'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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (61.3%) in the period of the last 5 years, the total return, or performance of 155.2% of ProShares Ultra QQQ is higher, thus better.
- Looking at total return in of 69.7% in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (31.6%).

'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:- Looking at the annual performance (CAGR) of 20.6% in the last 5 years of ProShares Ultra QQQ, we see it is relatively larger, thus better in comparison to the benchmark SPY (10%)
- Compared with SPY (9.6%) in the period of the last 3 years, the annual performance (CAGR) of 19.3% is larger, 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:- Compared with the benchmark SPY (20.8%) in the period of the last 5 years, the volatility of 50.6% of ProShares Ultra QQQ is higher, thus worse.
- During the last 3 years, the 30 days standard deviation is 56.8%, which is higher, thus worse than the value of 24% from the benchmark.

'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:- Compared with the benchmark SPY (15.3%) in the period of the last 5 years, the downside risk of 36.7% of ProShares Ultra QQQ is greater, thus worse.
- During the last 3 years, the downside risk is 41.3%, which is higher, thus worse than the value of 17.6% from the benchmark.

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (0.36) in the period of the last 5 years, the Sharpe Ratio of 0.36 of ProShares Ultra QQQ is higher, thus better.
- During the last 3 years, the risk / return profile (Sharpe) is 0.3, which is greater, thus better than the value of 0.3 from the benchmark.

'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:- Looking at the downside risk / excess return profile 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 (0.49)
- Compared with SPY (0.4) in the period of the last 3 years, the downside risk / excess return profile of 0.41 is greater, thus better.

'The ulcer index is a stock market risk measure or technical analysis indicator devised by Peter Martin in 1987, and published by him and Byron McCann in their 1989 book The Investors Guide to Fidelity Funds. It's designed as a measure of volatility, but only volatility in the downward direction, i.e. the amount of drawdown or retracement occurring over a period. Other volatility measures like standard deviation treat up and down movement equally, but a trader doesn't mind upward movement, it's the downside that causes stress and stomach ulcers that the index's name suggests.'

Using this definition on our asset we see for example:- Looking at the Ulcer Ratio of 20 in the last 5 years of ProShares Ultra QQQ, we see it is relatively larger, thus worse in comparison to the benchmark SPY (7.61 )
- Compared with SPY (8.93 ) in the period of the last 3 years, the Ulcer Index of 23 is larger, thus worse.

'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.'

Which means for our asset as example:- Looking at the maximum reduction from previous high of -58.1 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)
- Looking at maximum drop from peak to valley in of -58.1 days in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (-33.7 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) in days.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (185 days) in the period of the last 5 years, the maximum time in days below previous high water mark of 214 days of ProShares Ultra QQQ is higher, thus worse.
- During the last 3 years, the maximum days below previous high is 214 days, which is greater, thus worse than the value of 185 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.'

Using this definition on our asset we see for example:- The average time in days below previous high water mark over 5 years of ProShares Ultra QQQ is 55 days, which is larger, thus worse compared to the benchmark SPY (46 days) in the same period.
- Compared with SPY (44 days) in the period of the last 3 years, the average days below previous high of 51 days is larger, 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 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.