'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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (67.3%) in the period of the last 5 years, the total return of -12.6% of American Airlines Group is lower, thus worse.
- During the last 3 years, the total return, or increase in value is -26.6%, which is lower, thus worse than the value of 46.1% from the benchmark.

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (10.9%) in the period of the last 5 years, the annual return (CAGR) of -2.7% of American Airlines Group is smaller, thus worse.
- During the last 3 years, the annual return (CAGR) is -9.8%, which is smaller, thus worse than the value of 13.5% 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.'

Applying this definition to our asset in some examples:- The volatility over 5 years of American Airlines Group is 36.7%, which is higher, thus worse compared to the benchmark SPY (13.2%) in the same period.
- During the last 3 years, the historical 30 days volatility is 35.8%, which is greater, thus worse than the value of 12.4% from the benchmark.

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

Applying this definition to our asset in some examples:- The downside deviation over 5 years of American Airlines Group is 37.7%, which is larger, thus worse compared to the benchmark SPY (14.6%) in the same period.
- Compared with SPY (14%) in the period of the last 3 years, the downside deviation of 36.3% is larger, thus worse.

'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.'

Which means for our asset as example:- Looking at the Sharpe Ratio of -0.14 in the last 5 years of American Airlines Group, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.63)
- Compared with SPY (0.88) in the period of the last 3 years, the Sharpe Ratio of -0.34 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 (0.57) in the period of the last 5 years, the downside risk / excess return profile of -0.14 of American Airlines Group is lower, thus worse.
- Compared with SPY (0.79) in the period of the last 3 years, the ratio of annual return and downside deviation of -0.34 is smaller, thus worse.

'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.'

Applying this definition to our asset in some examples:- Looking at the Ulcer Ratio of 24 in the last 5 years of American Airlines Group, we see it is relatively larger, thus better in comparison to the benchmark SPY (3.95 )
- Looking at Ulcer Index in of 23 in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (4 ).

'A maximum drawdown is the maximum loss from a peak to a trough of a portfolio, before a new peak is attained. Maximum Drawdown is an indicator of downside risk over a specified time period. It can be used both as a stand-alone measure or as an input into other metrics such as 'Return over Maximum Drawdown' and the Calmar Ratio. Maximum Drawdown is expressed in percentage terms.'

Applying this definition to our asset in some examples:- The maximum DrawDown over 5 years of American Airlines Group is -54.1 days, which is smaller, thus worse compared to the benchmark SPY (-19.3 days) in the same period.
- Compared with SPY (-19.3 days) in the period of the last 3 years, the maximum DrawDown of -48.7 days is lower, thus worse.

'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:- The maximum time in days below previous high water mark over 5 years of American Airlines Group is 708 days, which is higher, thus worse compared to the benchmark SPY (187 days) in the same period.
- Looking at maximum days under water in of 296 days in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (131 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.'

Which means for our asset as example:- The average time in days below previous high water mark over 5 years of American Airlines Group is 245 days, which is higher, thus worse compared to the benchmark SPY (39 days) in the same period.
- Looking at average days under water in of 99 days in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (33 days).

Historical returns have been extended using synthetic data.
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- "Year" returns in the table above are not equal to the sum of monthly returns due to compounding.
- Performance results of American Airlines Group 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.