'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:- Looking at the total return, or performance of -30.1% in the last 5 years of ProShares Ultra Silver, we see it is relatively lower, thus worse in comparison to the benchmark SPY (124.9%)
- Looking at total return, or increase in value in of 46.3% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (60.5%).

'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.'

Using this definition on our asset we see for example:- The compounded annual growth rate (CAGR) over 5 years of ProShares Ultra Silver is -6.9%, which is lower, thus worse compared to the benchmark SPY (17.6%) in the same period.
- Looking at compounded annual growth rate (CAGR) in of 13.6% in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (17.1%).

'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.'

Which means for our asset as example:- The 30 days standard deviation over 5 years of ProShares Ultra Silver is 55%, which is higher, thus worse compared to the benchmark SPY (18.7%) in the same period.
- Looking at historical 30 days volatility in of 64.7% in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (22.6%).

'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:- Looking at the downside deviation of 39.8% in the last 5 years of ProShares Ultra Silver, we see it is relatively greater, thus worse in comparison to the benchmark SPY (13.5%)
- During the last 3 years, the downside deviation is 46.1%, which is greater, thus worse than the value of 16.4% 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:- Looking at the risk / return profile (Sharpe) of -0.17 in the last 5 years of ProShares Ultra Silver, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.81)
- Looking at ratio of return and volatility (Sharpe) in of 0.17 in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (0.65).

'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:- Looking at the ratio of annual return and downside deviation of -0.24 in the last 5 years of ProShares Ultra Silver, we see it is relatively lower, thus worse in comparison to the benchmark SPY (1.12)
- Looking at downside risk / excess return profile in of 0.24 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.89).

'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:- The Ulcer Ratio over 5 years of ProShares Ultra Silver is 37 , which is larger, thus worse compared to the benchmark SPY (5.58 ) in the same period.
- Compared with SPY (6.82 ) in the period of the last 3 years, the Downside risk index of 28 is larger, thus worse.

'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.'

Using this definition on our asset we see for example:- The maximum drop from peak to valley over 5 years of ProShares Ultra Silver is -72.1 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 reduction from previous high of -66.1 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'

Applying this definition to our asset in some examples:- The maximum days below previous high over 5 years of ProShares Ultra Silver is 959 days, which is larger, thus worse compared to the benchmark SPY (139 days) in the same period.
- Looking at maximum days under water in of 285 days in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (128 days).

'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:- The average time in days below previous high water mark over 5 years of ProShares Ultra Silver is 401 days, which is greater, thus worse compared to the benchmark SPY (32 days) in the same period.
- Compared with SPY (33 days) in the period of the last 3 years, the average days under water of 101 days is larger, thus worse.

Historical returns have been extended using synthetic data.
[Show Details]

- 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.