'Total return, when measuring performance, is the actual rate of return of an investment or a pool of investments over a given evaluation period. Total return includes interest, capital gains, dividends and distributions realized over a given period of time. Total return accounts for two categories of return: income including interest paid by fixed-income investments, distributions or dividends and capital appreciation, representing the change in the market price of an asset.'

Which means for our asset as example:- Compared with the benchmark SPY (95%) in the period of the last 5 years, the total return, or increase in value of 477% of ProShares Ultra QQQ is greater, thus better.
- During the last 3 years, the total return is 185.6%, which is higher, thus better than the value of 40.5% from the benchmark.

'The compound annual growth rate (CAGR) is a useful measure of growth over multiple time periods. It can be thought of as the growth rate that gets you from the initial investment value to the ending investment value if you assume that the investment has been compounding over the time period.'

Using this definition on our asset we see for example:- Looking at the annual return (CAGR) of 42% in the last 5 years of ProShares Ultra QQQ, we see it is relatively larger, thus better in comparison to the benchmark SPY (14.3%)
- Compared with SPY (12%) in the period of the last 3 years, the annual return (CAGR) of 41.9% is higher, thus better.

'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.'

Applying this definition to our asset in some examples:- Looking at the historical 30 days volatility of 43.5% in the last 5 years of ProShares Ultra QQQ, we see it is relatively greater, thus worse in comparison to the benchmark SPY (18.8%)
- Compared with SPY (22.4%) in the period of the last 3 years, the historical 30 days volatility of 51.1% is greater, thus worse.

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

Which means for our asset as example:- The downside deviation over 5 years of ProShares Ultra QQQ is 31.3%, which is higher, thus worse compared to the benchmark SPY (13.7%) in the same period.
- Compared with SPY (16.5%) in the period of the last 3 years, the downside deviation of 36.9% is larger, thus worse.

'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:- The Sharpe Ratio over 5 years of ProShares Ultra QQQ is 0.91, which is higher, thus better compared to the benchmark SPY (0.63) in the same period.
- During the last 3 years, the ratio of return and volatility (Sharpe) is 0.77, which is higher, thus better than the value of 0.43 from the benchmark.

'The Sortino ratio, a variation of the Sharpe ratio only factors in the downside, or negative volatility, rather than the total volatility used in calculating the Sharpe ratio. The theory behind the Sortino variation is that upside volatility is a plus for the investment, and it, therefore, should not be included in the risk calculation. Therefore, the Sortino ratio takes upside volatility out of the equation and uses only the downside standard deviation in its calculation instead of the total standard deviation that is used in calculating the Sharpe ratio.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (0.86) in the period of the last 5 years, the ratio of annual return and downside deviation of 1.26 of ProShares Ultra QQQ is higher, thus better.
- During the last 3 years, the excess return divided by the downside deviation is 1.07, which is larger, thus better than the value of 0.58 from the benchmark.

'The Ulcer Index is a technical indicator that measures downside risk, in terms of both the depth and duration of price declines. The index increases in value as the price moves farther away from a recent high and falls as the price rises to new highs. The indicator is usually calculated over a 14-day period, with the Ulcer Index showing the percentage drawdown a trader can expect from the high over that period. The greater the value of the Ulcer Index, the longer it takes for a stock to get back to the former high.'

Which means for our asset as example:- Compared with the benchmark SPY (5.79 ) in the period of the last 5 years, the Downside risk index of 12 of ProShares Ultra QQQ is greater, thus worse.
- Looking at Ulcer Index in of 14 in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (7.09 ).

'Maximum drawdown is defined as the peak-to-trough decline of an investment during a specific period. It is usually quoted as a percentage of the peak value. The maximum drawdown can be calculated based on absolute returns, in order to identify strategies that suffer less during market downturns, such as low-volatility strategies. However, the maximum drawdown can also be calculated based on returns relative to a benchmark index, for identifying strategies that show steady outperformance over time.'

Applying this definition to our asset in some examples:- The maximum reduction from previous high over 5 years of ProShares Ultra QQQ is -51.7 days, which is smaller, thus worse compared to the benchmark SPY (-33.7 days) in the same period.
- During the last 3 years, the maximum reduction from previous high is -51.7 days, which is lower, thus worse than the value of -33.7 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.'

Using this definition on our asset we see for example:- Looking at the maximum days under water of 214 days in the last 5 years of ProShares Ultra QQQ, we see it is relatively larger, thus worse in comparison to the benchmark SPY (139 days)
- Looking at maximum days under water in of 214 days in the period of the last 3 years, we see it is relatively larger, 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.'

Which means for our asset as example:- The average days under water over 5 years of ProShares Ultra QQQ is 49 days, which is higher, thus worse compared to the benchmark SPY (37 days) in the same period.
- Looking at average days below previous high in of 51 days in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (45 days).

Historical returns have been extended using synthetic data.
[Show Details]

- 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.