'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:- The total return, or increase in value over 5 years of ProShares Ultra Silver is 57.7%, which is lower, thus worse compared to the benchmark SPY (103%) in the same period.
- During the last 3 years, the total return, or performance is -30.6%, which is smaller, thus worse than the value of 33.6% from the benchmark.

'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:- Looking at the annual performance (CAGR) of 9.5% in the last 5 years of ProShares Ultra Silver, we see it is relatively lower, thus worse in comparison to the benchmark SPY (15.2%)
- Compared with SPY (10.1%) in the period of the last 3 years, the compounded annual growth rate (CAGR) of -11.5% 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.'

Which means for our asset as example:- Looking at the historical 30 days volatility of 64.4% 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 (17.3%) in the period of the last 3 years, the historical 30 days volatility of 56.4% 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.'

Applying this definition to our asset in some examples:- The downside risk over 5 years of ProShares Ultra Silver is 44.6%, which is higher, thus worse compared to the benchmark SPY (14.9%) in the same period.
- During the last 3 years, the downside deviation is 38.2%, which is higher, thus worse than the value of 12.1% from the benchmark.

'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:- The risk / return profile (Sharpe) over 5 years of ProShares Ultra Silver is 0.11, which is smaller, thus worse compared to the benchmark SPY (0.61) in the same period.
- Compared with SPY (0.44) in the period of the last 3 years, the risk / return profile (Sharpe) of -0.25 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 0.16, which is lower, thus worse compared to the benchmark SPY (0.85) in the same period.
- Looking at ratio of annual return and downside deviation in of -0.37 in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (0.63).

'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:- Looking at the Ulcer Ratio of 47 in the last 5 years of ProShares Ultra Silver, we see it is relatively greater, thus worse in comparison to the benchmark SPY (9.32 )
- During the last 3 years, the Downside risk index is 44 , which is greater, thus worse than the value of 10 from the benchmark.

'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 Silver is -74.2 days, which is lower, thus worse compared to the benchmark SPY (-33.7 days) in the same period.
- Compared with SPY (-24.5 days) in the period of the last 3 years, the maximum DrawDown of -66.2 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'

Applying this definition to our asset in some examples:- The maximum days below previous high over 5 years of ProShares Ultra Silver is 967 days, which is greater, thus worse compared to the benchmark SPY (488 days) in the same period.
- Compared with SPY (488 days) in the period of the last 3 years, the maximum time in days below previous high water mark of 756 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:- Looking at the average time in days below previous high water mark of 399 days in the last 5 years of ProShares Ultra Silver, we see it is relatively higher, thus worse in comparison to the benchmark SPY (123 days)
- Compared with SPY (180 days) in the period of the last 3 years, the average days under water of 379 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 and do not account for slippage, fees or taxes.