'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:- Compared with the benchmark SPY (62.6%) in the period of the last 5 years, the total return of -72.7% of American Airlines Group is lower, thus worse.
- Looking at total return, or performance in of -50.8% in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (32.1%).

'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.'

Using this definition on our asset we see for example:- Looking at the annual return (CAGR) of -22.9% in the last 5 years of American Airlines Group, we see it is relatively lower, thus worse in comparison to the benchmark SPY (10.2%)
- During the last 3 years, the compounded annual growth rate (CAGR) is -21%, which is lower, thus worse than the value of 9.7% from the benchmark.

'Volatility is a statistical measure of the dispersion of returns for a given security or market index. Volatility can either be measured by using the standard deviation or variance between returns from that same security or market index. Commonly, the higher the volatility, the riskier the security. In the securities markets, volatility is often associated with big swings in either direction. For example, when the stock market rises and falls more than one percent over a sustained period of time, it is called a 'volatile' market.'

Using this definition on our asset we see for example:- The volatility over 5 years of American Airlines Group is 61.6%, which is larger, thus worse compared to the benchmark SPY (21.5%) in the same period.
- Compared with SPY (24.8%) in the period of the last 3 years, the volatility of 73.3% is larger, thus worse.

'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 deviation over 5 years of American Airlines Group is 40.5%, which is larger, thus worse compared to the benchmark SPY (15.6%) in the same period.
- Looking at downside deviation in of 47% in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (17.9%).

'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.'

Applying this definition to our asset in some examples:- Looking at the ratio of return and volatility (Sharpe) of -0.41 in the last 5 years of American Airlines Group, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.36)
- Looking at ratio of return and volatility (Sharpe) in of -0.32 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.29).

'The Sortino ratio measures the risk-adjusted return of an investment asset, portfolio, or strategy. It is a modification of the Sharpe ratio but penalizes only those returns falling below a user-specified target or required rate of return, while the Sharpe ratio penalizes both upside and downside volatility equally. Though both ratios measure an investment's risk-adjusted return, they do so in significantly different ways that will frequently lead to differing conclusions as to the true nature of the investment's return-generating efficiency. The Sortino ratio is used as a way to compare the risk-adjusted performance of programs with differing risk and return profiles. In general, risk-adjusted returns seek to normalize the risk across programs and then see which has the higher return unit per risk.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (0.5) in the period of the last 5 years, the ratio of annual return and downside deviation of -0.63 of American Airlines Group is lower, thus worse.
- Looking at excess return divided by the downside deviation in of -0.5 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.4).

'The ulcer index is a stock market risk measure or technical analysis indicator devised by Peter Martin in 1987, and published by him and Byron McCann in their 1989 book The Investors Guide to Fidelity Funds. It's designed as a measure of volatility, but only volatility in the downward direction, i.e. the amount of drawdown or retracement occurring over a period. Other volatility measures like standard deviation treat up and down movement equally, but a trader doesn't mind upward movement, it's the downside that causes stress and stomach ulcers that the index's name suggests.'

Using this definition on our asset we see for example:- The Ulcer Index over 5 years of American Airlines Group is 59 , which is higher, thus worse compared to the benchmark SPY (8.52 ) in the same period.
- Compared with SPY (10 ) in the period of the last 3 years, the Ulcer Index of 46 is larger, thus worse.

'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:- Compared with the benchmark SPY (-33.7 days) in the period of the last 5 years, the maximum DrawDown of -84.1 days of American Airlines Group is smaller, thus worse.
- During the last 3 years, the maximum reduction from previous high is -70.3 days, which is smaller, thus worse 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (235 days) in the period of the last 5 years, the maximum days below previous high of 1235 days of American Airlines Group is greater, thus worse.
- During the last 3 years, the maximum days under water is 712 days, which is greater, thus worse than the value of 235 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.'

Applying this definition to our asset in some examples:- The average days below previous high over 5 years of American Airlines Group is 611 days, which is larger, thus worse compared to the benchmark SPY (55 days) in the same period.
- Looking at average days under water in of 340 days in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (59 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 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.