'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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (61.9%) in the period of the last 5 years, the total return of 51.7% of ProShares Ultra Gold is smaller, thus worse.
- During the last 3 years, the total return is 36.8%, which is smaller, thus worse than the value of 79.4% 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:- The annual performance (CAGR) over 5 years of ProShares Ultra Gold is 8.7%, which is lower, thus worse compared to the benchmark SPY (10.1%) in the same period.
- During the last 3 years, the annual performance (CAGR) is 11%, which is smaller, thus worse than the value of 21.5% 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 historical 30 days volatility of 30.1% in the last 5 years of ProShares Ultra Gold, we see it is relatively higher, thus worse in comparison to the benchmark SPY (21.5%)
- During the last 3 years, the volatility is 33.3%, which is greater, thus worse than the value of 21.2% 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.'

Which means for our asset as example:- Compared with the benchmark SPY (15.5%) in the period of the last 5 years, the downside risk of 21.2% of ProShares Ultra Gold is higher, thus worse.
- Compared with SPY (14.1%) in the period of the last 3 years, the downside deviation of 23.2% is higher, 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:- Looking at the risk / return profile (Sharpe) of 0.21 in the last 5 years of ProShares Ultra Gold, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (0.36)
- Compared with SPY (0.9) in the period of the last 3 years, the ratio of return and volatility (Sharpe) of 0.26 is lower, 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:- Compared with the benchmark SPY (0.49) in the period of the last 5 years, the ratio of annual return and downside deviation of 0.29 of ProShares Ultra Gold is smaller, thus worse.
- Compared with SPY (1.35) in the period of the last 3 years, the downside risk / excess return profile of 0.37 is smaller, 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.'

Which means for our asset as example:- Looking at the Ulcer Index of 23 in the last 5 years of ProShares Ultra Gold, we see it is relatively higher, thus worse in comparison to the benchmark SPY (9.15 )
- Compared with SPY (9.78 ) in the period of the last 3 years, the Ulcer Index of 28 is greater, 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.'

Applying this definition to our asset in some examples:- Looking at the maximum reduction from previous high of -46.2 days in the last 5 years of ProShares Ultra Gold, we see it is relatively lower, thus worse in comparison to the benchmark SPY (-33.7 days)
- During the last 3 years, the maximum drop from peak to valley is -46.2 days, which is smaller, thus worse than the value of -24.5 days from the benchmark.

'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:- Looking at the maximum days below previous high of 660 days in the last 5 years of ProShares Ultra Gold, we see it is relatively greater, thus worse in comparison to the benchmark SPY (305 days)
- During the last 3 years, the maximum days below previous high is 660 days, which is higher, thus worse than the value of 305 days from the benchmark.

'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:- Looking at the average days under water of 226 days in the last 5 years of ProShares Ultra Gold, we see it is relatively higher, thus worse in comparison to the benchmark SPY (65 days)
- Compared with SPY (80 days) in the period of the last 3 years, the average time in days below previous high water mark of 299 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.