'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.'

Using this definition on our asset we see for example:- Looking at the total return, or performance of 10.2% in the last 5 years of Ulta Beauty, we see it is relatively lower, thus worse in comparison to the benchmark SPY (103.4%)
- Compared with SPY (33.4%) in the period of the last 3 years, the total return of 16% is lower, thus worse.

'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.'

Using this definition on our asset we see for example:- The annual return (CAGR) over 5 years of Ulta Beauty is 2%, which is lower, thus worse compared to the benchmark SPY (15.3%) in the same period.
- Compared with SPY (10.1%) in the period of the last 3 years, the annual return (CAGR) of 5.1% is lower, 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (20.9%) in the period of the last 5 years, the 30 days standard deviation of 43.1% of Ulta Beauty is higher, thus worse.
- Compared with SPY (17.3%) in the period of the last 3 years, the volatility of 32.2% is greater, thus worse.

'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 risk over 5 years of Ulta Beauty is 31.1%, which is higher, thus worse compared to the benchmark SPY (14.9%) in the same period.
- During the last 3 years, the downside risk is 23.7%, which is higher, thus worse than the value of 12.1% 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.'

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 -0.01 of Ulta Beauty is lower, thus worse.
- Compared with SPY (0.44) in the period of the last 3 years, the risk / return profile (Sharpe) of 0.08 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.'

Applying this definition to our asset in some examples:- The downside risk / excess return profile over 5 years of Ulta Beauty is -0.02, which is lower, thus worse compared to the benchmark SPY (0.85) in the same period.
- During the last 3 years, the excess return divided by the downside deviation is 0.11, which is lower, thus worse than the value of 0.63 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (9.32 ) in the period of the last 5 years, the Ulcer Index of 22 of Ulta Beauty is higher, thus worse.
- Compared with SPY (10 ) in the period of the last 3 years, the Ulcer Index of 14 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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (-33.7 days) in the period of the last 5 years, the maximum DrawDown of -64.9 days of Ulta Beauty is lower, thus worse.
- During the last 3 years, the maximum reduction from previous high is -33.7 days, which is lower, thus worse than the value of -24.5 days from the benchmark.

'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:- The maximum time in days below previous high water mark over 5 years of Ulta Beauty is 521 days, which is larger, thus worse compared to the benchmark SPY (488 days) in the same period.
- During the last 3 years, the maximum days under water is 206 days, which is lower, thus better than the value of 488 days from the benchmark.

'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.'

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 time in days below previous high water mark of 140 days of Ulta Beauty is larger, thus worse.
- During the last 3 years, the average time in days below previous high water mark is 48 days, which is lower, thus better than the value of 180 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 Ulta Beauty are hypothetical and do not account for slippage, fees or taxes.