'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.'

Which means for our asset as example:- The total return over 5 years of ProShares Ultra 20+ Year Treasury is -8.6%, which is lower, thus worse compared to the benchmark SPY (81.9%) in the same period.
- Compared with SPY (46.1%) in the period of the last 3 years, the total return, or increase in value of -17.6% is lower, thus worse.

'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 annual performance (CAGR) over 5 years of ProShares Ultra 20+ Year Treasury is -1.8%, which is smaller, thus worse compared to the benchmark SPY (12.7%) in the same period.
- Looking at annual performance (CAGR) in of -6.3% in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (13.5%).

'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:- The historical 30 days volatility over 5 years of ProShares Ultra 20+ Year Treasury is 28.7%, which is higher, thus worse compared to the benchmark SPY (19.8%) in the same period.
- During the last 3 years, the historical 30 days volatility is 33.7%, which is higher, thus worse than the value of 23% from the benchmark.

'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.'

Using this definition on our asset we see for example:- Looking at the downside deviation of 20.2% 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 (14.5%)
- Compared with SPY (16.8%) in the period of the last 3 years, the downside deviation of 23.7% is larger, 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:- Compared with the benchmark SPY (0.52) in the period of the last 5 years, the risk / return profile (Sharpe) of -0.15 of ProShares Ultra 20+ Year Treasury is lower, thus worse.
- Looking at risk / return profile (Sharpe) in of -0.26 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.48).

'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:- Looking at the excess return divided by the downside deviation of -0.21 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 (0.7)
- Compared with SPY (0.65) in the period of the last 3 years, the ratio of annual return and downside deviation of -0.37 is smaller, 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:- The Ulcer Ratio over 5 years of ProShares Ultra 20+ Year Treasury is 21 , which is greater, thus worse compared to the benchmark SPY (6.08 ) in the same period.
- During the last 3 years, the Downside risk index is 26 , which is larger, thus worse than the value of 6.77 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:- The maximum drop from peak to valley over 5 years of ProShares Ultra 20+ Year Treasury is -58.6 days, which is smaller, thus worse compared to the benchmark SPY (-33.7 days) in the same period.
- Compared with SPY (-33.7 days) in the period of the last 3 years, the maximum drop from peak to valley of -58.6 days is smaller, thus worse.

'The Maximum 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. It is the length of time the account was in the Max Drawdown. A Max Drawdown measures a retrenchment from when an equity curve reaches a new high. It’s the maximum an account lost during that retrenchment. This method is applied because a valley can’t be measured until a new high occurs. Once the new high is reached, the percentage change from the old high to the bottom of the largest trough is recorded.'

Applying this definition to our asset in some examples:- Looking at the maximum time in days below previous high water mark of 552 days 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 (139 days)
- During the last 3 years, the maximum days below previous high is 552 days, which is higher, thus worse than the value of 119 days from the benchmark.

'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:- Looking at the average days below previous high of 209 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 (35 days)
- Looking at average time in days below previous high water mark in of 222 days in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (27 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.