'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:- Compared with the benchmark SPY (95.5%) in the period of the last 5 years, the total return, or performance of 99.9% of American Express is greater, thus better.
- Compared with SPY (25.3%) in the period of the last 3 years, the total return of 41.8% is greater, thus better.

'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 (14.4%) in the period of the last 5 years, the compounded annual growth rate (CAGR) of 14.9% of American Express is greater, thus better.
- Compared with SPY (7.8%) in the period of the last 3 years, the compounded annual growth rate (CAGR) of 12.4% is larger, thus better.

'Volatility is a rate at which the price of a security increases or decreases for a given set of returns. Volatility is measured by calculating the standard deviation of the annualized returns over a given period of time. It shows the range to which the price of a security may increase or decrease. Volatility measures the risk of a security. It is used in option pricing formula to gauge the fluctuations in the returns of the underlying assets. Volatility indicates the pricing behavior of the security and helps estimate the fluctuations that may happen in a short period of time.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (20.9%) in the period of the last 5 years, the historical 30 days volatility of 38.2% of American Express is greater, thus worse.
- Looking at 30 days standard deviation in of 29.6% in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (17.5%).

'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:- Compared with the benchmark SPY (15%) in the period of the last 5 years, the downside deviation of 24.9% of American Express is greater, thus worse.
- Compared with SPY (12.3%) in the period of the last 3 years, the downside volatility of 20.2% is greater, thus worse.

'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.'

Applying this definition to our asset in some examples:- Looking at the ratio of return and volatility (Sharpe) of 0.32 in the last 5 years of American Express, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.57)
- Compared with SPY (0.3) in the period of the last 3 years, the risk / return profile (Sharpe) of 0.33 is greater, thus better.

'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:- The downside risk / excess return profile over 5 years of American Express is 0.5, which is lower, thus worse compared to the benchmark SPY (0.79) in the same period.
- Compared with SPY (0.43) in the period of the last 3 years, the downside risk / excess return profile of 0.49 is higher, thus better.

'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:- The Ulcer Index over 5 years of American Express is 17 , which is larger, thus worse compared to the benchmark SPY (9.32 ) in the same period.
- Looking at Ulcer Index in of 15 in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (10 ).

'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.'

Which means for our asset as example:- Looking at the maximum reduction from previous high of -49.6 days in the last 5 years of American Express, we see it is relatively lower, thus worse in comparison to the benchmark SPY (-33.7 days)
- During the last 3 years, the maximum reduction from previous high is -31.5 days, which is smaller, thus worse than the value of -24.5 days from the benchmark.

'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 Express is 486 days, which is lower, thus better compared to the benchmark SPY (488 days) in the same period.
- Looking at maximum days under water in of 486 days in the period of the last 3 years, we see it is relatively smaller, thus better in comparison to SPY (488 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:- Compared with the benchmark SPY (123 days) in the period of the last 5 years, the average time in days below previous high water mark of 137 days of American Express is higher, thus worse.
- Compared with SPY (179 days) in the period of the last 3 years, the average days under water of 172 days is smaller, thus better.

Historical returns have been extended using synthetic data.
[Show Details]

- Note that yearly returns do not equal the sum of monthly returns due to compounding.
- Performance results of American Express are hypothetical and do not account for slippage, fees or taxes.