'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:- Looking at the total return, or increase in value of 85.3% 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 (95%)
- During the last 3 years, the total return is 75%, which is higher, thus better than the value of 40.5% from the benchmark.

'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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (14.3%) in the period of the last 5 years, the annual performance (CAGR) of 13.1% of ProShares Ultra 20+ Year Treasury is smaller, thus worse.
- Looking at compounded annual growth rate (CAGR) in of 20.5% in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (12%).

'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:- The volatility over 5 years of ProShares Ultra 20+ Year Treasury is 27%, which is higher, thus worse compared to the benchmark SPY (18.8%) in the same period.
- Compared with SPY (22.4%) in the period of the last 3 years, the volatility of 29.1% is larger, thus worse.

'The downside volatility is similar to the volatility, or standard deviation, but only takes losing/negative periods into account.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (13.7%) in the period of the last 5 years, the downside risk of 18.7% of ProShares Ultra 20+ Year Treasury is greater, thus worse.
- Looking at downside volatility in of 19.7% in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (16.5%).

'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:- Looking at the ratio of return and volatility (Sharpe) of 0.39 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 (0.63)
- Looking at Sharpe Ratio in of 0.62 in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (0.43).

'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.'

Which means for our asset as example:- The ratio of annual return and downside deviation over 5 years of ProShares Ultra 20+ Year Treasury is 0.57, which is smaller, thus worse compared to the benchmark SPY (0.86) in the same period.
- Looking at ratio of annual return and downside deviation in of 0.92 in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (0.58).

'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 Downside risk index of 20 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 (5.79 )
- Compared with SPY (7.09 ) in the period of the last 3 years, the Ulcer Index of 11 is higher, 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.'

Using this definition on our asset we see for example:- 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.
- Looking at maximum drop from peak to valley in of -28 days in the period of the last 3 years, we see it is relatively larger, thus better 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'

Using this definition on our asset we see for example:- The maximum days under water over 5 years of ProShares Ultra 20+ Year Treasury is 773 days, which is higher, thus worse compared to the benchmark SPY (139 days) in the same period.
- Compared with SPY (139 days) in the period of the last 3 years, the maximum days below previous high of 358 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 (37 days) in the period of the last 5 years, the average days under water of 265 days of ProShares Ultra 20+ Year Treasury is greater, thus worse.
- During the last 3 years, the average days below previous high is 116 days, which is higher, thus worse than the value of 45 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.