'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:- Looking at the total return of 259.4% in the last 5 years of ProShares Ultra S&P500, we see it is relatively greater, thus better in comparison to the benchmark SPY (121.6%)
- Looking at total return, or increase in value in of 112.6% in the period of the last 3 years, we see it is relatively greater, thus better in comparison to SPY (64.5%).

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (17.3%) in the period of the last 5 years, the compounded annual growth rate (CAGR) of 29.2% of ProShares Ultra S&P500 is greater, thus better.
- Looking at annual return (CAGR) in of 28.6% in the period of the last 3 years, we see it is relatively greater, thus better in comparison to SPY (18.1%).

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (18.7%) in the period of the last 5 years, the volatility of 37.8% of ProShares Ultra S&P500 is higher, thus worse.
- During the last 3 years, the historical 30 days volatility is 45.8%, which is higher, thus worse than the value of 22.5% 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.'

Which means for our asset as example:- Looking at the downside deviation of 27.4% in the last 5 years of ProShares Ultra S&P500, we see it is relatively greater, thus worse in comparison to the benchmark SPY (13.5%)
- Compared with SPY (16.4%) in the period of the last 3 years, the downside risk of 33.2% is greater, thus worse.

'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.'

Applying this definition to our asset in some examples:- Looking at the Sharpe Ratio of 0.71 in the last 5 years of ProShares Ultra S&P500, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (0.79)
- Looking at risk / return profile (Sharpe) in of 0.57 in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (0.69).

'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.'

Using this definition on our asset we see for example:- Looking at the ratio of annual return and downside deviation of 0.97 in the last 5 years of ProShares Ultra S&P500, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (1.09)
- Compared with SPY (0.95) in the period of the last 3 years, the downside risk / excess return profile of 0.79 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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (5.58 ) in the period of the last 5 years, the Ulcer Ratio of 12 of ProShares Ultra S&P500 is greater, thus worse.
- Compared with SPY (6.83 ) in the period of the last 3 years, the Downside risk index of 15 is greater, thus worse.

'Maximum drawdown is defined as the peak-to-trough decline of an investment during a specific period. It is usually quoted as a percentage of the peak value. The maximum drawdown can be calculated based on absolute returns, in order to identify strategies that suffer less during market downturns, such as low-volatility strategies. However, the maximum drawdown can also be calculated based on returns relative to a benchmark index, for identifying strategies that show steady outperformance over time.'

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 -59.3 days of ProShares Ultra S&P500 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 -59.3 days is lower, thus worse.

'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) in days.'

Which means for our asset as example:- Compared with the benchmark SPY (139 days) in the period of the last 5 years, the maximum days under water of 193 days of ProShares Ultra S&P500 is higher, thus worse.
- Compared with SPY (139 days) in the period of the last 3 years, the maximum days under water of 193 days is higher, 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:- Compared with the benchmark SPY (33 days) in the period of the last 5 years, the average days under water of 44 days of ProShares Ultra S&P500 is higher, thus worse.
- Looking at average days below previous high in of 50 days in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (35 days).

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 S&P500 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.