'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (63%) in the period of the last 5 years, the total return of 37% of ProShares Ultra Gold is lower, thus worse.
- Looking at total return, or increase in value in of 15.3% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (31.2%).

'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.'

Using this definition on our asset we see for example:- The annual return (CAGR) over 5 years of ProShares Ultra Gold is 6.5%, which is smaller, thus worse compared to the benchmark SPY (10.3%) in the same period.
- Looking at compounded annual growth rate (CAGR) in of 4.9% in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (9.5%).

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (21.4%) in the period of the last 5 years, the volatility of 29.5% of ProShares Ultra Gold is greater, thus worse.
- During the last 3 years, the historical 30 days volatility is 33.6%, which is larger, thus worse than the value of 24.9% from the benchmark.

'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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (15.6%) in the period of the last 5 years, the downside deviation of 20.9% of ProShares Ultra Gold is higher, thus worse.
- Looking at downside deviation in of 24% in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (18%).

'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:- The risk / return profile (Sharpe) over 5 years of ProShares Ultra Gold is 0.14, which is lower, thus worse compared to the benchmark SPY (0.36) in the same period.
- Compared with SPY (0.28) in the period of the last 3 years, the risk / return profile (Sharpe) of 0.07 is smaller, 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.'

Which means for our asset as example:- The excess return divided by the downside deviation over 5 years of ProShares Ultra Gold is 0.19, which is smaller, thus worse compared to the benchmark SPY (0.5) in the same period.
- During the last 3 years, the downside risk / excess return profile is 0.1, which is lower, thus worse than the value of 0.39 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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (8.49 ) in the period of the last 5 years, the Ulcer Index of 22 of ProShares Ultra Gold is larger, thus worse.
- Looking at Downside risk index in of 26 in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (10 ).

'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.'

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 -46.2 days of ProShares Ultra Gold is lower, thus worse.
- Compared with SPY (-33.7 days) in the period of the last 3 years, the maximum reduction from previous high of -46.2 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.'

Using this definition on our asset we see for example:- Looking at the maximum time in days below previous high water mark of 588 days in the last 5 years of ProShares Ultra Gold, we see it is relatively larger, thus worse in comparison to the benchmark SPY (233 days)
- Looking at maximum time in days below previous high water mark in of 588 days in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (233 days).

'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:- Compared with the benchmark SPY (54 days) in the period of the last 5 years, the average time in days below previous high water mark of 202 days of ProShares Ultra Gold is larger, thus worse.
- Compared with SPY (59 days) in the period of the last 3 years, the average time in days below previous high water mark of 246 days is higher, 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 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.