'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 of 49.2% in the last 5 years of Ulta Beauty, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (111.3%)
- During the last 3 years, the total return, or increase in value is -2.7%, which is lower, thus worse than the value of 39.3% from the benchmark.

'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:- The annual return (CAGR) over 5 years of Ulta Beauty is 8.3%, which is lower, thus worse compared to the benchmark SPY (16.2%) in the same period.
- Compared with SPY (11.7%) in the period of the last 3 years, the annual performance (CAGR) of -0.9% is smaller, thus worse.

'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.'

Applying this definition to our asset in some examples:- Looking at the volatility of 41.3% in the last 5 years of Ulta Beauty, we see it is relatively larger, thus worse in comparison to the benchmark SPY (20.9%)
- Compared with SPY (17.5%) in the period of the last 3 years, the 30 days standard deviation of 33.4% is larger, thus worse.

'The downside volatility is similar to the volatility, or standard deviation, but only takes losing/negative periods into account.'

Applying this definition to our asset in some examples:- The downside deviation over 5 years of Ulta Beauty is 28.2%, which is greater, thus worse compared to the benchmark SPY (14.9%) in the same period.
- Looking at downside deviation in of 24.4% in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (12.2%).

'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.'

Using this definition on our asset we see for example:- The risk / return profile (Sharpe) over 5 years of Ulta Beauty is 0.14, which is lower, thus worse compared to the benchmark SPY (0.66) in the same period.
- Compared with SPY (0.53) in the period of the last 3 years, the risk / return profile (Sharpe) of -0.1 is lower, 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:- The downside risk / excess return profile over 5 years of Ulta Beauty is 0.21, which is lower, thus worse compared to the benchmark SPY (0.92) in the same period.
- During the last 3 years, the ratio of annual return and downside deviation is -0.14, which is lower, thus worse than the value of 0.75 from the benchmark.

'The ulcer index is a stock market risk measure or technical analysis indicator devised by Peter Martin in 1987, and published by him and Byron McCann in their 1989 book The Investors Guide to Fidelity Funds. It's designed as a measure of volatility, but only volatility in the downward direction, i.e. the amount of drawdown or retracement occurring over a period. Other volatility measures like standard deviation treat up and down movement equally, but a trader doesn't mind upward movement, it's the downside that causes stress and stomach ulcers that the index's name suggests.'

Applying this definition to our asset in some examples:- Looking at the Ulcer Ratio of 18 in the last 5 years of Ulta Beauty, we see it is relatively larger, thus worse in comparison to the benchmark SPY (9.32 )
- Looking at Downside risk index in of 18 in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (10 ).

'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:- Looking at the maximum DrawDown of -57.4 days in the last 5 years of Ulta Beauty, we see it is relatively lower, thus worse in comparison to the benchmark SPY (-33.7 days)
- Compared with SPY (-24.5 days) in the period of the last 3 years, the maximum DrawDown of -43.5 days is lower, thus worse.

'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) in days.'

Which means for our asset as example:- Compared with the benchmark SPY (488 days) in the period of the last 5 years, the maximum time in days below previous high water mark of 227 days of Ulta Beauty is smaller, thus better.
- During the last 3 years, the maximum days below previous high is 206 days, which is smaller, 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (124 days) in the period of the last 5 years, the average days below previous high of 61 days of Ulta Beauty is smaller, thus better.
- Compared with SPY (179 days) in the period of the last 3 years, the average time in days below previous high water mark of 59 days is lower, thus better.

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 Ulta Beauty are hypothetical and do not account for slippage, fees or taxes.