'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.'

Which means for our asset as example:- Compared with the benchmark SPY (67.9%) in the period of the last 5 years, the total return, or performance of 476.4% of Amazon.com is greater, thus better.
- Looking at total return, or performance in of 146.6% in the period of the last 3 years, we see it is relatively larger, thus better in comparison to SPY (38.6%).

'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 (10.9%) in the period of the last 5 years, the annual performance (CAGR) of 42% of Amazon.com is higher, thus better.
- Looking at annual performance (CAGR) in of 35.1% in the period of the last 3 years, we see it is relatively larger, thus better in comparison to SPY (11.5%).

'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.'

Which means for our asset as example:- Looking at the 30 days standard deviation of 29.8% in the last 5 years of Amazon.com, we see it is relatively larger, thus worse in comparison to the benchmark SPY (18.7%)
- During the last 3 years, the historical 30 days volatility is 31.1%, which is larger, thus worse than the value of 21.5% 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.'

Applying this definition to our asset in some examples:- Looking at the downside deviation of 19.6% in the last 5 years of Amazon.com, we see it is relatively larger, thus worse in comparison to the benchmark SPY (13.6%)
- During the last 3 years, the downside risk is 20.8%, which is larger, thus worse than the value of 15.7% from the benchmark.

'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:- Looking at the ratio of return and volatility (Sharpe) of 1.32 in the last 5 years of Amazon.com, we see it is relatively greater, thus better in comparison to the benchmark SPY (0.45)
- During the last 3 years, the Sharpe Ratio is 1.05, which is higher, thus better than the value of 0.42 from the benchmark.

'The Sortino ratio measures the risk-adjusted return of an investment asset, portfolio, or strategy. It is a modification of the Sharpe ratio but penalizes only those returns falling below a user-specified target or required rate of return, while the Sharpe ratio penalizes both upside and downside volatility equally. Though both ratios measure an investment's risk-adjusted return, they do so in significantly different ways that will frequently lead to differing conclusions as to the true nature of the investment's return-generating efficiency. The Sortino ratio is used as a way to compare the risk-adjusted performance of programs with differing risk and return profiles. In general, risk-adjusted returns seek to normalize the risk across programs and then see which has the higher return unit per risk.'

Applying this definition to our asset in some examples:- Looking at the downside risk / excess return profile of 2.01 in the last 5 years of Amazon.com, we see it is relatively larger, thus better in comparison to the benchmark SPY (0.62)
- During the last 3 years, the excess return divided by the downside deviation is 1.57, which is larger, thus better than the value of 0.57 from the benchmark.

'The Ulcer Index is a technical indicator that measures downside risk, in terms of both the depth and duration of price declines. The index increases in value as the price moves farther away from a recent high and falls as the price rises to new highs. The indicator is usually calculated over a 14-day period, with the Ulcer Index showing the percentage drawdown a trader can expect from the high over that period. The greater the value of the Ulcer Index, the longer it takes for a stock to get back to the former high.'

Applying this definition to our asset in some examples:- The Ulcer Index over 5 years of Amazon.com is 9.51 , which is larger, thus worse compared to the benchmark SPY (5.82 ) in the same period.
- Compared with SPY (6.87 ) in the period of the last 3 years, the Downside risk index of 10 is larger, thus worse.

'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.'

Using this definition on our asset we see for example:- The maximum drop from peak to valley over 5 years of Amazon.com is -34.1 days, which is lower, thus worse compared to the benchmark SPY (-33.7 days) in the same period.
- During the last 3 years, the maximum DrawDown is -34.1 days, which is lower, thus worse than the value of -33.7 days from the benchmark.

'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.'

Using this definition on our asset we see for example:- The maximum time in days below previous high water mark over 5 years of Amazon.com is 355 days, which is larger, thus worse compared to the benchmark SPY (187 days) in the same period.
- Looking at maximum days below previous high in of 355 days in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (139 days).

'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.'

Which means for our asset as example:- The average days below previous high over 5 years of Amazon.com is 72 days, which is larger, thus worse compared to the benchmark SPY (43 days) in the same period.
- Compared with SPY (39 days) in the period of the last 3 years, the average days under water of 102 days is larger, thus worse.

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.