'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:- Compared with the benchmark SPY (60.6%) in the period of the last 5 years, the total return, or performance of -69.5% of American Airlines Group is smaller, thus worse.
- During the last 3 years, the total return, or increase in value is 7%, which is lower, thus worse than the value of 38% from the benchmark.

'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:- Looking at the compounded annual growth rate (CAGR) of -21.2% in the last 5 years of American Airlines Group, we see it is relatively lower, thus worse in comparison to the benchmark SPY (10%)
- During the last 3 years, the annual return (CAGR) is 2.3%, which is smaller, thus worse than the value of 11.3% 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:- Compared with the benchmark SPY (21.5%) in the period of the last 5 years, the historical 30 days volatility of 62% of American Airlines Group is higher, thus worse.
- During the last 3 years, the historical 30 days volatility is 49.5%, which is higher, thus worse than the value of 17.9% from the benchmark.

'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (15.5%) in the period of the last 5 years, the downside risk of 40.6% of American Airlines Group is greater, thus worse.
- Looking at downside volatility in of 33.1% in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (12.5%).

'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:- Looking at the ratio of return and volatility (Sharpe) of -0.38 in the last 5 years of American Airlines Group, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (0.35)
- Looking at risk / return profile (Sharpe) in of 0 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.49).

'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:- Looking at the ratio of annual return and downside deviation of -0.58 in the last 5 years of American Airlines Group, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.48)
- Compared with SPY (0.71) in the period of the last 3 years, the excess return divided by the downside deviation of -0.01 is lower, 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (9.55 ) in the period of the last 5 years, the Downside risk index of 55 of American Airlines Group is greater, thus worse.
- During the last 3 years, the Downside risk index is 33 , which is larger, thus worse than the value of 10 from the benchmark.

'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.'

Which means for our asset as example:- Looking at the maximum drop from peak to valley of -78.9 days in the last 5 years of American Airlines Group, we see it is relatively lower, thus worse in comparison to the benchmark SPY (-33.7 days)
- Looking at maximum reduction from previous high in of -54.1 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) in days.'

Using this definition on our asset we see for example:- The maximum days below previous high over 5 years of American Airlines Group is 1257 days, which is greater, thus worse compared to the benchmark SPY (431 days) in the same period.
- Looking at maximum days under water in of 580 days in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (431 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 days under water of 629 days in the last 5 years of American Airlines Group, we see it is relatively higher, thus worse in comparison to the benchmark SPY (105 days)
- Looking at average days below previous high in of 234 days in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (144 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.