'Total return is the amount of value an investor earns from a security over a specific period, typically one year, when all distributions are reinvested. Total return is expressed as a percentage of the amount invested. For example, a total return of 20% means the security increased by 20% of its original value due to a price increase, distribution of dividends (if a stock), coupons (if a bond) or capital gains (if a fund). Total return is a strong measure of an investment’s overall performance.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (58.9%) in the period of the last 5 years, the total return, or increase in value of 86.4% of American Express is larger, thus better.
- Compared with SPY (33.9%) in the period of the last 3 years, the total return, or performance of 39.4% is greater, thus better.

'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:- Compared with the benchmark SPY (9.7%) in the period of the last 5 years, the compounded annual growth rate (CAGR) of 13.3% of American Express is greater, thus better.
- During the last 3 years, the annual performance (CAGR) is 11.7%, which is greater, thus better than the value of 10.2% from the benchmark.

'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.'

Using this definition on our asset we see for example:- The 30 days standard deviation over 5 years of American Express is 37.9%, which is higher, thus worse compared to the benchmark SPY (21.6%) in the same period.
- During the last 3 years, the 30 days standard deviation is 45.7%, which is larger, thus worse than the value of 25% 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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (15.7%) in the period of the last 5 years, the downside risk of 24.8% of American Express is higher, thus worse.
- Compared with SPY (18.1%) in the period of the last 3 years, the downside risk of 29.5% is larger, 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.'

Using this definition on our asset we see for example:- The ratio of return and volatility (Sharpe) over 5 years of American Express is 0.28, which is smaller, thus worse compared to the benchmark SPY (0.33) in the same period.
- During the last 3 years, the ratio of return and volatility (Sharpe) is 0.2, which is smaller, thus worse than the value of 0.31 from the benchmark.

'The Sortino ratio, a variation of the Sharpe ratio only factors in the downside, or negative volatility, rather than the total volatility used in calculating the Sharpe ratio. The theory behind the Sortino variation is that upside volatility is a plus for the investment, and it, therefore, should not be included in the risk calculation. Therefore, the Sortino ratio takes upside volatility out of the equation and uses only the downside standard deviation in its calculation instead of the total standard deviation that is used in calculating the Sharpe ratio.'

Using this definition on our asset we see for example:- The excess return divided by the downside deviation over 5 years of American Express is 0.44, which is smaller, thus worse compared to the benchmark SPY (0.46) in the same period.
- Compared with SPY (0.43) in the period of the last 3 years, the excess return divided by the downside deviation of 0.31 is lower, thus worse.

'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:- Looking at the Ulcer Index of 16 in the last 5 years of American Express, we see it is relatively greater, thus worse in comparison to the benchmark SPY (8.91 )
- During the last 3 years, the Ulcer Index is 19 , which is higher, thus worse than the value of 11 from the benchmark.

'Maximum drawdown measures the loss in any losing period during a fund’s investment record. It is defined as the percent retrenchment from a fund’s peak value to the fund’s valley value. The drawdown is in effect from the time the fund’s retrenchment begins until a new fund high is reached. The maximum drawdown encompasses both the period from the fund’s peak to the fund’s valley (length), and the time from the fund’s valley to a new fund high (recovery). It measures the largest percentage drawdown that has occurred in any fund’s data record.'

Which means for our asset as example:- The maximum reduction from previous high over 5 years of American Express is -49.6 days, which is lower, thus worse compared to the benchmark SPY (-33.7 days) in the same period.
- Looking at maximum DrawDown in of -49.6 days in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (-33.7 days).

'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 253 days, which is lower, thus better compared to the benchmark SPY (271 days) in the same period.
- During the last 3 years, the maximum days below previous high is 253 days, which is lower, thus better than the value of 271 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 days below previous high over 5 years of American Express is 68 days, which is greater, thus worse compared to the benchmark SPY (60 days) in the same period.
- During the last 3 years, the average days below previous high is 93 days, which is greater, thus worse than the value of 72 days from the benchmark.

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.