'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.'

Using this definition on our asset we see for example:- Looking at the total return, or performance of 67% in the last 5 years of American Express, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (68.1%)
- Compared with SPY (47%) in the period of the last 3 years, the total return, or increase in value of 73.6% 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:- Looking at the compounded annual growth rate (CAGR) of 10.8% in the last 5 years of American Express, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (11%)
- Compared with SPY (13.7%) in the period of the last 3 years, the compounded annual growth rate (CAGR) of 20.1% is higher, thus better.

'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 historical 30 days volatility over 5 years of American Express is 37.8%, which is greater, thus worse compared to the benchmark SPY (21.4%) in the same period.
- During the last 3 years, the historical 30 days volatility is 34.8%, which is larger, thus worse than the value of 18.7% 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 (15.4%) in the period of the last 5 years, the downside risk of 24.8% of American Express is higher, thus worse.
- Looking at downside deviation in of 22.1% in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (13.3%).

'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 Sharpe Ratio of 0.22 in the last 5 years of American Express, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.4)
- Compared with SPY (0.6) in the period of the last 3 years, the Sharpe Ratio of 0.51 is smaller, thus worse.

'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 (0.55) in the period of the last 5 years, the excess return divided by the downside deviation of 0.34 of American Express is smaller, thus worse.
- Looking at excess return divided by the downside deviation in of 0.8 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.84).

'Ulcer Index is a method for measuring investment risk that addresses the real concerns of investors, unlike the widely used standard deviation of return. UI is a measure of the depth and duration of drawdowns in prices from earlier highs. Using Ulcer Index instead of standard deviation can lead to very different conclusions about investment risk and risk-adjusted return, especially when evaluating strategies that seek to avoid major declines in portfolio value (market timing, dynamic asset allocation, hedge funds, etc.). The Ulcer Index was originally developed in 1987. Since then, it has been widely recognized and adopted by the investment community. According to Nelson Freeburg, editor of Formula Research, Ulcer Index is “perhaps the most fully realized statistical portrait of risk there is.'

Using this definition on our asset we see for example:- The Downside risk index over 5 years of American Express is 16 , which is greater, thus worse compared to the benchmark SPY (9.45 ) in the same period.
- Compared with SPY (10 ) in the period of the last 3 years, the Downside risk index of 14 is higher, 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:- The maximum reduction from previous high over 5 years of American Express is -49.6 days, which is smaller, thus worse compared to the benchmark SPY (-33.7 days) in the same period.
- Compared with SPY (-24.5 days) in the period of the last 3 years, the maximum reduction from previous high of -31.5 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 time in days below previous high water mark over 5 years of American Express is 320 days, which is lower, thus better compared to the benchmark SPY (351 days) in the same period.
- Looking at maximum time in days below previous high water mark in of 320 days in the period of the last 3 years, we see it is relatively lower, thus better in comparison to SPY (351 days).

'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.'

Applying this definition to our asset in some examples:- Looking at the average days below previous high of 86 days in the last 5 years of American Express, we see it is relatively greater, thus worse in comparison to the benchmark SPY (78 days)
- Looking at average days under water in of 89 days in the period of the last 3 years, we see it is relatively smaller, thus better in comparison to SPY (101 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.