to Fidelity Funds. It's designed as a measure of volatility, but only volatility in the downward direction, i.e. the amount of drawdown or retracement occurring over a period. Other volatility measures like standard deviation treat up and down movement equally, but a trader doesn't mind upward movement, it's the downside that causes stress and stomach ulcers that the index's name suggests.'

Applying this definition to our asset in some examples:- Looking at the Ulcer Ratio of 20 in the last 5 years of ProShares Ultra 20+ Year Treasury, we see it is relatively higher, thus worse in comparison to the benchmark SPY (5.91 )
- Looking at Ulcer Index in of 11 in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (7 ).

'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 -36.4 days of ProShares Ultra 20+ Year Treasury is lower, thus worse.
- Compared with SPY (-33.7 days) in the period of the last 3 years, the maximum DrawDown of -28 days is greater, thus better.

'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) in days.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (187 days) in the period of the last 5 years, the maximum days below previous high of 771 days of ProShares Ultra 20+ Year Treasury is larger, thus worse.
- Compared with SPY (139 days) in the period of the last 3 years, the maximum days under water of 427 days is higher, 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.'

Which means for our asset as example:- Looking at the average time in days below previous high water mark of 264 days 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 (45 days)
- Looking at average time in days below previous high water mark in of 145 days in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (42 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, 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.