'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, or performance over 5 years of ProShares UltraShort Basic Materials is -68.2%, which is lower, thus worse compared to the benchmark SPY (66.6%) in the same period.
- Compared with SPY (36.1%) in the period of the last 3 years, the total return, or increase in value of -47.3% 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.'

Using this definition on our asset we see for example:- Looking at the annual return (CAGR) of -20.5% in the last 5 years of ProShares UltraShort Basic Materials, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (10.8%)
- Compared with SPY (10.8%) in the period of the last 3 years, the annual performance (CAGR) of -19.2% 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:- The 30 days standard deviation over 5 years of ProShares UltraShort Basic Materials is 46%, which is higher, thus worse compared to the benchmark SPY (19%) in the same period.
- During the last 3 years, the 30 days standard deviation is 51%, which is greater, thus worse than the value of 22% from the benchmark.

'Downside risk is the financial risk associated with losses. That is, it is the risk of the actual return being below the expected return, or the uncertainty about the magnitude of that difference. 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 volatility of 31.8% in the last 5 years of ProShares UltraShort Basic Materials, we see it is relatively larger, thus worse in comparison to the benchmark SPY (13.9%)
- During the last 3 years, the downside risk is 34.8%, which is larger, thus worse than the value of 16.2% from the benchmark.

'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.'

Applying this definition to our asset in some examples:- Looking at the ratio of return and volatility (Sharpe) of -0.5 in the last 5 years of ProShares UltraShort Basic Materials, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.43)
- Looking at risk / return profile (Sharpe) in of -0.43 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.38).

'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 excess return divided by the downside deviation over 5 years of ProShares UltraShort Basic Materials is -0.72, which is smaller, thus worse compared to the benchmark SPY (0.59) in the same period.
- Looking at downside risk / excess return profile in of -0.62 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.52).

'Ulcer Index is a method for measuring investment risk that addresses the real concerns of investors, unlike the widely used standard deviation of return. UI is a measure of the depth and duration of drawdowns in prices from earlier highs. Using Ulcer Index instead of standard deviation can lead to very different conclusions about investment risk and risk-adjusted return, especially when evaluating strategies that seek to avoid major declines in portfolio value (market timing, dynamic asset allocation, hedge funds, etc.). The Ulcer Index was originally developed in 1987. Since then, it has been widely recognized and adopted by the investment community. According to Nelson Freeburg, editor of Formula Research, Ulcer Index is “perhaps the most fully realized statistical portrait of risk there is.'

Which means for our asset as example:- The Ulcer Ratio over 5 years of ProShares UltraShort Basic Materials is 60 , which is higher, thus worse compared to the benchmark SPY (5.9 ) in the same period.
- Compared with SPY (6.98 ) in the period of the last 3 years, the Ulcer Ratio of 30 is larger, thus worse.

'Maximum drawdown measures the loss in any losing period during a fund’s investment record. It is defined as the percent retrenchment from a fund’s peak value to the fund’s valley value. The drawdown is in effect from the time the fund’s retrenchment begins until a new fund high is reached. The maximum drawdown encompasses both the period from the fund’s peak to the fund’s valley (length), and the time from the fund’s valley to a new fund high (recovery). It measures the largest percentage drawdown that has occurred in any fund’s data record.'

Applying this definition to our asset in some examples:- The maximum drop from peak to valley over 5 years of ProShares UltraShort Basic Materials is -81.5 days, which is lower, thus worse compared to the benchmark SPY (-33.7 days) in the same period.
- During the last 3 years, the maximum DrawDown is -66.8 days, which is lower, thus worse than the value of -33.7 days from the benchmark.

'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.'

Which means for our asset as example:- The maximum days below previous high over 5 years of ProShares UltraShort Basic Materials is 1120 days, which is larger, thus worse compared to the benchmark SPY (187 days) in the same period.
- Looking at maximum days below previous high in of 367 days in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (139 days).

'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.'

Using this definition on our asset we see for example:- The average days below previous high over 5 years of ProShares UltraShort Basic Materials is 507 days, which is larger, thus worse compared to the benchmark SPY (44 days) in the same period.
- During the last 3 years, the average days under water is 156 days, which is greater, thus worse than the value of 41 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 UltraShort Basic Materials 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.