'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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (67.1%) in the period of the last 5 years, the total return, or performance of -1% of ProShares Ultra Silver is smaller, thus worse.
- Compared with SPY (61.5%) in the period of the last 3 years, the total return of 65.4% is larger, thus better.

'Compound annual growth rate (CAGR) is a business and investing specific term for the geometric progression ratio that provides a constant rate of return over the time period. CAGR is not an accounting term, but it is often used to describe some element of the business, for example revenue, units delivered, registered users, etc. CAGR dampens the effect of volatility of periodic returns that can render arithmetic means irrelevant. It is particularly useful to compare growth rates from various data sets of common domain such as revenue growth of companies in the same industry.'

Which means for our asset as example:- The compounded annual growth rate (CAGR) over 5 years of ProShares Ultra Silver is -0.2%, which is lower, thus worse compared to the benchmark SPY (10.8%) in the same period.
- Looking at annual performance (CAGR) in of 18.3% in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (17.3%).

'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:- The 30 days standard deviation over 5 years of ProShares Ultra Silver is 60.4%, which is larger, thus worse compared to the benchmark SPY (21.4%) in the same period.
- During the last 3 years, the volatility is 68%, which is higher, thus worse than the value of 20% from the benchmark.

'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:- The downside deviation over 5 years of ProShares Ultra Silver is 42.4%, which is greater, thus worse compared to the benchmark SPY (15.4%) in the same period.
- During the last 3 years, the downside volatility is 46%, which is larger, thus worse than the value of 13.9% from the benchmark.

'The Sharpe ratio (also known as the Sharpe index, the Sharpe measure, and the reward-to-variability ratio) is a way to examine the performance of an investment by adjusting for its risk. The ratio measures the excess return (or risk premium) per unit of deviation in an investment asset or a trading strategy, typically referred to as risk, named after William F. Sharpe.'

Using this definition on our asset we see for example:- The ratio of return and volatility (Sharpe) over 5 years of ProShares Ultra Silver is -0.04, which is smaller, thus worse compared to the benchmark SPY (0.39) in the same period.
- Looking at risk / return profile (Sharpe) in of 0.23 in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (0.74).

'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:- Compared with the benchmark SPY (0.54) in the period of the last 5 years, the ratio of annual return and downside deviation of -0.06 of ProShares Ultra Silver is lower, thus worse.
- During the last 3 years, the downside risk / excess return profile is 0.34, which is lower, thus worse than the value of 1.06 from the benchmark.

'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 40 in the last 5 years of ProShares Ultra Silver, we see it is relatively larger, thus worse in comparison to the benchmark SPY (9.21 )
- Looking at Ulcer Index in of 46 in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (9.87 ).

'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:- Compared with the benchmark SPY (-33.7 days) in the period of the last 5 years, the maximum drop from peak to valley of -74.2 days of ProShares Ultra Silver is smaller, thus worse.
- Looking at maximum DrawDown in of -74.2 days in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (-24.5 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.'

Which means for our asset as example:- Looking at the maximum days under water of 664 days in the last 5 years of ProShares Ultra Silver, we see it is relatively greater, thus worse in comparison to the benchmark SPY (311 days)
- Compared with SPY (311 days) in the period of the last 3 years, the maximum days under water of 664 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:- The average days below previous high over 5 years of ProShares Ultra Silver is 244 days, which is larger, thus worse compared to the benchmark SPY (66 days) in the same period.
- During the last 3 years, the average days under water is 302 days, which is greater, thus worse than the value of 82 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 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.