American Express (AXP)

TotalReturn:

'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.'

• Looking at the total return, or increase in value of 253% in the last 5 years of American Express, we see it is relatively greater, thus better in comparison to the benchmark SPY (109.7%)
• Looking at total return in of 130% in the period of the last 3 years, we see it is relatively larger, thus better in comparison to SPY (70.1%).

CAGR:

'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.'

• The annual return (CAGR) over 5 years of American Express is 28.8%, which is larger, thus better compared to the benchmark SPY (16%) in the same period.
• Looking at annual return (CAGR) in of 32.2% in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (19.5%).

Volatility:

'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.'

• The historical 30 days volatility over 5 years of American Express is 31.2%, which is higher, thus worse compared to the benchmark SPY (17.5%) in the same period.
• Looking at volatility in of 28.4% in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (17.4%).

DownVol:

'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.'

• The downside volatility over 5 years of American Express is 20%, which is higher, thus worse compared to the benchmark SPY (12.1%) in the same period.
• Looking at downside risk in of 18.5% in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (11.5%).

Sharpe:

'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.'

• Looking at the ratio of return and volatility (Sharpe) of 0.84 in the last 5 years of American Express, we see it is relatively larger, thus better in comparison to the benchmark SPY (0.77)
• Compared with SPY (0.97) in the period of the last 3 years, the Sharpe Ratio of 1.05 is higher, thus better.

Sortino:

'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.'

• Looking at the ratio of annual return and downside deviation of 1.31 in the last 5 years of American Express, we see it is relatively greater, thus better in comparison to the benchmark SPY (1.12)
• Looking at excess return divided by the downside deviation in of 1.6 in the period of the last 3 years, we see it is relatively greater, thus better in comparison to SPY (1.47).

Ulcer:

'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.'

• The Downside risk index over 5 years of American Express is 13 , which is greater, thus worse compared to the benchmark SPY (8.48 ) in the same period.
• Looking at Ulcer Ratio in of 9.07 in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (5.3 ).

MaxDD:

'A maximum drawdown is the maximum loss from a peak to a trough of a portfolio, before a new peak is attained. Maximum Drawdown is an indicator of downside risk over a specified time period. It can be used both as a stand-alone measure or as an input into other metrics such as 'Return over Maximum Drawdown' and the Calmar Ratio. Maximum Drawdown is expressed in percentage terms.'

• Compared with the benchmark SPY (-24.5 days) in the period of the last 5 years, the maximum reduction from previous high of -31.5 days of American Express is lower, thus worse.
• Looking at maximum drop from peak to valley in of -28.8 days in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (-18.8 days).

MaxDuration:

'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.'

• Compared with the benchmark SPY (488 days) in the period of the last 5 years, the maximum days below previous high of 486 days of American Express is lower, thus better.
• During the last 3 years, the maximum time in days below previous high water mark is 211 days, which is greater, thus worse than the value of 199 days from the benchmark.

AveDuration:

'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.'

• Looking at the average days under water of 117 days in the last 5 years of American Express, we see it is relatively smaller, thus better in comparison to the benchmark SPY (120 days)
• During the last 3 years, the average days under water is 55 days, which is larger, thus worse than the value of 47 days from the benchmark.