'Total return is the amount of value an investor earns from a security over a specific period, typically one year, when all distributions are reinvested. Total return is expressed as a percentage of the amount invested. For example, a total return of 20% means the security increased by 20% of its original value due to a price increase, distribution of dividends (if a stock), coupons (if a bond) or capital gains (if a fund). Total return is a strong measure of an investment’s overall performance.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (80%) in the period of the last 5 years, the total return, or increase in value of 238.5% of ProShares Ultra QQQ is greater, thus better.
- Compared with SPY (31.8%) in the period of the last 3 years, the total return, or increase in value of 31.9% is higher, thus better.

'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:- Compared with the benchmark SPY (12.5%) in the period of the last 5 years, the compounded annual growth rate (CAGR) of 27.7% of ProShares Ultra QQQ is larger, thus better.
- Compared with SPY (9.7%) in the period of the last 3 years, the annual return (CAGR) of 9.7% is higher, 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.'

Which means for our asset as example:- The volatility over 5 years of ProShares Ultra QQQ is 51.7%, which is larger, thus worse compared to the benchmark SPY (21.3%) in the same period.
- Compared with SPY (17.6%) in the period of the last 3 years, the 30 days standard deviation of 47.6% is higher, thus worse.

'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 deviation over 5 years of ProShares Ultra QQQ is 36.7%, which is greater, thus worse compared to the benchmark SPY (15.3%) in the same period.
- Compared with SPY (12.3%) in the period of the last 3 years, the downside deviation of 33.6% is higher, 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:- Looking at the risk / return profile (Sharpe) of 0.49 in the last 5 years of ProShares Ultra QQQ, we see it is relatively greater, thus better in comparison to the benchmark SPY (0.47)
- Compared with SPY (0.41) in the period of the last 3 years, the Sharpe Ratio of 0.15 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:- The downside risk / excess return profile over 5 years of ProShares Ultra QQQ is 0.69, which is higher, thus better compared to the benchmark SPY (0.66) in the same period.
- During the last 3 years, the downside risk / excess return profile is 0.21, which is lower, thus worse than the value of 0.58 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 Ulcer Index over 5 years of ProShares Ultra QQQ is 29 , which is larger, thus worse compared to the benchmark SPY (9.43 ) in the same period.
- During the last 3 years, the Ulcer Ratio is 35 , which is larger, thus worse than the value of 10 from the benchmark.

'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.'

Using this definition on our asset we see for example:- Looking at the maximum reduction from previous high of -63.7 days in the last 5 years of ProShares Ultra QQQ, we see it is relatively lower, thus worse in comparison to the benchmark SPY (-33.7 days)
- During the last 3 years, the maximum drop from peak to valley is -63.7 days, which is lower, thus worse than the value of -24.5 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). 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 under water of 509 days in the last 5 years of ProShares Ultra QQQ, we see it is relatively greater, thus worse in comparison to the benchmark SPY (480 days)
- Looking at maximum days under water in of 509 days in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (480 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:- Compared with the benchmark SPY (119 days) in the period of the last 5 years, the average days below previous high of 130 days of ProShares Ultra QQQ is larger, thus worse.
- Looking at average days under water in of 190 days in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (174 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 QQQ 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.