'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:- Looking at the total return, or performance of 109.7% in the last 5 years of ProShares UltraShort Yen New, we see it is relatively larger, thus better in comparison to the benchmark SPY (97%)
- Compared with SPY (39.3%) in the period of the last 3 years, the total return, or increase in value of 122.1% is higher, thus better.

'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:- The compounded annual growth rate (CAGR) over 5 years of ProShares UltraShort Yen New is 16%, which is larger, thus better compared to the benchmark SPY (14.6%) in the same period.
- Looking at compounded annual growth rate (CAGR) in of 30.6% in the period of the last 3 years, we see it is relatively greater, thus better in comparison to SPY (11.7%).

'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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (20.9%) in the period of the last 5 years, the volatility of 18.3% of ProShares UltraShort Yen New is smaller, thus better.
- Compared with SPY (17.5%) in the period of the last 3 years, the historical 30 days volatility of 19.7% is greater, thus worse.

'The downside volatility is similar to the volatility, or standard deviation, but only takes losing/negative periods into account.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (15%) in the period of the last 5 years, the downside volatility of 12.9% of ProShares UltraShort Yen New is lower, thus better.
- During the last 3 years, the downside deviation is 14%, which is higher, thus worse than the value of 12.1% from the benchmark.

'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (0.58) in the period of the last 5 years, the risk / return profile (Sharpe) of 0.74 of ProShares UltraShort Yen New is greater, thus better.
- Looking at ratio of return and volatility (Sharpe) in of 1.42 in the period of the last 3 years, we see it is relatively larger, thus better in comparison to SPY (0.53).

'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:- The ratio of annual return and downside deviation over 5 years of ProShares UltraShort Yen New is 1.05, which is greater, thus better compared to the benchmark SPY (0.8) in the same period.
- Compared with SPY (0.76) in the period of the last 3 years, the downside risk / excess return profile of 2.01 is greater, thus better.

'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:- Looking at the Ulcer Ratio of 9.34 in the last 5 years of ProShares UltraShort Yen New, we see it is relatively greater, thus worse in comparison to the benchmark SPY (9.33 )
- During the last 3 years, the Downside risk index is 8.85 , which is lower, thus better than the value of 10 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.'

Which means for our asset as example:- The maximum DrawDown 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.
- Compared with SPY (-24.5 days) in the period of the last 3 years, the maximum reduction from previous high of -27.3 days is smaller, 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). 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:- Looking at the maximum time in days below previous high water mark of 417 days in the last 5 years of ProShares UltraShort Yen New, we see it is relatively lower, thus better in comparison to the benchmark SPY (488 days)
- Looking at maximum days under water in of 204 days in the period of the last 3 years, we see it is relatively lower, thus better in comparison to SPY (488 days).

'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:- Looking at the average time in days below previous high water mark of 115 days in the last 5 years of ProShares UltraShort Yen New, we see it is relatively smaller, thus better in comparison to the benchmark SPY (123 days)
- Looking at average days below previous high in of 44 days in the period of the last 3 years, we see it is relatively smaller, thus better in comparison to SPY (181 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, 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.