'Total return, when measuring performance, is the actual rate of return of an investment or a pool of investments over a given evaluation period. Total return includes interest, capital gains, dividends and distributions realized over a given period of time. Total return accounts for two categories of return: income including interest paid by fixed-income investments, distributions or dividends and capital appreciation, representing the change in the market price of an asset.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (111.3%) in the period of the last 5 years, the total return of -95.3% of Direxion Daily Energy Bear 3X Shares is lower, thus worse.
- Looking at total return, or increase in value in of -79.5% in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (39.3%).

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (16.2%) in the period of the last 5 years, the annual performance (CAGR) of -45.9% of Direxion Daily Energy Bear 3X Shares is lower, thus worse.
- During the last 3 years, the annual return (CAGR) is -41%, which is smaller, thus worse than the value of 11.7% 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.'

Using this definition on our asset we see for example:- Looking at the 30 days standard deviation of 83.9% in the last 5 years of Direxion Daily Energy Bear 3X Shares, we see it is relatively greater, thus worse in comparison to the benchmark SPY (20.9%)
- Looking at historical 30 days volatility in of 53.4% in the period of the last 3 years, we see it is relatively higher, 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.'

Which means for our asset as example:- The downside risk over 5 years of Direxion Daily Energy Bear 3X Shares is 56.6%, which is larger, thus worse compared to the benchmark SPY (14.9%) in the same period.
- Compared with SPY (12.2%) in the period of the last 3 years, the downside deviation of 37.9% is greater, thus worse.

'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:- Looking at the ratio of return and volatility (Sharpe) of -0.58 in the last 5 years of Direxion Daily Energy Bear 3X Shares, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (0.66)
- Looking at ratio of return and volatility (Sharpe) in of -0.82 in the period of the last 3 years, we see it is relatively lower, thus worse 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.'

Which means for our asset as example:- The excess return divided by the downside deviation over 5 years of Direxion Daily Energy Bear 3X Shares is -0.85, which is smaller, thus worse compared to the benchmark SPY (0.92) in the same period.
- Looking at excess return divided by the downside deviation in of -1.15 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.75).

'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 Index of 91 in the last 5 years of Direxion Daily Energy Bear 3X Shares, we see it is relatively greater, thus worse in comparison to the benchmark SPY (9.32 )
- Looking at Ulcer Ratio in of 69 in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (10 ).

'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.'

Using this definition on our asset we see for example:- The maximum DrawDown over 5 years of Direxion Daily Energy Bear 3X Shares is -99.3 days, which is lower, thus worse compared to the benchmark SPY (-33.7 days) in the same period.
- Looking at maximum DrawDown in of -82.6 days in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (-24.5 days).

'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:- The maximum days under water over 5 years of Direxion Daily Energy Bear 3X Shares is 1150 days, which is higher, thus worse compared to the benchmark SPY (488 days) in the same period.
- During the last 3 years, the maximum days under water is 706 days, which is greater, thus worse 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.'

Using this definition on our asset we see for example:- Looking at the average days under water of 535 days in the last 5 years of Direxion Daily Energy Bear 3X Shares, we see it is relatively larger, thus worse in comparison to the benchmark SPY (124 days)
- Compared with SPY (179 days) in the period of the last 3 years, the average days below previous high of 333 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 Direxion Daily Energy Bear 3X Shares are hypothetical and do not account for slippage, fees or taxes.