'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.'

Applying this definition to our asset in some examples:- Looking at the total return, or increase in value of 113.1% in the last 5 years of American Express, we see it is relatively higher, thus better in comparison to the benchmark SPY (94.8%)
- Compared with SPY (31.6%) in the period of the last 3 years, the total return, or performance of 53.5% is larger, 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 (14.3%) in the period of the last 5 years, the annual return (CAGR) of 16.4% of American Express is higher, thus better.
- Compared with SPY (9.6%) in the period of the last 3 years, the annual return (CAGR) of 15.4% is higher, 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:- The 30 days standard deviation over 5 years of American Express is 37.9%, which is higher, thus worse compared to the benchmark SPY (20.9%) in the same period.
- During the last 3 years, the historical 30 days volatility is 29.4%, which is greater, thus worse than the value of 17.3% 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:- Looking at the downside volatility of 24.7% in the last 5 years of American Express, we see it is relatively greater, thus worse in comparison to the benchmark SPY (15%)
- Looking at downside risk in of 20% in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (12.1%).

'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.'

Applying this definition to our asset in some examples:- The ratio of return and volatility (Sharpe) over 5 years of American Express is 0.37, which is smaller, thus worse compared to the benchmark SPY (0.56) in the same period.
- During the last 3 years, the ratio of return and volatility (Sharpe) is 0.44, which is larger, thus better than the value of 0.41 from the benchmark.

'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 (0.79) in the period of the last 5 years, the excess return divided by the downside deviation of 0.56 of American Express is lower, thus worse.
- Compared with SPY (0.59) in the period of the last 3 years, the downside risk / excess return profile of 0.64 is larger, 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.'

Applying this definition to our asset in some examples:- The Ulcer Ratio over 5 years of American Express is 17 , which is larger, thus worse compared to the benchmark SPY (9.33 ) in the same period.
- Looking at Downside risk index in of 15 in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (10 ).

'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:- Looking at the maximum DrawDown of -49.6 days in the last 5 years of American Express, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (-33.7 days)
- During the last 3 years, the maximum reduction from previous high is -31.5 days, which is lower, thus worse than the value of -24.5 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 is 486 days, which is lower, thus better compared to the benchmark SPY (488 days) in the same period.
- During the last 3 years, the maximum time in days below previous high water mark is 486 days, which is smaller, thus better than the value of 488 days from the benchmark.

'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:- The average days under water over 5 years of American Express is 140 days, which is greater, thus worse compared to the benchmark SPY (123 days) in the same period.
- Looking at average days below previous high in of 175 days in the period of the last 3 years, we see it is relatively smaller, thus better in comparison to SPY (179 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.