'The total return on a portfolio of investments takes into account not only the capital appreciation on the portfolio, but also the income received on the portfolio. The income typically consists of interest, dividends, and securities lending fees. This contrasts with the price return, which takes into account only the capital gain on an investment.'

Which means for our asset as example:- The total return over 5 years of ProShares Ultra S&P500 is 297.9%, which is larger, thus better compared to the benchmark SPY (133.2%) in the same period.
- Looking at total return, or performance in of 157.1% in the period of the last 3 years, we see it is relatively greater, thus better in comparison to SPY (80.4%).

'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 compounded annual growth rate (CAGR) over 5 years of ProShares Ultra S&P500 is 31.9%, which is larger, thus better compared to the benchmark SPY (18.5%) in the same period.
- Looking at compounded annual growth rate (CAGR) in of 37.1% in the period of the last 3 years, we see it is relatively larger, thus better in comparison to SPY (21.8%).

'In finance, volatility (symbol σ) is the degree of variation of a trading price series over time as measured by the standard deviation of logarithmic returns. Historic volatility measures a time series of past market prices. Implied volatility looks forward in time, being derived from the market price of a market-traded derivative (in particular, an option). Commonly, the higher the volatility, the riskier the security.'

Which means for our asset as example:- Looking at the 30 days standard deviation of 37.9% in the last 5 years of ProShares Ultra S&P500, we see it is relatively larger, thus worse in comparison to the benchmark SPY (18.7%)
- Compared with SPY (22.4%) in the period of the last 3 years, the volatility of 45.5% is larger, thus worse.

'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 (13.6%) in the period of the last 5 years, the downside risk of 27.5% of ProShares Ultra S&P500 is greater, thus worse.
- During the last 3 years, the downside risk is 32.8%, which is higher, thus worse than the value of 16.2% from the benchmark.

'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:- Looking at the risk / return profile (Sharpe) of 0.77 in the last 5 years of ProShares Ultra S&P500, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.85)
- During the last 3 years, the ratio of return and volatility (Sharpe) is 0.76, which is smaller, thus worse than the value of 0.86 from the benchmark.

'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:- Compared with the benchmark SPY (1.18) in the period of the last 5 years, the excess return divided by the downside deviation of 1.07 of ProShares Ultra S&P500 is lower, thus worse.
- Looking at downside risk / excess return profile in of 1.05 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (1.19).

'Ulcer Index is a method for measuring investment risk that addresses the real concerns of investors, unlike the widely used standard deviation of return. UI is a measure of the depth and duration of drawdowns in prices from earlier highs. Using Ulcer Index instead of standard deviation can lead to very different conclusions about investment risk and risk-adjusted return, especially when evaluating strategies that seek to avoid major declines in portfolio value (market timing, dynamic asset allocation, hedge funds, etc.). The Ulcer Index was originally developed in 1987. Since then, it has been widely recognized and adopted by the investment community. According to Nelson Freeburg, editor of Formula Research, Ulcer Index is “perhaps the most fully realized statistical portrait of risk there is.'

Which means for our asset as example:- Looking at the Ulcer Ratio of 12 in the last 5 years of ProShares Ultra S&P500, we see it is relatively larger, thus worse in comparison to the benchmark SPY (5.59 )
- Compared with SPY (6.36 ) in the period of the last 3 years, the Ulcer Ratio of 14 is higher, thus worse.

'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.'

Applying this definition to our asset in some examples:- The maximum DrawDown over 5 years of ProShares Ultra S&P500 is -59.3 days, which is lower, thus worse compared to the benchmark SPY (-33.7 days) in the same period.
- Looking at maximum reduction from previous high 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.'

Applying this definition to our asset in some examples:- The maximum days under water over 5 years of ProShares Ultra S&P500 is 194 days, which is higher, thus worse compared to the benchmark SPY (139 days) in the same period.
- Compared with SPY (119 days) in the period of the last 3 years, the maximum days below previous high of 136 days is greater, 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.'

Which means for our asset as example:- Compared with the benchmark SPY (32 days) in the period of the last 5 years, the average days under water of 44 days of ProShares Ultra S&P500 is greater, thus worse.
- During the last 3 years, the average days below previous high is 30 days, which is greater, thus worse than the value of 25 days from the benchmark.

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.