'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 increase in value over 5 years of ProShares UltraShort Basic Materials is -83%, which is smaller, thus worse compared to the benchmark SPY (63%) in the same period.
- Looking at total return, or increase in value in of -82.5% in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (33.5%).

'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.'

Which means for our asset as example:- The annual return (CAGR) over 5 years of ProShares UltraShort Basic Materials is -29.8%, which is lower, thus worse compared to the benchmark SPY (10.3%) in the same period.
- Compared with SPY (10.1%) in the period of the last 3 years, the annual performance (CAGR) of -44.1% is lower, thus worse.

'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:- Looking at the volatility of 51.3% in the last 5 years of ProShares UltraShort Basic Materials, we see it is relatively higher, thus worse in comparison to the benchmark SPY (21.6%)
- Looking at historical 30 days volatility in of 59.2% in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (25.1%).

'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 deviation of 36.1% in the last 5 years of ProShares UltraShort Basic Materials, we see it is relatively higher, thus worse in comparison to the benchmark SPY (15.6%)
- Looking at downside volatility in of 42% in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (18.1%).

'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:- Looking at the ratio of return and volatility (Sharpe) of -0.63 in the last 5 years of ProShares UltraShort Basic Materials, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.36)
- Compared with SPY (0.3) in the period of the last 3 years, the ratio of return and volatility (Sharpe) of -0.79 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (0.5) in the period of the last 5 years, the downside risk / excess return profile of -0.9 of ProShares UltraShort Basic Materials is smaller, thus worse.
- Compared with SPY (0.42) in the period of the last 3 years, the downside risk / excess return profile of -1.11 is lower, thus worse.

'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.'

Applying this definition to our asset in some examples:- The Ulcer Index over 5 years of ProShares UltraShort Basic Materials is 64 , which is higher, thus worse compared to the benchmark SPY (8.88 ) in the same period.
- During the last 3 years, the Ulcer Index is 80 , which is larger, thus worse than the value of 11 from the benchmark.

'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 drop from peak to valley of -91.5 days of ProShares UltraShort Basic Materials is lower, thus worse.
- Compared with SPY (-33.7 days) in the period of the last 3 years, the maximum drop from peak to valley of -91.5 days is smaller, thus worse.

'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 below previous high over 5 years of ProShares UltraShort Basic Materials is 723 days, which is greater, thus worse compared to the benchmark SPY (273 days) in the same period.
- During the last 3 years, the maximum time in days below previous high water mark is 723 days, which is larger, thus worse than the value of 273 days from the benchmark.

'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:- Compared with the benchmark SPY (57 days) in the period of the last 5 years, the average time in days below previous high water mark of 257 days of ProShares UltraShort Basic Materials is higher, thus worse.
- During the last 3 years, the average days under water is 351 days, which is higher, thus worse than the value of 73 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.