'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.'

Applying this definition to our asset in some examples:- The total return, or performance over 5 years of American Express Company is 46.8%, which is lower, thus worse compared to the benchmark SPY (66.2%) in the same period.
- Looking at total return, or performance in of 100.3% in the period of the last 3 years, we see it is relatively larger, thus better in comparison to SPY (47.5%).

'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.'

Using this definition on our asset we see for example:- Looking at the annual performance (CAGR) of 8% in the last 5 years of American Express Company, we see it is relatively lower, thus worse in comparison to the benchmark SPY (10.7%)
- Compared with SPY (13.9%) in the period of the last 3 years, the annual return (CAGR) of 26.1% is greater, thus better.

'In finance, volatility (symbol σ) is the degree of variation of a trading price series over time as measured by the standard deviation of logarithmic returns. Historic volatility measures a time series of past market prices. Implied volatility looks forward in time, being derived from the market price of a market-traded derivative (in particular, an option). Commonly, the higher the volatility, the riskier the security.'

Using this definition on our asset we see for example:- Looking at the 30 days standard deviation of 20.4% in the last 5 years of American Express Company, we see it is relatively larger, thus worse in comparison to the benchmark SPY (13.3%)
- Compared with SPY (12.5%) in the period of the last 3 years, the historical 30 days volatility of 19.7% is larger, thus worse.

'Downside risk is the financial risk associated with losses. That is, it is the risk of the actual return being below the expected return, or the uncertainty about the magnitude of that difference. 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:- Looking at the downside volatility of 21.9% in the last 5 years of American Express Company, we see it is relatively higher, thus worse in comparison to the benchmark SPY (14.6%)
- Looking at downside volatility in of 20.5% in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (14.2%).

'The Sharpe ratio was developed by Nobel laureate William F. Sharpe, and is used to help investors understand the return of an investment compared to its risk. The ratio is the average return earned in excess of the risk-free rate per unit of volatility or total risk. Subtracting the risk-free rate from the mean return allows an investor to better isolate the profits associated with risk-taking activities. One intuition of this calculation is that a portfolio engaging in 'zero risk' investments, such as the purchase of U.S. Treasury bills (for which the expected return is the risk-free rate), has a Sharpe ratio of exactly zero. Generally, the greater the value of the Sharpe ratio, the more attractive the risk-adjusted return.'

Which means for our asset as example:- The risk / return profile (Sharpe) over 5 years of American Express Company is 0.27, which is lower, thus worse compared to the benchmark SPY (0.62) in the same period.
- Compared with SPY (0.91) in the period of the last 3 years, the Sharpe Ratio of 1.2 is larger, thus better.

'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:- Compared with the benchmark SPY (0.56) in the period of the last 5 years, the downside risk / excess return profile of 0.25 of American Express Company is lower, thus worse.
- Compared with SPY (0.8) in the period of the last 3 years, the ratio of annual return and downside deviation of 1.15 is greater, 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.'

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 Ulcer Index in of 4.5 in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (4.01 ).

'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 (-19.3 days) in the period of the last 5 years, the maximum DrawDown of -45.4 days of American Express Company is smaller, thus worse.
- During the last 3 years, the maximum drop from peak to valley is -20.7 days, which is smaller, thus worse than the value of -19.3 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 under water over 5 years of American Express Company is 818 days, which is larger, thus worse compared to the benchmark SPY (187 days) in the same period.
- Looking at maximum time in days below previous high water mark in of 75 days in the period of the last 3 years, we see it is relatively lower, thus better in comparison to SPY (139 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.'

Applying this definition to our asset in some examples:- Looking at the average days under water of 285 days in the last 5 years of American Express Company, we see it is relatively greater, thus worse in comparison to the benchmark SPY (41 days)
- Compared with SPY (36 days) in the period of the last 3 years, the average days under water of 20 days is lower, thus better.

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.