'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.'

Which means for our asset as example:- Compared with the benchmark SPY (103.4%) in the period of the last 5 years, the total return, or increase in value of 88.6% of Exxon Mobil is lower, thus worse.
- Looking at total return, or increase in value in of 97.9% in the period of the last 3 years, we see it is relatively greater, thus better in comparison to SPY (33.4%).

'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.'

Applying this definition to our asset in some examples:- Looking at the annual performance (CAGR) of 13.5% in the last 5 years of Exxon Mobil, we see it is relatively lower, thus worse in comparison to the benchmark SPY (15.3%)
- During the last 3 years, the compounded annual growth rate (CAGR) is 25.5%, which is larger, thus better than the value of 10.1% from the benchmark.

'Volatility is a rate at which the price of a security increases or decreases for a given set of returns. Volatility is measured by calculating the standard deviation of the annualized returns over a given period of time. It shows the range to which the price of a security may increase or decrease. Volatility measures the risk of a security. It is used in option pricing formula to gauge the fluctuations in the returns of the underlying assets. Volatility indicates the pricing behavior of the security and helps estimate the fluctuations that may happen in a short period of time.'

Applying this definition to our asset in some examples:- The historical 30 days volatility over 5 years of Exxon Mobil is 34.3%, which is greater, thus worse compared to the benchmark SPY (20.9%) in the same period.
- During the last 3 years, the volatility is 28.3%, which is higher, 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:- The downside risk over 5 years of Exxon Mobil is 23.4%, which is greater, thus worse compared to the benchmark SPY (14.9%) in the same period.
- Looking at downside risk in of 19.3% in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (12.1%).

'The Sharpe ratio (also known as the Sharpe index, the Sharpe measure, and the reward-to-variability ratio) is a way to examine the performance of an investment by adjusting for its risk. The ratio measures the excess return (or risk premium) per unit of deviation in an investment asset or a trading strategy, typically referred to as risk, named after William F. Sharpe.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (0.61) in the period of the last 5 years, the Sharpe Ratio of 0.32 of Exxon Mobil is smaller, thus worse.
- Looking at Sharpe Ratio in of 0.81 in the period of the last 3 years, we see it is relatively greater, thus better in comparison to SPY (0.44).

'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.'

Applying this definition to our asset in some examples:- The ratio of annual return and downside deviation over 5 years of Exxon Mobil is 0.47, which is lower, thus worse compared to the benchmark SPY (0.85) in the same period.
- Looking at ratio of annual return and downside deviation in of 1.2 in the period of the last 3 years, we see it is relatively larger, thus better in comparison to SPY (0.63).

'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:- Looking at the Downside risk index of 21 in the last 5 years of Exxon Mobil, we see it is relatively larger, thus worse in comparison to the benchmark SPY (9.32 )
- During the last 3 years, the Downside risk index is 8.8 , which is lower, thus better than the value of 10 from the benchmark.

'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.'

Applying this definition to our asset in some examples:- The maximum drop from peak to valley over 5 years of Exxon Mobil is -57.9 days, which is smaller, thus worse compared to the benchmark SPY (-33.7 days) in the same period.
- Looking at maximum DrawDown in of -20.5 days in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (-24.5 days).

'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.'

Which means for our asset as example:- The maximum time in days below previous high water mark over 5 years of Exxon Mobil is 640 days, which is higher, thus worse compared to the benchmark SPY (488 days) in the same period.
- During the last 3 years, the maximum days under water is 127 days, which is lower, thus better than the value of 488 days from the benchmark.

'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:- Compared with the benchmark SPY (123 days) in the period of the last 5 years, the average days under water of 189 days of Exxon Mobil is higher, thus worse.
- Looking at average days under water in of 36 days in the period of the last 3 years, we see it is relatively lower, thus better in comparison to SPY (180 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 Exxon Mobil are hypothetical and do not account for slippage, fees or taxes.