'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.'

Applying this definition to our asset in some examples:- The total return over 5 years of ProShares Ultra Gold is 78.8%, which is greater, thus better compared to the benchmark SPY (67.6%) in the same period.
- Compared with SPY (36.7%) in the period of the last 3 years, the total return of 79.7% is higher, thus better.

'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:- Looking at the compounded annual growth rate (CAGR) of 12.3% in the last 5 years of ProShares Ultra Gold, we see it is relatively larger, thus better in comparison to the benchmark SPY (10.9%)
- Looking at compounded annual growth rate (CAGR) in of 21.6% in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (11%).

'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.'

Which means for our asset as example:- The volatility over 5 years of ProShares Ultra Gold is 27.5%, which is higher, thus worse compared to the benchmark SPY (19%) in the same period.
- Compared with SPY (22%) in the period of the last 3 years, the historical 30 days volatility of 26.8% is higher, thus worse.

'The downside volatility is similar to the volatility, or standard deviation, but only takes losing/negative periods into account.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (13.9%) in the period of the last 5 years, the downside deviation of 18.4% of ProShares Ultra Gold is greater, thus worse.
- Looking at downside deviation in of 17.7% in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (16.2%).

'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 0.36 in the last 5 years of ProShares Ultra Gold, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (0.44)
- During the last 3 years, the Sharpe Ratio is 0.71, which is larger, thus better than the value of 0.39 from the benchmark.

'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:- Looking at the ratio of annual return and downside deviation of 0.53 in the last 5 years of ProShares Ultra Gold, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (0.6)
- Looking at excess return divided by the downside deviation in of 1.08 in the period of the last 3 years, we see it is relatively greater, thus better in comparison to SPY (0.53).

'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 Downside risk index of 17 in the last 5 years of ProShares Ultra Gold, we see it is relatively greater, thus worse in comparison to the benchmark SPY (5.91 )
- Looking at Ulcer Index in of 12 in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (7 ).

'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:- The maximum reduction from previous high over 5 years of ProShares Ultra Gold is -33.3 days, which is larger, thus better compared to the benchmark SPY (-33.7 days) in the same period.
- Looking at maximum DrawDown in of -27.5 days in the period of the last 3 years, we see it is relatively larger, thus better in comparison to SPY (-33.7 days).

'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) in days.'

Which means for our asset as example:- Compared with the benchmark SPY (187 days) in the period of the last 5 years, the maximum days under water of 774 days of ProShares Ultra Gold is larger, thus worse.
- Compared with SPY (139 days) in the period of the last 3 years, the maximum time in days below previous high water mark of 449 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (45 days) in the period of the last 5 years, the average days below previous high of 257 days of ProShares Ultra Gold is higher, thus worse.
- During the last 3 years, the average days below previous high is 153 days, which is higher, thus worse than the value of 42 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 Gold 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.