'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.'

Applying this definition to our asset in some examples:- The total return, or performance over 5 years of ProShares Ultra Gold is 41.8%, which is smaller, thus worse compared to the benchmark SPY (129.1%) in the same period.
- During the last 3 years, the total return, or performance is 63.1%, which is lower, thus worse than the value of 71.3% 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.'

Applying this definition to our asset in some examples:- The annual performance (CAGR) over 5 years of ProShares Ultra Gold is 7.2%, which is lower, thus worse compared to the benchmark SPY (18.1%) in the same period.
- Looking at annual performance (CAGR) in of 17.7% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (19.7%).

'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:- The volatility over 5 years of ProShares Ultra Gold is 27.7%, which is greater, thus worse compared to the benchmark SPY (18.7%) in the same period.
- Compared with SPY (22.5%) in the period of the last 3 years, the 30 days standard deviation of 31.5% is higher, thus worse.

'The downside volatility is similar to the volatility, or standard deviation, but only takes losing/negative periods into account.'

Which means for our asset as example:- Compared with the benchmark SPY (13.6%) in the period of the last 5 years, the downside volatility of 19.8% of ProShares Ultra Gold is larger, thus worse.
- Looking at downside deviation in of 22.4% in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (16.3%).

'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:- The risk / return profile (Sharpe) over 5 years of ProShares Ultra Gold is 0.17, which is smaller, thus worse compared to the benchmark SPY (0.83) in the same period.
- Compared with SPY (0.76) in the period of the last 3 years, the ratio of return and volatility (Sharpe) of 0.48 is smaller, thus worse.

'The Sortino ratio measures the risk-adjusted return of an investment asset, portfolio, or strategy. It is a modification of the Sharpe ratio but penalizes only those returns falling below a user-specified target or required rate of return, while the Sharpe ratio penalizes both upside and downside volatility equally. Though both ratios measure an investment's risk-adjusted return, they do so in significantly different ways that will frequently lead to differing conclusions as to the true nature of the investment's return-generating efficiency. The Sortino ratio is used as a way to compare the risk-adjusted performance of programs with differing risk and return profiles. In general, risk-adjusted returns seek to normalize the risk across programs and then see which has the higher return unit per risk.'

Applying this definition to our asset in some examples:- The excess return divided by the downside deviation over 5 years of ProShares Ultra Gold is 0.24, which is lower, thus worse compared to the benchmark SPY (1.15) in the same period.
- Compared with SPY (1.05) in the period of the last 3 years, the downside risk / excess return profile of 0.68 is lower, thus worse.

'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 Ulcer Index of 17 in the last 5 years of ProShares Ultra Gold, we see it is relatively larger, thus worse in comparison to the benchmark SPY (5.59 )
- Compared with SPY (6.38 ) in the period of the last 3 years, the Ulcer Ratio of 17 is larger, thus worse.

'A maximum drawdown is the maximum loss from a peak to a trough of a portfolio, before a new peak is attained. Maximum Drawdown is an indicator of downside risk over a specified time period. It can be used both as a stand-alone measure or as an input into other metrics such as 'Return over Maximum Drawdown' and the Calmar Ratio. Maximum Drawdown is expressed in percentage terms.'

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 -37.3 days of ProShares Ultra Gold is lower, thus worse.
- Looking at maximum reduction from previous high in of -37.3 days in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (-33.7 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.'

Applying this definition to our asset in some examples:- The maximum days below previous high over 5 years of ProShares Ultra Gold is 449 days, which is higher, thus worse compared to the benchmark SPY (139 days) in the same period.
- During the last 3 years, the maximum days below previous high is 301 days, which is greater, thus worse than the value of 119 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.'

Which means for our asset as example:- Looking at the average time in days below previous high water mark of 145 days in the last 5 years of ProShares Ultra Gold, we see it is relatively higher, thus worse in comparison to the benchmark SPY (32 days)
- During the last 3 years, the average days below previous high is 81 days, which is higher, thus worse than the value of 25 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 Gold 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.