'Total return, when measuring performance, is the actual rate of return of an investment or a pool of investments over a given evaluation period. Total return includes interest, capital gains, dividends and distributions realized over a given period of time. Total return accounts for two categories of return: income including interest paid by fixed-income investments, distributions or dividends and capital appreciation, representing the change in the market price of an asset.'

Using this definition on our asset we see for example:- Looking at the total return, or increase in value of 28.2% in the last 5 years of ProShares Ultra Gold, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (121.6%)
- Looking at total return, or performance in of 71.8% in the period of the last 3 years, we see it is relatively larger, thus better in comparison to SPY (64.5%).

'The compound annual growth rate isn't a true return rate, but rather a representational figure. It is essentially a number that describes the rate at which an investment would have grown if it had grown the same rate every year and the profits were reinvested at the end of each year. In reality, this sort of performance is unlikely. However, CAGR can be used to smooth returns so that they may be more easily understood when compared to alternative investments.'

Which means for our asset as example:- The annual return (CAGR) over 5 years of ProShares Ultra Gold is 5.1%, which is lower, thus worse compared to the benchmark SPY (17.3%) in the same period.
- During the last 3 years, the annual return (CAGR) is 19.8%, which is greater, thus better than the value of 18.1% from the benchmark.

'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (18.7%) in the period of the last 5 years, the volatility of 27.6% of ProShares Ultra Gold is greater, thus worse.
- Compared with SPY (22.5%) in the period of the last 3 years, the volatility of 31.1% is greater, 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:- Looking at the downside deviation of 19.7% in the last 5 years of ProShares Ultra Gold, we see it is relatively larger, thus worse in comparison to the benchmark SPY (13.5%)
- Compared with SPY (16.4%) in the period of the last 3 years, the downside risk of 21.9% is larger, thus worse.

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (0.79) in the period of the last 5 years, the ratio of return and volatility (Sharpe) of 0.09 of ProShares Ultra Gold is lower, thus worse.
- Compared with SPY (0.69) in the period of the last 3 years, the risk / return profile (Sharpe) of 0.56 is lower, thus worse.

'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.'

Applying this definition to our asset in some examples:- Looking at the excess return divided by the downside deviation of 0.13 in the last 5 years of ProShares Ultra Gold, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (1.09)
- Compared with SPY (0.95) in the period of the last 3 years, the downside risk / excess return profile of 0.79 is lower, thus worse.

'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 Downside risk index of 19 in the last 5 years of ProShares Ultra Gold, we see it is relatively higher, thus worse in comparison to the benchmark SPY (5.58 )
- Compared with SPY (6.83 ) in the period of the last 3 years, the Downside risk index of 15 is higher, thus worse.

'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.'

Which means for our asset as example:- The maximum drop from peak to valley over 5 years of ProShares Ultra Gold is -37.3 days, which is smaller, 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 -37.3 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'

Which means for our asset as example:- Compared with the benchmark SPY (139 days) in the period of the last 5 years, the maximum days under water of 757 days of ProShares Ultra Gold is greater, thus worse.
- During the last 3 years, the maximum days under water is 247 days, which is greater, thus worse than the value of 139 days from the benchmark.

'The Average 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. 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:- Looking at the average days below previous high of 266 days in the last 5 years of ProShares Ultra Gold, we see it is relatively higher, thus worse in comparison to the benchmark SPY (33 days)
- During the last 3 years, the average time in days below previous high water mark is 62 days, which is greater, thus worse than the value of 35 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.