'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.'

Which means for our asset as example:- Compared with the benchmark SPY (125.9%) in the period of the last 5 years, the total return, or performance of 101% of ProShares Ultra Gold is lower, thus worse.
- During the last 3 years, the total return, or increase in value is 52%, which is higher, thus better than the value of 44.4% 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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (17.7%) in the period of the last 5 years, the compounded annual growth rate (CAGR) of 15% of ProShares Ultra Gold is lower, thus worse.
- Compared with SPY (13%) in the period of the last 3 years, the compounded annual growth rate (CAGR) of 15% is greater, thus better.

'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 28.7% in the last 5 years of ProShares Ultra Gold, we see it is relatively greater, thus worse in comparison to the benchmark SPY (18.7%)
- During the last 3 years, the volatility is 30.1%, which is higher, thus worse than the value of 22.8% from the benchmark.

'Downside risk is the financial risk associated with losses. That is, it is the risk of the actual return being below the expected return, or the uncertainty about the magnitude of that difference. 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 (13.6%) in the period of the last 5 years, the downside risk of 19.8% of ProShares Ultra Gold is larger, thus worse.
- Compared with SPY (16.7%) in the period of the last 3 years, the downside risk of 21.1% is higher, 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:- The ratio of return and volatility (Sharpe) over 5 years of ProShares Ultra Gold is 0.43, which is lower, thus worse compared to the benchmark SPY (0.81) in the same period.
- Looking at ratio of return and volatility (Sharpe) in of 0.41 in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (0.46).

'The Sortino ratio, a variation of the Sharpe ratio only factors in the downside, or negative volatility, rather than the total volatility used in calculating the Sharpe ratio. The theory behind the Sortino variation is that upside volatility is a plus for the investment, and it, therefore, should not be included in the risk calculation. Therefore, the Sortino ratio takes upside volatility out of the equation and uses only the downside standard deviation in its calculation instead of the total standard deviation that is used in calculating the Sharpe ratio.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (1.12) in the period of the last 5 years, the downside risk / excess return profile of 0.63 of ProShares Ultra Gold is lower, thus worse.
- Compared with SPY (0.63) in the period of the last 3 years, the downside risk / excess return profile of 0.59 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.'

Which means for our asset as example:- The Ulcer Index over 5 years of ProShares Ultra Gold is 17 , which is higher, thus worse compared to the benchmark SPY (5.59 ) in the same period.
- Looking at Ulcer Ratio in of 14 in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (7.14 ).

'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:- Looking at the maximum drop from peak to valley of -33.3 days in the last 5 years of ProShares Ultra Gold, we see it is relatively larger, thus better in comparison to the benchmark SPY (-33.7 days)
- Compared with SPY (-33.7 days) in the period of the last 3 years, the maximum drop from peak to valley of -28.2 days is greater, thus better.

'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'

Applying this definition to our asset in some examples:- Looking at the maximum days under water of 774 days in the last 5 years of ProShares Ultra Gold, we see it is relatively greater, thus worse in comparison to the benchmark SPY (139 days)
- Compared with SPY (139 days) in the period of the last 3 years, the maximum days under water of 354 days is larger, thus worse.

'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:- The average days below previous high over 5 years of ProShares Ultra Gold is 262 days, which is higher, thus worse compared to the benchmark SPY (33 days) in the same period.
- Compared with SPY (45 days) in the period of the last 3 years, the average days below previous high of 108 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, 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.