'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 (66.2%) in the period of the last 5 years, the total return, or performance of 29.2% of American Express Company is lower, thus worse.
- Looking at total return, or increase in value in of 89.4% in the period of the last 3 years, we see it is relatively larger, thus better in comparison to SPY (45.7%).

'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:- The annual performance (CAGR) over 5 years of American Express Company is 5.3%, which is lower, thus worse compared to the benchmark SPY (10.7%) in the same period.
- Looking at compounded annual growth rate (CAGR) in of 23.8% in the period of the last 3 years, we see it is relatively larger, thus better in comparison to SPY (13.4%).

'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:- The historical 30 days volatility over 5 years of American Express Company is 20.5%, which is larger, thus worse compared to the benchmark SPY (13.3%) in the same period.
- During the last 3 years, the historical 30 days volatility is 19.8%, which is higher, thus worse than the value of 12.5% 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.'

Which means for our asset as example:- Compared with the benchmark SPY (14.6%) in the period of the last 5 years, the downside volatility of 22.1% of American Express Company is larger, thus worse.
- During the last 3 years, the downside deviation is 20.4%, which is higher, thus worse than the value of 14.1% from the benchmark.

'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:- Looking at the ratio of return and volatility (Sharpe) of 0.13 in the last 5 years of American Express Company, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.62)
- Looking at ratio of return and volatility (Sharpe) in of 1.08 in the period of the last 3 years, we see it is relatively larger, thus better in comparison to SPY (0.87).

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (0.56) in the period of the last 5 years, the ratio of annual return and downside deviation of 0.13 of American Express Company is lower, thus worse.
- Looking at excess return divided by the downside deviation in of 1.04 in the period of the last 3 years, we see it is relatively greater, thus better in comparison to SPY (0.77).

'The Ulcer Index is a technical indicator that measures downside risk, in terms of both the depth and duration of price declines. The index increases in value as the price moves farther away from a recent high and falls as the price rises to new highs. The indicator is usually calculated over a 14-day period, with the Ulcer Index showing the percentage drawdown a trader can expect from the high over that period. The greater the value of the Ulcer Index, the longer it takes for a stock to get back to the former high.'

Using this definition on our asset we see for example:- The Ulcer Ratio over 5 years of American Express Company is 17 , which is greater, thus better compared to the benchmark SPY (3.96 ) in the same period.
- Looking at Downside risk index in of 4.51 in the period of the last 3 years, we see it is relatively greater, thus better in comparison to SPY (4.01 ).

'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:- The maximum reduction from previous high over 5 years of American Express Company is -45.4 days, which is smaller, thus worse compared to the benchmark SPY (-19.3 days) in the same period.
- Compared with SPY (-19.3 days) in the period of the last 3 years, the maximum reduction from previous high 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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (187 days) in the period of the last 5 years, the maximum days under water of 818 days of American Express Company is greater, thus worse.
- Compared with SPY (131 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.'

Which means for our asset as example:- Looking at the average days below previous high of 284 days in the last 5 years of American Express Company, we see it is relatively larger, thus worse in comparison to the benchmark SPY (39 days)
- Looking at average time in days below previous high water mark in of 20 days in the period of the last 3 years, we see it is relatively lower, thus better in comparison to SPY (34 days).

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.