'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.'

Applying this definition to our asset in some examples:- The total return, or performance over 5 years of ProShares UltraShort Yen New is -15.1%, which is lower, thus worse compared to the benchmark SPY (32.9%) in the same period.
- Compared with SPY (11.6%) in the period of the last 3 years, the total return of 3.8% is lower, thus worse.

'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 -3.2% in the last 5 years of ProShares UltraShort Yen New, we see it is relatively lower, thus worse in comparison to the benchmark SPY (5.8%)
- During the last 3 years, the annual return (CAGR) is 1.3%, which is lower, thus worse than the value of 3.7% 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.'

Which means for our asset as example:- The 30 days standard deviation over 5 years of ProShares UltraShort Yen New is 18.2%, which is higher, thus worse compared to the benchmark SPY (18%) in the same period.
- During the last 3 years, the volatility is 15.6%, which is smaller, thus better than the value of 20.3% 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:- Looking at the downside deviation of 13.6% in the last 5 years of ProShares UltraShort Yen New, we see it is relatively higher, thus worse in comparison to the benchmark SPY (13.4%)
- Compared with SPY (15.3%) in the period of the last 3 years, the downside deviation of 11.2% is lower, thus better.

'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 (0.19) in the period of the last 5 years, the risk / return profile (Sharpe) of -0.31 of ProShares UltraShort Yen New is lower, thus worse.
- During the last 3 years, the Sharpe Ratio is -0.08, which is lower, thus worse than the value of 0.06 from the benchmark.

'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 (0.25) in the period of the last 5 years, the ratio of annual return and downside deviation of -0.42 of ProShares UltraShort Yen New is lower, thus worse.
- During the last 3 years, the excess return divided by the downside deviation is -0.11, which is lower, thus worse than the value of 0.08 from the benchmark.

'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.'

Which means for our asset as example:- The Downside risk index over 5 years of ProShares UltraShort Yen New is 23 , which is larger, thus worse compared to the benchmark SPY (5.17 ) in the same period.
- During the last 3 years, the Ulcer Ratio is 5.82 , which is lower, thus better than the value of 5.93 from the benchmark.

'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:- The maximum reduction from previous high over 5 years of ProShares UltraShort Yen New is -39.3 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 drop from peak to valley is -16.9 days, which is greater, thus better than the value of -33.7 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.'

Which means for our asset as example:- Compared with the benchmark SPY (187 days) in the period of the last 5 years, the maximum days below previous high of 1216 days of ProShares UltraShort Yen New is higher, thus worse.
- During the last 3 years, the maximum days under water is 344 days, which is higher, thus worse than the value of 139 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.'

Using this definition on our asset we see for example:- The average time in days below previous high water mark over 5 years of ProShares UltraShort Yen New is 593 days, which is greater, thus worse compared to the benchmark SPY (42 days) in the same period.
- Compared with SPY (36 days) in the period of the last 3 years, the average days under water of 125 days is greater, 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 UltraShort Yen New 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.