'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:- The total return over 5 years of ProShares Ultra Silver is 0.4%, which is lower, thus worse compared to the benchmark SPY (62.6%) in the same period.
- Looking at total return, or performance in of 9.2% in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (32.1%).

'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.'

Using this definition on our asset we see for example:- The annual return (CAGR) over 5 years of ProShares Ultra Silver is 0.1%, which is lower, thus worse compared to the benchmark SPY (10.2%) in the same period.
- Compared with SPY (9.7%) in the period of the last 3 years, the annual return (CAGR) of 3% is smaller, thus worse.

'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (21.5%) in the period of the last 5 years, the 30 days standard deviation of 59.3% of ProShares Ultra Silver is higher, thus worse.
- Compared with SPY (24.8%) in the period of the last 3 years, the historical 30 days volatility of 70.6% is greater, 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 (15.6%) in the period of the last 5 years, the downside volatility of 41.7% of ProShares Ultra Silver is greater, thus worse.
- Compared with SPY (17.9%) in the period of the last 3 years, the downside volatility of 49.4% is larger, thus worse.

'The Sharpe ratio was developed by Nobel laureate William F. Sharpe, and is used to help investors understand the return of an investment compared to its risk. The ratio is the average return earned in excess of the risk-free rate per unit of volatility or total risk. Subtracting the risk-free rate from the mean return allows an investor to better isolate the profits associated with risk-taking activities. One intuition of this calculation is that a portfolio engaging in 'zero risk' investments, such as the purchase of U.S. Treasury bills (for which the expected return is the risk-free rate), has a Sharpe ratio of exactly zero. Generally, the greater the value of the Sharpe ratio, the more attractive the risk-adjusted return.'

Applying this definition to our asset in some examples:- The Sharpe Ratio over 5 years of ProShares Ultra Silver is -0.04, which is lower, thus worse compared to the benchmark SPY (0.36) in the same period.
- Compared with SPY (0.29) in the period of the last 3 years, the ratio of return and volatility (Sharpe) of 0.01 is lower, thus worse.

'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.'

Using this definition on our asset we see for example:- The downside risk / excess return profile over 5 years of ProShares Ultra Silver is -0.06, which is lower, thus worse compared to the benchmark SPY (0.5) in the same period.
- Looking at downside risk / excess return profile in of 0.01 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.4).

'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.'

Which means for our asset as example:- Looking at the Ulcer Index of 38 in the last 5 years of ProShares Ultra Silver, we see it is relatively higher, thus worse in comparison to the benchmark SPY (8.52 )
- During the last 3 years, the Ulcer Index is 44 , which is larger, thus worse than the value of 10 from the benchmark.

'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:- Looking at the maximum drop from peak to valley of -74.2 days in the last 5 years of ProShares Ultra Silver, we see it is relatively lower, thus worse in comparison to the benchmark SPY (-33.7 days)
- Compared with SPY (-33.7 days) in the period of the last 3 years, the maximum drop from peak to valley of -74.2 days is lower, 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'

Using this definition on our asset we see for example:- Looking at the maximum days under water of 588 days in the last 5 years of ProShares Ultra Silver, we see it is relatively larger, thus worse in comparison to the benchmark SPY (235 days)
- During the last 3 years, the maximum days under water is 588 days, which is greater, thus worse than the value of 235 days from the benchmark.

'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:- The average time in days below previous high water mark over 5 years of ProShares Ultra Silver is 226 days, which is greater, thus worse compared to the benchmark SPY (55 days) in the same period.
- Compared with SPY (59 days) in the period of the last 3 years, the average days under water of 244 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 Silver 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.