'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:- The total return, or increase in value over 5 years of ProShares Ultra S&P500 is 81.8%, which is greater, thus better compared to the benchmark SPY (61.3%) in the same period.
- Looking at total return, or performance in of 35.5% in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (31.6%).

'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.'

Which means for our asset as example:- The annual return (CAGR) over 5 years of ProShares Ultra S&P500 is 12.7%, which is higher, thus better compared to the benchmark SPY (10%) in the same period.
- Compared with SPY (9.6%) in the period of the last 3 years, the annual performance (CAGR) of 10.7% is greater, thus better.

'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:- Looking at the 30 days standard deviation of 42% in the last 5 years of ProShares Ultra S&P500, we see it is relatively higher, thus worse in comparison to the benchmark SPY (20.8%)
- Looking at historical 30 days volatility in of 48.6% in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (24%).

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (15.3%) in the period of the last 5 years, the downside deviation of 30.8% of ProShares Ultra S&P500 is greater, thus worse.
- Compared with SPY (17.6%) in the period of the last 3 years, the downside risk of 35.6% is greater, thus worse.

'The Sharpe ratio is the measure of risk-adjusted return of a financial portfolio. Sharpe ratio is a measure of excess portfolio return over the risk-free rate relative to its standard deviation. Normally, the 90-day Treasury bill rate is taken as the proxy for risk-free rate. A portfolio with a higher Sharpe ratio is considered superior relative to its peers. The measure was named after William F Sharpe, a Nobel laureate and professor of finance, emeritus at Stanford University.'

Using this definition on our asset we see for example:- The Sharpe Ratio over 5 years of ProShares Ultra S&P500 is 0.24, which is lower, thus worse compared to the benchmark SPY (0.36) in the same period.
- During the last 3 years, the Sharpe Ratio is 0.17, which is smaller, thus worse than the value of 0.3 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:- Looking at the excess return divided by the downside deviation of 0.33 in the last 5 years of ProShares Ultra S&P500, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.49)
- During the last 3 years, the ratio of annual return and downside deviation is 0.23, which is lower, thus worse than the value of 0.4 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 (7.61 ) in the period of the last 5 years, the Ulcer Index of 16 of ProShares Ultra S&P500 is greater, thus worse.
- Looking at Ulcer Index in of 19 in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (8.93 ).

'A maximum drawdown is the maximum loss from a peak to a trough of a portfolio, before a new peak is attained. Maximum Drawdown is an indicator of downside risk over a specified time period. It can be used both as a stand-alone measure or as an input into other metrics such as 'Return over Maximum Drawdown' and the Calmar Ratio. Maximum Drawdown is expressed in percentage terms.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (-33.7 days) in the period of the last 5 years, the maximum DrawDown of -59.3 days of ProShares Ultra S&P500 is smaller, thus worse.
- During the last 3 years, the maximum drop from peak to valley is -59.3 days, which is lower, thus worse than the value of -33.7 days from the benchmark.

'The Maximum 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. It is the length of time the account was in the Max Drawdown. A Max Drawdown measures a retrenchment from when an equity curve reaches a new high. It’s the maximum an account lost during that retrenchment. This method is applied because a valley can’t be measured until a new high occurs. Once the new high is reached, the percentage change from the old high to the bottom of the largest trough is recorded.'

Applying this definition to our asset in some examples:- Looking at the maximum time in days below previous high water mark of 194 days in the last 5 years of ProShares Ultra S&P500, we see it is relatively greater, thus worse in comparison to the benchmark SPY (185 days)
- During the last 3 years, the maximum time in days below previous high water mark is 185 days, which is greater, thus worse than the value of 185 days from the benchmark.

'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.'

Which means for our asset as example:- The average days below previous high over 5 years of ProShares Ultra S&P500 is 56 days, which is larger, thus worse compared to the benchmark SPY (46 days) in the same period.
- Looking at average days below previous high in of 47 days in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (44 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 S&P500 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.