'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 S&P500 is 116.8%, which is higher, thus better compared to the benchmark SPY (80.1%) in the same period.
- During the last 3 years, the total return, or performance is 39.8%, which is greater, thus better than the value of 30.8% 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.'

Which means for our asset as example:- Looking at the compounded annual growth rate (CAGR) of 16.8% in the last 5 years of ProShares Ultra S&P500, we see it is relatively larger, thus better in comparison to the benchmark SPY (12.5%)
- During the last 3 years, the annual performance (CAGR) is 11.8%, which is higher, thus better than the value of 9.4% 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:- The volatility over 5 years of ProShares Ultra S&P500 is 43%, which is larger, thus worse compared to the benchmark SPY (21.3%) in the same period.
- Looking at historical 30 days volatility in of 35% in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (17.6%).

'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:- Looking at the downside deviation of 30.8% in the last 5 years of ProShares Ultra S&P500, we see it is relatively larger, thus worse in comparison to the benchmark SPY (15.3%)
- Looking at downside risk in of 24.6% in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (12.3%).

'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:- Looking at the Sharpe Ratio 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 (0.47)
- Compared with SPY (0.39) in the period of the last 3 years, the Sharpe Ratio of 0.27 is lower, thus worse.

'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:- Compared with the benchmark SPY (0.66) in the period of the last 5 years, the excess return divided by the downside deviation of 0.46 of ProShares Ultra S&P500 is smaller, thus worse.
- Looking at downside risk / excess return profile in of 0.38 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.56).

'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 S&P500 is 21 , which is greater, thus worse compared to the benchmark SPY (9.43 ) in the same period.
- During the last 3 years, the Downside risk index is 24 , which is greater, thus worse than the value of 10 from the benchmark.

'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.'

Which means for our asset as example:- Looking at the maximum reduction from previous high of -59.3 days in the last 5 years of ProShares Ultra S&P500, we see it is relatively lower, thus worse in comparison to the benchmark SPY (-33.7 days)
- Looking at maximum reduction from previous high in of -46.7 days in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (-24.5 days).

'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:- The maximum time in days below previous high water mark over 5 years of ProShares Ultra S&P500 is 478 days, which is higher, thus worse compared to the benchmark SPY (478 days) in the same period.
- Looking at maximum days below previous high in of 478 days in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (478 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.'

Applying this definition to our asset in some examples:- The average days below previous high over 5 years of ProShares Ultra S&P500 is 118 days, which is larger, thus worse compared to the benchmark SPY (118 days) in the same period.
- Looking at average days below previous high in of 172 days in the period of the last 3 years, we see it is relatively lower, thus better in comparison to SPY (173 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.