'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:- Compared with the benchmark SPY (110.3%) in the period of the last 5 years, the total return of 37.8% of ProShares Ultra Silver is smaller, thus worse.
- Compared with SPY (39.7%) in the period of the last 3 years, the total return of 28.5% is smaller, thus worse.

'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (16.1%) in the period of the last 5 years, the compounded annual growth rate (CAGR) of 6.6% of ProShares Ultra Silver is lower, thus worse.
- During the last 3 years, the compounded annual growth rate (CAGR) is 8.7%, which is lower, thus worse than the value of 11.8% from the benchmark.

'Volatility is a rate at which the price of a security increases or decreases for a given set of returns. Volatility is measured by calculating the standard deviation of the annualized returns over a given period of time. It shows the range to which the price of a security may increase or decrease. Volatility measures the risk of a security. It is used in option pricing formula to gauge the fluctuations in the returns of the underlying assets. Volatility indicates the pricing behavior of the security and helps estimate the fluctuations that may happen in a short period of time.'

Applying this definition to our asset in some examples:- Looking at the 30 days standard deviation of 64.9% in the last 5 years of ProShares Ultra Silver, we see it is relatively greater, thus worse in comparison to the benchmark SPY (20.9%)
- Compared with SPY (17.5%) in the period of the last 3 years, the 30 days standard deviation of 57.5% is larger, 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.'

Applying this definition to our asset in some examples:- Looking at the downside volatility of 45% in the last 5 years of ProShares Ultra Silver, we see it is relatively larger, thus worse in comparison to the benchmark SPY (14.9%)
- Looking at downside volatility in of 38.2% in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (12.2%).

'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 0.06 in the last 5 years of ProShares Ultra Silver, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.65)
- During the last 3 years, the ratio of return and volatility (Sharpe) is 0.11, which is lower, thus worse than the value of 0.53 from the benchmark.

'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 (0.91) in the period of the last 5 years, the excess return divided by the downside deviation of 0.09 of ProShares Ultra Silver is smaller, thus worse.
- Looking at downside risk / excess return profile in of 0.16 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.76).

'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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (9.32 ) in the period of the last 5 years, the Downside risk index of 48 of ProShares Ultra Silver is higher, thus worse.
- Compared with SPY (10 ) in the period of the last 3 years, the Downside risk index of 35 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:- Compared with the benchmark SPY (-33.7 days) in the period of the last 5 years, the maximum DrawDown of -74.2 days of ProShares Ultra Silver is lower, thus worse.
- During the last 3 years, the maximum DrawDown is -60.3 days, which is lower, thus worse than the value of -24.5 days from the benchmark.

'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 below previous high of 1045 days in the last 5 years of ProShares Ultra Silver, we see it is relatively larger, thus worse in comparison to the benchmark SPY (488 days)
- During the last 3 years, the maximum days below previous high is 552 days, which is larger, thus worse than the value of 488 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (124 days) in the period of the last 5 years, the average time in days below previous high water mark of 446 days of ProShares Ultra Silver is larger, thus worse.
- During the last 3 years, the average days under water is 215 days, which is higher, thus worse than the value of 179 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 and do not account for slippage, fees or taxes.