'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, or increase in value over 5 years of ProShares Ultra S&P500 is 80.8%, which is greater, thus better compared to the benchmark SPY (63%) in the same period.
- During the last 3 years, the total return, or performance is 35.9%, which is greater, thus better than the value of 33.5% 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.'

Using this definition on our asset we see for example:- The compounded annual growth rate (CAGR) over 5 years of ProShares Ultra S&P500 is 12.6%, which is larger, thus better compared to the benchmark SPY (10.3%) in the same period.
- During the last 3 years, the compounded annual growth rate (CAGR) is 10.8%, which is larger, thus better than the value of 10.1% from the benchmark.

'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.'

Using this definition on our asset we see for example:- Looking at the historical 30 days volatility of 43.6% in the last 5 years of ProShares Ultra S&P500, we see it is relatively greater, thus worse in comparison to the benchmark SPY (21.6%)
- Compared with SPY (25.1%) in the period of the last 3 years, the 30 days standard deviation of 50.7% is larger, thus worse.

'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 31.6% in the last 5 years of ProShares Ultra S&P500, we see it is relatively higher, thus worse in comparison to the benchmark SPY (15.6%)
- Looking at downside volatility in of 36.5% in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (18.1%).

'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 ratio of return and volatility (Sharpe) of 0.23 in the last 5 years of ProShares Ultra S&P500, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.36)
- Looking at ratio of return and volatility (Sharpe) in of 0.16 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.3).

'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:- The excess return divided by the downside deviation over 5 years of ProShares Ultra S&P500 is 0.32, which is lower, thus worse compared to the benchmark SPY (0.5) in the same period.
- Compared with SPY (0.42) in the period of the last 3 years, the downside risk / excess return profile of 0.23 is lower, thus worse.

'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.'

Applying this definition to our asset in some examples:- Looking at the Ulcer Index of 19 in the last 5 years of ProShares Ultra S&P500, we see it is relatively greater, thus worse in comparison to the benchmark SPY (8.88 )
- Looking at Ulcer Index in of 23 in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (11 ).

'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 drop from peak to valley 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.
- Compared with SPY (-33.7 days) in the period of the last 3 years, the maximum drop from peak to valley of -59.3 days is smaller, thus worse.

'The Drawdown Duration is the length of any peak to peak period, or the time between new equity highs. The Max Drawdown Duration is the worst (the maximum/longest) amount of time an investment has seen between peaks (equity highs). Many assume Max DD Duration is the length of time between new highs during which the Max DD (magnitude) occurred. But that isn’t always the case. The Max DD duration is the longest time between peaks, period. So it could be the time when the program also had its biggest peak to valley loss (and usually is, because the program needs a long time to recover from the largest loss), but it doesn’t have to be'

Applying this definition to our asset in some examples:- Looking at the maximum days under water of 273 days in the last 5 years of ProShares Ultra S&P500, we see it is relatively larger, thus worse in comparison to the benchmark SPY (273 days)
- Compared with SPY (273 days) in the period of the last 3 years, the maximum days below previous high of 273 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.'

Applying this definition to our asset in some examples:- Looking at the average days under water of 67 days in the last 5 years of ProShares Ultra S&P500, we see it is relatively larger, thus worse in comparison to the benchmark SPY (57 days)
- Compared with SPY (73 days) in the period of the last 3 years, the average days below previous high of 75 days is larger, 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.