'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.'

Which means for our asset as example:- The total return, or increase in value over 5 years of ProShares Ultra QQQ is 222.5%, which is greater, thus better compared to the benchmark SPY (81.9%) in the same period.
- Compared with SPY (46.1%) in the period of the last 3 years, the total return of 103% is higher, thus better.

'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.'

Applying this definition to our asset in some examples:- The annual performance (CAGR) over 5 years of ProShares Ultra QQQ is 26.4%, which is greater, thus better compared to the benchmark SPY (12.7%) in the same period.
- Looking at annual return (CAGR) in of 26.6% in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (13.5%).

'Volatility is a statistical measure of the dispersion of returns for a given security or market index. Volatility can either be measured by using the standard deviation or variance between returns from that same security or market index. Commonly, the higher the volatility, the riskier the security. In the securities markets, volatility is often associated with big swings in either direction. For example, when the stock market rises and falls more than one percent over a sustained period of time, it is called a 'volatile' market.'

Applying this definition to our asset in some examples:- The volatility over 5 years of ProShares Ultra QQQ is 48.2%, which is higher, thus worse compared to the benchmark SPY (19.8%) in the same period.
- During the last 3 years, the historical 30 days volatility is 54%, which is larger, thus worse than the value of 23% from the benchmark.

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

Applying this definition to our asset in some examples:- Looking at the downside deviation of 34.8% in the last 5 years of ProShares Ultra QQQ, we see it is relatively greater, thus worse in comparison to the benchmark SPY (14.5%)
- Looking at downside risk in of 39.1% in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (16.8%).

'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (0.52) in the period of the last 5 years, the risk / return profile (Sharpe) of 0.5 of ProShares Ultra QQQ is smaller, thus worse.
- Looking at Sharpe Ratio in of 0.45 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.48).

'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:- The excess return divided by the downside deviation over 5 years of ProShares Ultra QQQ is 0.69, which is smaller, thus worse compared to the benchmark SPY (0.7) in the same period.
- Looking at downside risk / excess return profile in of 0.62 in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (0.65).

'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.'

Using this definition on our asset we see for example:- The Ulcer Index over 5 years of ProShares Ultra QQQ is 14 , which is larger, thus worse compared to the benchmark SPY (6.08 ) in the same period.
- Looking at Ulcer Ratio in of 15 in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (6.77 ).

'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.'

Applying this definition to our asset in some examples:- Looking at the maximum drop from peak to valley of -51.7 days in the last 5 years of ProShares Ultra QQQ, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (-33.7 days)
- During the last 3 years, the maximum DrawDown 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). 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'

Using this definition on our asset we see for example:- Looking at the maximum time in days below previous high water mark of 214 days in the last 5 years of ProShares Ultra QQQ, we see it is relatively greater, thus worse in comparison to the benchmark SPY (139 days)
- During the last 3 years, the maximum time in days below previous high water mark is 121 days, which is higher, thus worse than the value of 119 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:- The average days under water over 5 years of ProShares Ultra QQQ is 42 days, which is higher, thus worse compared to the benchmark SPY (35 days) in the same period.
- Looking at average days under water in of 30 days in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (27 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.