'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:- Looking at the total return, or performance of 70.4% in the last 5 years of American Express, we see it is relatively larger, thus better in comparison to the benchmark SPY (60.7%)
- Looking at total return, or performance in of 23.7% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (29.5%).

'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 performance (CAGR) of 11.3% in the last 5 years of American Express, we see it is relatively higher, thus better in comparison to the benchmark SPY (10%)
- Compared with SPY (9%) in the period of the last 3 years, the annual return (CAGR) of 7.3% is smaller, thus worse.

'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.'

Which means for our asset as example:- Looking at the 30 days standard deviation of 36.9% in the last 5 years of American Express, we see it is relatively greater, thus worse in comparison to the benchmark SPY (20.8%)
- Compared with SPY (24%) in the period of the last 3 years, the historical 30 days volatility of 44.5% 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.'

Applying this definition to our asset in some examples:- The downside risk over 5 years of American Express is 24.4%, which is larger, thus worse compared to the benchmark SPY (15.3%) in the same period.
- Compared with SPY (17.6%) in the period of the last 3 years, the downside volatility of 29.1% is greater, 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.'

Using this definition on our asset we see for example:- The ratio of return and volatility (Sharpe) over 5 years of American Express is 0.24, which is lower, thus worse compared to the benchmark SPY (0.36) in the same period.
- Looking at Sharpe Ratio in of 0.11 in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (0.27).

'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.'

Applying this definition to our asset in some examples:- The downside risk / excess return profile over 5 years of American Express is 0.36, which is lower, thus worse compared to the benchmark SPY (0.49) in the same period.
- Looking at ratio of annual return and downside deviation in of 0.17 in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (0.37).

'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:- Compared with the benchmark SPY (7.52 ) in the period of the last 5 years, the Downside risk index of 14 of American Express is greater, thus worse.
- During the last 3 years, the Ulcer Index is 18 , which is larger, thus worse than the value of 8.81 from the benchmark.

'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.'

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 -49.6 days of American Express is smaller, thus worse.
- Compared with SPY (-33.7 days) in the period of the last 3 years, the maximum drop from peak to valley of -49.6 days is lower, 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 days under water of 253 days in the last 5 years of American Express, we see it is relatively greater, thus worse in comparison to the benchmark SPY (182 days)
- During the last 3 years, the maximum days below previous high is 253 days, which is larger, thus worse than the value of 182 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 Express is 55 days, which is higher, thus worse compared to the benchmark SPY (45 days) in the same period.
- Compared with SPY (43 days) in the period of the last 3 years, the average time in days below previous high water mark of 70 days is larger, 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 American Express 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.