'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:- Compared with the benchmark SPY (67.8%) in the period of the last 5 years, the total return, or increase in value of -87.2% of ProShares UltraShort Technology is smaller, thus worse.
- Looking at total return, or increase in value in of -79% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (47.2%).

'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.'

Applying this definition to our asset in some examples:- The annual return (CAGR) over 5 years of ProShares UltraShort Technology is -33.8%, which is lower, thus worse compared to the benchmark SPY (10.9%) in the same period.
- During the last 3 years, the annual return (CAGR) is -40.6%, which is lower, thus worse than the value of 13.8% from the benchmark.

'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.'

Using this definition on our asset we see for example:- The historical 30 days volatility over 5 years of ProShares UltraShort Technology is 36.4%, which is greater, thus worse compared to the benchmark SPY (13.4%) in the same period.
- Compared with SPY (12.3%) in the period of the last 3 years, the volatility of 36.7% is greater, thus worse.

'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 (14.7%) in the period of the last 5 years, the downside deviation of 33.3% of ProShares UltraShort Technology is larger, thus worse.
- Compared with SPY (13.9%) in the period of the last 3 years, the downside volatility of 32.7% is greater, thus worse.

'The Sharpe ratio was developed by Nobel laureate William F. Sharpe, and is used to help investors understand the return of an investment compared to its risk. The ratio is the average return earned in excess of the risk-free rate per unit of volatility or total risk. Subtracting the risk-free rate from the mean return allows an investor to better isolate the profits associated with risk-taking activities. One intuition of this calculation is that a portfolio engaging in 'zero risk' investments, such as the purchase of U.S. Treasury bills (for which the expected return is the risk-free rate), has a Sharpe ratio of exactly zero. Generally, the greater the value of the Sharpe ratio, the more attractive the risk-adjusted return.'

Using this definition on our asset we see for example:- The risk / return profile (Sharpe) over 5 years of ProShares UltraShort Technology is -1, which is lower, thus worse compared to the benchmark SPY (0.63) in the same period.
- Looking at risk / return profile (Sharpe) in of -1.18 in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (0.92).

'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (0.57) in the period of the last 5 years, the excess return divided by the downside deviation of -1.09 of ProShares UltraShort Technology is lower, thus worse.
- During the last 3 years, the downside risk / excess return profile is -1.32, which is lower, thus worse than the value of 0.81 from the benchmark.

'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.'

Using this definition on our asset we see for example:- The Downside risk index over 5 years of ProShares UltraShort Technology is 60 , which is larger, thus worse compared to the benchmark SPY (3.99 ) in the same period.
- Looking at Ulcer Index in of 57 in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (4.04 ).

'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:- Compared with the benchmark SPY (-19.3 days) in the period of the last 5 years, the maximum reduction from previous high of -88.2 days of ProShares UltraShort Technology is lower, thus worse.
- Looking at maximum DrawDown in of -79.3 days in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (-19.3 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'

Which means for our asset as example:- Looking at the maximum days below previous high of 1193 days in the last 5 years of ProShares UltraShort Technology, we see it is relatively larger, thus worse in comparison to the benchmark SPY (187 days)
- Compared with SPY (139 days) in the period of the last 3 years, the maximum days under water of 754 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:- The average days under water over 5 years of ProShares UltraShort Technology is 571 days, which is higher, thus worse compared to the benchmark SPY (41 days) in the same period.
- Compared with SPY (36 days) in the period of the last 3 years, the average time in days below previous high water mark of 378 days is larger, thus worse.

Historical returns have been extended using synthetic data.
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- "Year" returns in the table above are not equal to the sum of monthly returns due to compounding.
- Performance results of ProShares UltraShort Technology 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.