'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 increase in value of -7.3% in the last 5 years of ProShares Ultra Silver, we see it is relatively lower, thus worse in comparison to the benchmark SPY (57.1%)
- During the last 3 years, the total return, or increase in value is -48.7%, which is lower, thus worse than the value of 32% from the benchmark.

'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:- Looking at the annual performance (CAGR) of -1.5% in the last 5 years of ProShares Ultra Silver, we see it is relatively lower, thus worse in comparison to the benchmark SPY (9.5%)
- Looking at compounded annual growth rate (CAGR) in of -20% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (9.7%).

'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:- Compared with the benchmark SPY (21.5%) in the period of the last 5 years, the volatility of 61.5% of ProShares Ultra Silver is higher, thus worse.
- Looking at volatility in of 58.8% in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (17.9%).

'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 volatility of 43.1% in the last 5 years of ProShares Ultra Silver, we see it is relatively greater, thus worse in comparison to the benchmark SPY (15.5%)
- Compared with SPY (12.5%) in the period of the last 3 years, the downside volatility of 40.6% is greater, 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.'

Using this definition on our asset we see for example:- Looking at the risk / return profile (Sharpe) of -0.07 in the last 5 years of ProShares Ultra Silver, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.32)
- During the last 3 years, the Sharpe Ratio is -0.38, which is lower, thus worse than the value of 0.41 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:- The downside risk / excess return profile over 5 years of ProShares Ultra Silver is -0.09, which is lower, thus worse compared to the benchmark SPY (0.45) in the same period.
- During the last 3 years, the ratio of annual return and downside deviation is -0.55, which is smaller, thus worse than the value of 0.58 from the benchmark.

'The ulcer index is a stock market risk measure or technical analysis indicator devised by Peter Martin in 1987, and published by him and Byron McCann in their 1989 book The Investors Guide to Fidelity Funds. It's designed as a measure of volatility, but only volatility in the downward direction, i.e. the amount of drawdown or retracement occurring over a period. Other volatility measures like standard deviation treat up and down movement equally, but a trader doesn't mind upward movement, it's the downside that causes stress and stomach ulcers that the index's name suggests.'

Using this definition on our asset we see for example:- Looking at the Downside risk index of 43 in the last 5 years of ProShares Ultra Silver, we see it is relatively higher, thus worse in comparison to the benchmark SPY (9.57 )
- Looking at Ulcer Ratio in of 44 in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (10 ).

'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.'

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 smaller, 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 -69.8 days is lower, thus worse.

'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (439 days) in the period of the last 5 years, the maximum days under water of 792 days of ProShares Ultra Silver is larger, thus worse.
- During the last 3 years, the maximum time in days below previous high water mark is 672 days, which is greater, thus worse than the value of 439 days from the benchmark.

'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.'

Applying this definition to our asset in some examples:- The average days under water over 5 years of ProShares Ultra Silver is 282 days, which is greater, thus worse compared to the benchmark SPY (106 days) in the same period.
- During the last 3 years, the average days under water is 305 days, which is higher, thus worse than the value of 149 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.