'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:- The total return, or performance over 5 years of ProShares Ultra QQQ is 690.7%, which is greater, thus better compared to the benchmark SPY (128%) in the same period.
- During the last 3 years, the total return, or performance is 198.6%, which is larger, thus better than the value of 44.9% from the benchmark.

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (17.9%) in the period of the last 5 years, the annual performance (CAGR) of 51.2% of ProShares Ultra QQQ is greater, thus better.
- During the last 3 years, the compounded annual growth rate (CAGR) is 44%, which is larger, thus better than the value of 13.2% from the benchmark.

'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.'

Using this definition on our asset we see for example:- Looking at the historical 30 days volatility of 43.8% in the last 5 years of ProShares Ultra QQQ, we see it is relatively larger, thus worse in comparison to the benchmark SPY (18.7%)
- Looking at volatility in of 52.6% in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (22.9%).

'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:- Compared with the benchmark SPY (13.6%) in the period of the last 5 years, the downside deviation of 31.2% of ProShares Ultra QQQ is higher, thus worse.
- During the last 3 years, the downside volatility is 37.8%, which is higher, thus worse than the value of 16.7% from the benchmark.

'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:- Looking at the risk / return profile (Sharpe) of 1.11 in the last 5 years of ProShares Ultra QQQ, we see it is relatively greater, thus better in comparison to the benchmark SPY (0.82)
- During the last 3 years, the ratio of return and volatility (Sharpe) is 0.79, which is greater, thus better than the value of 0.47 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.'

Applying this definition to our asset in some examples:- The ratio of annual return and downside deviation over 5 years of ProShares Ultra QQQ is 1.56, which is greater, thus better compared to the benchmark SPY (1.14) in the same period.
- Looking at downside risk / excess return profile in of 1.1 in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (0.64).

'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.'

Applying this definition to our asset in some examples:- Looking at the Downside risk index of 12 in the last 5 years of ProShares Ultra QQQ, we see it is relatively greater, thus worse in comparison to the benchmark SPY (5.59 )
- Compared with SPY (7.15 ) in the period of the last 3 years, the Ulcer Index of 15 is higher, 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.'

Using this definition on our asset we see for example:- Looking at the maximum DrawDown of -51.7 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)
- Compared with SPY (-33.7 days) in the period of the last 3 years, the maximum drop from peak to valley of -51.7 days is lower, 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) in days.'

Using this definition on our asset we see for example:- The maximum days under water over 5 years of ProShares Ultra QQQ is 214 days, which is higher, thus worse compared to the benchmark SPY (139 days) in the same period.
- Compared with SPY (139 days) in the period of the last 3 years, the maximum days under water of 214 days is larger, thus worse.

'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:- Looking at the average days below previous high of 37 days in the last 5 years of ProShares Ultra QQQ, we see it is relatively greater, thus worse in comparison to the benchmark SPY (33 days)
- Compared with SPY (45 days) in the period of the last 3 years, the average time in days below previous high water mark of 52 days is higher, 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.