'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.'

Applying this definition to our asset in some examples:- The total return, or performance over 5 years of American Express is 161.3%, which is larger, thus better compared to the benchmark SPY (120.8%) in the same period.
- Compared with SPY (66.3%) in the period of the last 3 years, the total return, or increase in value of 68.8% is higher, 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 (17.2%) in the period of the last 5 years, the annual return (CAGR) of 21.2% of American Express is higher, thus better.
- During the last 3 years, the compounded annual growth rate (CAGR) is 19%, which is higher, thus better than the value of 18.5% 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:- Compared with the benchmark SPY (18.7%) in the period of the last 5 years, the volatility of 33.9% of American Express is higher, thus worse.
- Looking at volatility in of 40.9% in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (22.4%).

'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 (13.6%) in the period of the last 5 years, the downside volatility of 21.7% of American Express is higher, thus worse.
- Compared with SPY (16.3%) in the period of the last 3 years, the downside deviation of 26.1% 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.'

Using this definition on our asset we see for example:- Looking at the ratio of return and volatility (Sharpe) of 0.55 in the last 5 years of American Express, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.78)
- Looking at ratio of return and volatility (Sharpe) in of 0.4 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.71).

'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (1.08) in the period of the last 5 years, the downside risk / excess return profile of 0.86 of American Express is lower, thus worse.
- During the last 3 years, the ratio of annual return and downside deviation is 0.63, which is smaller, thus worse than the value of 0.98 from the benchmark.

'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.'

Applying this definition to our asset in some examples:- The Downside risk index over 5 years of American Express is 12 , which is greater, thus worse compared to the benchmark SPY (5.59 ) in the same period.
- Compared with SPY (6.83 ) in the period of the last 3 years, the Downside risk index of 16 is larger, thus worse.

'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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (-33.7 days) in the period of the last 5 years, the maximum drop from peak to valley of -49.6 days of American Express is lower, thus worse.
- Compared with SPY (-33.7 days) in the period of the last 3 years, the maximum DrawDown of -49.6 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:- The maximum days below previous high over 5 years of American Express is 253 days, which is higher, thus worse compared to the benchmark SPY (139 days) in the same period.
- Compared with SPY (139 days) in the period of the last 3 years, the maximum days below previous high of 253 days is greater, thus worse.

'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:- Compared with the benchmark SPY (33 days) in the period of the last 5 years, the average days below previous high of 48 days of American Express is larger, thus worse.
- Compared with SPY (35 days) in the period of the last 3 years, the average days under water of 65 days is larger, thus worse.

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.