'Total return, when measuring performance, is the actual rate of return of an investment or a pool of investments over a given evaluation period. Total return includes interest, capital gains, dividends and distributions realized over a given period of time. Total return accounts for two categories of return: income including interest paid by fixed-income investments, distributions or dividends and capital appreciation, representing the change in the market price of an asset.'

Which means for our asset as example:- The total return, or performance over 5 years of Amazon.com is 55.5%, which is smaller, thus worse compared to the benchmark SPY (62.6%) in the same period.
- Compared with SPY (32.1%) in the period of the last 3 years, the total return, or performance of 3.2% is lower, thus worse.

'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:- Looking at the annual return (CAGR) of 9.2% in the last 5 years of Amazon.com, we see it is relatively lower, thus worse in comparison to the benchmark SPY (10.2%)
- Looking at annual performance (CAGR) in of 1% in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (9.7%).

'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:- Compared with the benchmark SPY (21.5%) in the period of the last 5 years, the historical 30 days volatility of 35.6% of Amazon.com is larger, thus worse.
- During the last 3 years, the volatility is 38.8%, which is higher, thus worse than the value of 24.8% from the benchmark.

'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.'

Using this definition on our asset we see for example:- The downside deviation over 5 years of Amazon.com is 24.8%, which is larger, thus worse compared to the benchmark SPY (15.6%) in the same period.
- During the last 3 years, the downside volatility is 27%, which is greater, thus worse than the value of 17.9% from the benchmark.

'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.'

Using this definition on our asset we see for example:- Looking at the risk / return profile (Sharpe) of 0.19 in the last 5 years of Amazon.com, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (0.36)
- During the last 3 years, the risk / return profile (Sharpe) is -0.04, which is lower, thus worse than the value of 0.29 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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (0.5) in the period of the last 5 years, the ratio of annual return and downside deviation of 0.27 of Amazon.com is lower, thus worse.
- Compared with SPY (0.4) in the period of the last 3 years, the excess return divided by the downside deviation of -0.05 is smaller, thus worse.

'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.'

Which means for our asset as example:- The Ulcer Index over 5 years of Amazon.com is 17 , which is greater, thus worse compared to the benchmark SPY (8.52 ) in the same period.
- Compared with SPY (10 ) in the period of the last 3 years, the Ulcer Index of 20 is larger, 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.'

Which means for our asset as example:- The maximum reduction from previous high over 5 years of Amazon.com is -53.8 days, which is lower, thus worse compared to the benchmark SPY (-33.7 days) in the same period.
- Looking at maximum DrawDown in of -53.8 days in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (-33.7 days).

'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). Many assume Max DD Duration is the length of time between new highs during which the Max DD (magnitude) occurred. But that isn’t always the case. The Max DD duration is the longest time between peaks, period. So it could be the time when the program also had its biggest peak to valley loss (and usually is, because the program needs a long time to recover from the largest loss), but it doesn’t have to be'

Which means for our asset as example:- Looking at the maximum days under water of 359 days in the last 5 years of Amazon.com, we see it is relatively higher, thus worse in comparison to the benchmark SPY (235 days)
- Looking at maximum days under water in of 359 days in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (235 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.'

Using this definition on our asset we see for example:- Looking at the average time in days below previous high water mark of 131 days in the last 5 years of Amazon.com, we see it is relatively larger, thus worse in comparison to the benchmark SPY (55 days)
- During the last 3 years, the average days under water is 124 days, which is greater, thus worse than the value of 59 days from the benchmark.

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 Amazon.com 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.