'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 of 116.9% in the last 5 years of ProShares Ultra Gold, we see it is relatively larger, thus better in comparison to the benchmark SPY (109.2%)
- During the last 3 years, the total return, or performance is 65.2%, which is larger, thus better than the value of 33.3% from the benchmark.

'The compound annual growth rate (CAGR) is a useful measure of growth over multiple time periods. It can be thought of as the growth rate that gets you from the initial investment value to the ending investment value if you assume that the investment has been compounding over the time period.'

Using this definition on our asset we see for example:- Looking at the compounded annual growth rate (CAGR) of 16.8% in the last 5 years of ProShares Ultra Gold, we see it is relatively greater, thus better in comparison to the benchmark SPY (15.9%)
- During the last 3 years, the compounded annual growth rate (CAGR) is 18.3%, which is greater, thus better than the value of 10.1% from the benchmark.

'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.'

Applying this definition to our asset in some examples:- Looking at the volatility of 31.3% in the last 5 years of ProShares Ultra Gold, we see it is relatively higher, thus worse in comparison to the benchmark SPY (20.9%)
- Looking at historical 30 days volatility in of 28.8% in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (17.6%).

'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.'

Applying this definition to our asset in some examples:- Looking at the downside risk of 21.9% in the last 5 years of ProShares Ultra Gold, we see it is relatively greater, thus worse in comparison to the benchmark SPY (14.9%)
- Compared with SPY (12.3%) in the period of the last 3 years, the downside volatility of 19.6% is greater, thus worse.

'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (0.64) in the period of the last 5 years, the Sharpe Ratio of 0.46 of ProShares Ultra Gold is smaller, thus worse.
- During the last 3 years, the Sharpe Ratio is 0.55, which is greater, thus better than the value of 0.43 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.'

Which means for our asset as example:- Looking at the excess return divided by the downside deviation of 0.65 in the last 5 years of ProShares Ultra Gold, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (0.9)
- Looking at excess return divided by the downside deviation in of 0.8 in the period of the last 3 years, we see it is relatively larger, thus better in comparison to SPY (0.62).

'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:- Looking at the Ulcer Ratio of 25 in the last 5 years of ProShares Ultra Gold, we see it is relatively larger, thus worse in comparison to the benchmark SPY (9.32 )
- Compared with SPY (10 ) in the period of the last 3 years, the Ulcer Index of 20 is higher, 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 -46.2 days of ProShares Ultra Gold is smaller, thus worse.
- Looking at maximum DrawDown in of -40.2 days in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (-24.5 days).

'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'

Which means for our asset as example:- Looking at the maximum time in days below previous high water mark of 950 days in the last 5 years of ProShares Ultra Gold, we see it is relatively higher, thus worse in comparison to the benchmark SPY (488 days)
- Looking at maximum time in days below previous high water mark in of 518 days in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (488 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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (123 days) in the period of the last 5 years, the average days under water of 381 days of ProShares Ultra Gold is greater, thus worse.
- Compared with SPY (176 days) in the period of the last 3 years, the average days under water of 193 days is larger, 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 and do not account for slippage, fees or taxes.