'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:- Looking at the total return of 104.5% in the last 5 years of ProShares Ultra S&P500, we see it is relatively higher, thus better in comparison to the benchmark SPY (67.6%)
- During the last 3 years, the total return is 45.5%, which is higher, thus better than the value of 36.7% 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:- Compared with the benchmark SPY (10.9%) in the period of the last 5 years, the annual performance (CAGR) of 15.4% of ProShares Ultra S&P500 is larger, thus better.
- Compared with SPY (11%) in the period of the last 3 years, the annual performance (CAGR) of 13.3% 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (19%) in the period of the last 5 years, the volatility of 38.5% of ProShares Ultra S&P500 is larger, thus worse.
- Compared with SPY (22%) in the period of the last 3 years, the 30 days standard deviation of 44.7% is higher, thus worse.

'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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (13.9%) in the period of the last 5 years, the downside volatility of 28% of ProShares Ultra S&P500 is greater, thus worse.
- During the last 3 years, the downside risk is 32.8%, which is greater, thus worse than the value of 16.2% 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.'

Applying this definition to our asset in some examples:- The ratio of return and volatility (Sharpe) over 5 years of ProShares Ultra S&P500 is 0.33, which is lower, thus worse compared to the benchmark SPY (0.44) in the same period.
- Looking at risk / return profile (Sharpe) in of 0.24 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.39).

'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.'

Which means for our asset as example:- Looking at the excess return divided by the downside deviation of 0.46 in the last 5 years of ProShares Ultra S&P500, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (0.6)
- Compared with SPY (0.53) in the period of the last 3 years, the excess return divided by the downside deviation of 0.33 is lower, thus worse.

'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:- Compared with the benchmark SPY (5.91 ) in the period of the last 5 years, the Ulcer Ratio of 13 of ProShares Ultra S&P500 is larger, thus worse.
- Looking at Ulcer Index in of 15 in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (7 ).

'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.'

Using this definition on our asset we see for example:- The maximum drop from peak to valley over 5 years of ProShares Ultra S&P500 is -59.3 days, which is smaller, thus worse compared to the benchmark SPY (-33.7 days) in the same period.
- Looking at maximum DrawDown in of -59.3 days in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (-33.7 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (187 days) in the period of the last 5 years, the maximum days under water of 244 days of ProShares Ultra S&P500 is higher, thus worse.
- During the last 3 years, the maximum time in days below previous high water mark is 194 days, which is greater, thus worse than the value of 139 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.'

Applying this definition to our asset in some examples:- Looking at the average time in days below previous high water mark of 64 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 (45 days)
- Looking at average days under water in of 57 days in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (42 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.