'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 Ultra S&P500 is 90.7%, which is greater, thus better compared to the benchmark SPY (67.9%) in the same period.
- Compared with SPY (44.5%) in the period of the last 3 years, the total return of 72.9% is higher, thus better.

'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.'

Applying this definition to our asset in some examples:- Looking at the annual return (CAGR) of 13.8% in the last 5 years of ProShares Ultra S&P500, we see it is relatively higher, thus better in comparison to the benchmark SPY (10.9%)
- Compared with SPY (13.1%) in the period of the last 3 years, the annual return (CAGR) of 20% is greater, thus better.

'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.'

Using this definition on our asset we see for example:- The historical 30 days volatility over 5 years of ProShares Ultra S&P500 is 43.2%, which is greater, thus worse compared to the benchmark SPY (21.4%) in the same period.
- During the last 3 years, the 30 days standard deviation is 37.4%, which is greater, thus worse than the value of 18.7% from the benchmark.

'The downside volatility is similar to the volatility, or standard deviation, but only takes losing/negative periods into account.'

Using this definition on our asset we see for example:- The downside volatility over 5 years of ProShares Ultra S&P500 is 31.1%, which is greater, thus worse compared to the benchmark SPY (15.4%) in the same period.
- Looking at downside risk in of 26.6% in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (13.3%).

'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:- The ratio of return and volatility (Sharpe) over 5 years of ProShares Ultra S&P500 is 0.26, which is smaller, thus worse compared to the benchmark SPY (0.39) in the same period.
- Compared with SPY (0.56) in the period of the last 3 years, the Sharpe Ratio of 0.47 is lower, thus worse.

'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 (0.55) in the period of the last 5 years, the downside risk / excess return profile of 0.36 of ProShares Ultra S&P500 is smaller, thus worse.
- During the last 3 years, the downside risk / excess return profile is 0.66, which is lower, thus worse than the value of 0.79 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 Ultra S&P500 is 20 , which is greater, thus worse compared to the benchmark SPY (9.47 ) in the same period.
- During the last 3 years, the Ulcer Index is 22 , which is greater, thus worse than the value of 10 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 reduction from previous high over 5 years of ProShares Ultra S&P500 is -59.3 days, which is lower, thus worse compared to the benchmark SPY (-33.7 days) in the same period.
- Compared with SPY (-24.5 days) in the period of the last 3 years, the maximum drop from peak to valley of -46.7 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'

Applying this definition to our asset in some examples:- Looking at the maximum days under water of 354 days in the last 5 years of ProShares Ultra S&P500, we see it is relatively higher, thus worse in comparison to the benchmark SPY (354 days)
- During the last 3 years, the maximum days below previous high is 354 days, which is higher, thus worse than the value of 354 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:- Looking at the average time in days below previous high water mark of 87 days in the last 5 years of ProShares Ultra S&P500, we see it is relatively larger, thus worse in comparison to the benchmark SPY (79 days)
- Looking at average days under water in of 102 days in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (102 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 S&P500 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.