'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 -73.5% in the last 5 years of ProShares UltraShort Consumer Services, we see it is relatively lower, thus worse in comparison to the benchmark SPY (100.7%)
- Compared with SPY (33.2%) in the period of the last 3 years, the total return, or performance of -20.3% is lower, thus worse.

'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.'

Using this definition on our asset we see for example:- Looking at the annual performance (CAGR) of -23.3% in the last 5 years of ProShares UltraShort Consumer Services, we see it is relatively lower, thus worse in comparison to the benchmark SPY (15%)
- Looking at compounded annual growth rate (CAGR) in of -7.3% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (10%).

'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:- Looking at the 30 days standard deviation of 43.6% in the last 5 years of ProShares UltraShort Consumer Services, we see it is relatively greater, thus worse in comparison to the benchmark SPY (20.9%)
- Compared with SPY (17.3%) in the period of the last 3 years, the 30 days standard deviation of 43.5% is greater, thus worse.

'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:- The downside volatility over 5 years of ProShares UltraShort Consumer Services is 29.6%, which is larger, thus worse compared to the benchmark SPY (15%) in the same period.
- Looking at downside risk in of 29.7% in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (12%).

'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 Sharpe Ratio over 5 years of ProShares UltraShort Consumer Services is -0.59, which is lower, thus worse compared to the benchmark SPY (0.6) in the same period.
- Compared with SPY (0.44) in the period of the last 3 years, the ratio of return and volatility (Sharpe) of -0.23 is lower, 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (0.83) in the period of the last 5 years, the excess return divided by the downside deviation of -0.87 of ProShares UltraShort Consumer Services is lower, thus worse.
- Looking at excess return divided by the downside deviation in of -0.33 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.62).

'Ulcer Index is a method for measuring investment risk that addresses the real concerns of investors, unlike the widely used standard deviation of return. UI is a measure of the depth and duration of drawdowns in prices from earlier highs. Using Ulcer Index instead of standard deviation can lead to very different conclusions about investment risk and risk-adjusted return, especially when evaluating strategies that seek to avoid major declines in portfolio value (market timing, dynamic asset allocation, hedge funds, etc.). The Ulcer Index was originally developed in 1987. Since then, it has been widely recognized and adopted by the investment community. According to Nelson Freeburg, editor of Formula Research, Ulcer Index is “perhaps the most fully realized statistical portrait of risk there is.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (9.32 ) in the period of the last 5 years, the Ulcer Index of 66 of ProShares UltraShort Consumer Services is higher, thus worse.
- During the last 3 years, the Ulcer Ratio is 32 , which is larger, thus worse than the value of 10 from the benchmark.

'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.'

Using this definition on our asset we see for example:- The maximum DrawDown over 5 years of ProShares UltraShort Consumer Services is -82.2 days, which is lower, thus worse compared to the benchmark SPY (-33.7 days) in the same period.
- During the last 3 years, the maximum DrawDown is -55.8 days, which is lower, 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 under water of 1047 days in the last 5 years of ProShares UltraShort Consumer Services, we see it is relatively larger, thus worse in comparison to the benchmark SPY (488 days)
- During the last 3 years, the maximum days under water is 482 days, which is smaller, thus better than the value of 488 days from the benchmark.

'The Average 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. 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 (123 days) in the period of the last 5 years, the average days below previous high of 454 days of ProShares UltraShort Consumer Services is greater, thus worse.
- Looking at average time in days below previous high water mark in of 179 days in the period of the last 3 years, we see it is relatively smaller, thus better in comparison to SPY (180 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 UltraShort Consumer Services are hypothetical and do not account for slippage, fees or taxes.