'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:- Compared with the benchmark SPY (125.9%) in the period of the last 5 years, the total return, or performance of 273% of ProShares Ultra S&P500 is greater, thus better.
- During the last 3 years, the total return, or performance is 61.3%, which is greater, thus better than the value of 44.4% 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.'

Applying this definition to our asset in some examples:- The annual performance (CAGR) over 5 years of ProShares Ultra S&P500 is 30.1%, which is greater, thus better compared to the benchmark SPY (17.7%) in the same period.
- Looking at annual performance (CAGR) in of 17.3% in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (13%).

'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:- The volatility over 5 years of ProShares Ultra S&P500 is 37.9%, which is larger, thus worse compared to the benchmark SPY (18.7%) in the same period.
- Compared with SPY (22.8%) in the period of the last 3 years, the historical 30 days volatility of 46.3% is larger, 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.'

Which means for our asset as example:- Compared with the benchmark SPY (13.6%) in the period of the last 5 years, the downside risk of 27.5% of ProShares Ultra S&P500 is larger, thus worse.
- During the last 3 years, the downside risk is 33.9%, which is greater, 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.'

Applying this definition to our asset in some examples:- Looking at the risk / return profile (Sharpe) of 0.73 in the last 5 years of ProShares Ultra S&P500, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.81)
- Looking at Sharpe Ratio in of 0.32 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.46).

'The Sortino ratio measures the risk-adjusted return of an investment asset, portfolio, or strategy. It is a modification of the Sharpe ratio but penalizes only those returns falling below a user-specified target or required rate of return, while the Sharpe ratio penalizes both upside and downside volatility equally. Though both ratios measure an investment's risk-adjusted return, they do so in significantly different ways that will frequently lead to differing conclusions as to the true nature of the investment's return-generating efficiency. The Sortino ratio is used as a way to compare the risk-adjusted performance of programs with differing risk and return profiles. In general, risk-adjusted returns seek to normalize the risk across programs and then see which has the higher return unit per risk.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (1.12) in the period of the last 5 years, the excess return divided by the downside deviation of 1.01 of ProShares Ultra S&P500 is lower, thus worse.
- Looking at ratio of annual return and downside deviation in of 0.43 in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (0.63).

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (5.59 ) in the period of the last 5 years, the Downside risk index of 12 of ProShares Ultra S&P500 is greater, thus worse.
- Looking at Ulcer Ratio in of 15 in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (7.14 ).

'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:- 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 lower, thus worse.
- During the last 3 years, the maximum DrawDown 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:- The maximum days below previous high over 5 years of ProShares Ultra S&P500 is 193 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 time in days below previous high water mark of 193 days is higher, thus worse.

'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 days under water of 44 days in the last 5 years of ProShares Ultra S&P500, we see it is relatively higher, 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 62 days is greater, 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 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.