'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 Industrials is -73.2%, which is lower, thus worse compared to the benchmark SPY (67.7%) in the same period.
- During the last 3 years, the total return, or performance is -54.5%, which is smaller, thus worse than the value of 46.7% from the benchmark.

'The compound annual growth rate isn't a true return rate, but rather a representational figure. It is essentially a number that describes the rate at which an investment would have grown if it had grown the same rate every year and the profits were reinvested at the end of each year. In reality, this sort of performance is unlikely. However, CAGR can be used to smooth returns so that they may be more easily understood when compared to alternative investments.'

Which means for our asset as example:- The annual return (CAGR) over 5 years of ProShares UltraShort Industrials is -27.5%, which is lower, thus worse compared to the benchmark SPY (10.9%) in the same period.
- Compared with SPY (13.7%) in the period of the last 3 years, the annual performance (CAGR) of -27.4% is smaller, 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.'

Which means for our asset as example:- Looking at the volatility of 34.3% in the last 5 years of ProShares UltraShort Industrials, we see it is relatively higher, thus worse in comparison to the benchmark SPY (13.5%)
- Compared with SPY (12.8%) in the period of the last 3 years, the volatility of 33.8% is greater, thus worse.

'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (14.8%) in the period of the last 5 years, the downside deviation of 31.3% of ProShares UltraShort Industrials is larger, thus worse.
- During the last 3 years, the downside risk is 29.8%, which is larger, thus worse than the value of 14.6% from the benchmark.

'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.'

Using this definition on our asset we see for example:- Looking at the Sharpe Ratio of -0.87 in the last 5 years of ProShares UltraShort Industrials, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (0.62)
- Looking at risk / return profile (Sharpe) in of -0.88 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.87).

'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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (0.57) in the period of the last 5 years, the excess return divided by the downside deviation of -0.96 of ProShares UltraShort Industrials is lower, thus worse.
- During the last 3 years, the downside risk / excess return profile is -1, which is lower, thus worse than the value of 0.76 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.'

Which means for our asset as example:- Compared with the benchmark SPY (3.99 ) in the period of the last 5 years, the Ulcer Ratio of 54 of ProShares UltraShort Industrials is greater, thus worse.
- Compared with SPY (4.1 ) in the period of the last 3 years, the Ulcer Ratio of 39 is larger, thus worse.

'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.'

Applying this definition to our asset in some examples:- The maximum drop from peak to valley over 5 years of ProShares UltraShort Industrials is -77.8 days, which is smaller, thus worse compared to the benchmark SPY (-19.3 days) in the same period.
- During the last 3 years, the maximum reduction from previous high is -58 days, which is lower, thus worse than the value of -19.3 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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (187 days) in the period of the last 5 years, the maximum days below previous high of 899 days of ProShares UltraShort Industrials is larger, thus worse.
- Looking at maximum time in days below previous high water mark in of 608 days in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (139 days).

'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:- Looking at the average days below previous high of 402 days in the last 5 years of ProShares UltraShort Industrials, we see it is relatively higher, thus worse in comparison to the benchmark SPY (42 days)
- Compared with SPY (36 days) in the period of the last 3 years, the average days below previous high of 300 days is greater, thus worse.

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 Industrials 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.