'Total return is the amount of value an investor earns from a security over a specific period, typically one year, when all distributions are reinvested. Total return is expressed as a percentage of the amount invested. For example, a total return of 20% means the security increased by 20% of its original value due to a price increase, distribution of dividends (if a stock), coupons (if a bond) or capital gains (if a fund). Total return is a strong measure of an investment’s overall performance.'

Using this definition on our asset we see for example:- Looking at the total return, or increase in value of 123.2% in the last 5 years of ProShares UltraShort Yen New, we see it is relatively higher, thus better in comparison to the benchmark SPY (94.9%)
- Looking at total return in of 108.9% in the period of the last 3 years, we see it is relatively larger, thus better in comparison to SPY (22.5%).

'Compound annual growth rate (CAGR) is a business and investing specific term for the geometric progression ratio that provides a constant rate of return over the time period. CAGR is not an accounting term, but it is often used to describe some element of the business, for example revenue, units delivered, registered users, etc. CAGR dampens the effect of volatility of periodic returns that can render arithmetic means irrelevant. It is particularly useful to compare growth rates from various data sets of common domain such as revenue growth of companies in the same industry.'

Applying this definition to our asset in some examples:- Looking at the annual return (CAGR) of 17.4% in the last 5 years of ProShares UltraShort Yen New, we see it is relatively higher, thus better in comparison to the benchmark SPY (14.3%)
- During the last 3 years, the annual performance (CAGR) is 27.9%, which is higher, thus better than the value of 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 volatility over 5 years of ProShares UltraShort Yen New is 19.1%, which is smaller, thus better compared to the benchmark SPY (20.9%) in the same period.
- Looking at 30 days standard deviation in of 21.1% in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (17.5%).

'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:- Looking at the downside volatility of 13.7% in the last 5 years of ProShares UltraShort Yen New, we see it is relatively smaller, thus better in comparison to the benchmark SPY (15%)
- Looking at downside deviation in of 15.5% in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (12.3%).

'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:- Compared with the benchmark SPY (0.56) in the period of the last 5 years, the Sharpe Ratio of 0.78 of ProShares UltraShort Yen New is higher, thus better.
- During the last 3 years, the ratio of return and volatility (Sharpe) is 1.2, which is higher, thus better than the value of 0.26 from the benchmark.

'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.'

Which means for our asset as example:- Looking at the downside risk / excess return profile of 1.09 in the last 5 years of ProShares UltraShort Yen New, we see it is relatively larger, thus better in comparison to the benchmark SPY (0.79)
- During the last 3 years, the excess return divided by the downside deviation is 1.64, which is higher, thus better than the value of 0.37 from the benchmark.

'The Ulcer Index is a technical indicator that measures downside risk, in terms of both the depth and duration of price declines. The index increases in value as the price moves farther away from a recent high and falls as the price rises to new highs. The indicator is usually calculated over a 14-day period, with the Ulcer Index showing the percentage drawdown a trader can expect from the high over that period. The greater the value of the Ulcer Index, the longer it takes for a stock to get back to the former high.'

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 9.23 of ProShares UltraShort Yen New is smaller, thus better.
- Looking at Ulcer Ratio in of 8.98 in the period of the last 3 years, we see it is relatively lower, thus better in comparison to SPY (10 ).

'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:- The maximum drop from peak to valley over 5 years of ProShares UltraShort Yen New is -27.3 days, which is greater, thus better compared to the benchmark SPY (-33.7 days) in the same period.
- During the last 3 years, the maximum DrawDown is -27.3 days, which is lower, thus worse than the value of -24.5 days from the benchmark.

'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'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (488 days) in the period of the last 5 years, the maximum time in days below previous high water mark of 417 days of ProShares UltraShort Yen New is lower, thus better.
- Compared with SPY (488 days) in the period of the last 3 years, the maximum days under water of 204 days is lower, thus better.

'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (123 days) in the period of the last 5 years, the average time in days below previous high water mark of 102 days of ProShares UltraShort Yen New is lower, thus better.
- Looking at average days below previous high in of 42 days in the period of the last 3 years, we see it is relatively smaller, thus better in comparison to SPY (179 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 Yen New are hypothetical and do not account for slippage, fees or taxes.