'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.'

Which means for our asset as example:- Looking at the total return, or performance of 45.3% in the last 5 years of American Express Company, we see it is relatively lower, thus worse in comparison to the benchmark SPY (66.1%)
- Looking at total return in of 108.6% in the period of the last 3 years, we see it is relatively greater, thus better in comparison to SPY (46.2%).

'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 (10.7%) in the period of the last 5 years, the compounded annual growth rate (CAGR) of 7.8% of American Express Company is lower, thus worse.
- During the last 3 years, the annual performance (CAGR) is 27.8%, which is higher, thus better 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.'

Which means for our asset as example:- The volatility over 5 years of American Express Company is 20.5%, which is larger, thus worse compared to the benchmark SPY (13.4%) in the same period.
- Compared with SPY (12.3%) in the period of the last 3 years, the historical 30 days volatility of 18.9% is greater, 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 volatility over 5 years of American Express Company is 21.9%, which is greater, thus worse compared to the benchmark SPY (14.6%) in the same period.
- Looking at downside volatility in of 19.3% in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (13.9%).

'The Sharpe ratio is the measure of risk-adjusted return of a financial portfolio. Sharpe ratio is a measure of excess portfolio return over the risk-free rate relative to its standard deviation. Normally, the 90-day Treasury bill rate is taken as the proxy for risk-free rate. A portfolio with a higher Sharpe ratio is considered superior relative to its peers. The measure was named after William F Sharpe, a Nobel laureate and professor of finance, emeritus at Stanford University.'

Which means for our asset as example:- Compared with the benchmark SPY (0.61) in the period of the last 5 years, the Sharpe Ratio of 0.26 of American Express Company is smaller, thus worse.
- Looking at ratio of return and volatility (Sharpe) in of 1.34 in the period of the last 3 years, we see it is relatively larger, thus better in comparison to SPY (0.9).

'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 (0.56) in the period of the last 5 years, the excess return divided by the downside deviation of 0.24 of American Express Company is lower, thus worse.
- During the last 3 years, the excess return divided by the downside deviation is 1.31, which is higher, thus better than the value of 0.8 from the benchmark.

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (3.99 ) in the period of the last 5 years, the Ulcer Index of 17 of American Express Company is higher, thus worse.
- Looking at Ulcer Index in of 4.27 in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (4.04 ).

'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:- Looking at the maximum DrawDown of -44.8 days in the last 5 years of American Express Company, we see it is relatively lower, thus worse in comparison to the benchmark SPY (-19.3 days)
- Compared with SPY (-19.3 days) in the period of the last 3 years, the maximum drop from peak to valley of -20.7 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (187 days) in the period of the last 5 years, the maximum time in days below previous high water mark of 694 days of American Express Company is larger, thus worse.
- Compared with SPY (139 days) in the period of the last 3 years, the maximum days under water of 75 days is lower, thus better.

'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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (41 days) in the period of the last 5 years, the average days under water of 213 days of American Express Company is greater, thus worse.
- Compared with SPY (36 days) in the period of the last 3 years, the average days below previous high of 17 days is smaller, thus better.

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 Express Company 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.