'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.'

Which means for our asset as example:- Compared with the benchmark SPY (78.4%) in the period of the last 5 years, the total return, or performance of 114.3% of American Express is higher, thus better.
- Compared with SPY (44.1%) in the period of the last 3 years, the total return, or performance of 33.3% is smaller, thus worse.

'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (12.3%) in the period of the last 5 years, the annual return (CAGR) of 16.5% of American Express is higher, thus better.
- Looking at compounded annual growth rate (CAGR) in of 10% in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (12.9%).

'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.'

Which means for our asset as example:- Looking at the volatility of 35.9% in the last 5 years of American Express, we see it is relatively greater, thus worse in comparison to the benchmark SPY (19.9%)
- During the last 3 years, the historical 30 days volatility is 43.5%, which is greater, thus worse than the value of 23.1% from the benchmark.

'The downside volatility is similar to the volatility, or standard deviation, but only takes losing/negative periods into account.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (14.6%) in the period of the last 5 years, the downside risk of 23.5% of American Express is greater, thus worse.
- Looking at downside risk in of 28.3% in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (16.9%).

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (0.49) in the period of the last 5 years, the risk / return profile (Sharpe) of 0.39 of American Express is smaller, thus worse.
- Looking at ratio of return and volatility (Sharpe) in of 0.17 in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (0.45).

'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:- Looking at the excess return divided by the downside deviation of 0.59 in the last 5 years of American Express, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (0.67)
- Looking at excess return divided by the downside deviation in of 0.27 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.62).

'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:- Looking at the Ulcer Index of 13 in the last 5 years of American Express, we see it is relatively larger, thus worse in comparison to the benchmark SPY (6.16 )
- During the last 3 years, the Ulcer Ratio is 16 , which is higher, thus worse than the value of 6.87 from the benchmark.

'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.'

Applying this definition to our asset in some examples:- Looking at the maximum drop from peak to valley 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)
- 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:- The maximum time in days below previous high water mark over 5 years of American Express is 253 days, which is greater, thus worse compared to the benchmark SPY (139 days) in the same period.
- During the last 3 years, the maximum days under water is 253 days, which is higher, thus worse than the value of 119 days from the benchmark.

'The Average 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. 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:- The average time in days below previous high water mark over 5 years of American Express is 48 days, which is larger, thus worse compared to the benchmark SPY (35 days) in the same period.
- Looking at average time in days below previous high water mark in of 67 days in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (27 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 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.