'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (83.6%) in the period of the last 5 years, the total return, or performance of 30.9% of Ulta Beauty is lower, thus worse.
- During the last 3 years, the total return is -1%, which is lower, thus worse than the value of 36.9% from the benchmark.

'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:- The annual return (CAGR) over 5 years of Ulta Beauty is 5.5%, which is lower, thus worse compared to the benchmark SPY (12.9%) in the same period.
- During the last 3 years, the annual performance (CAGR) is -0.3%, which is lower, thus worse than the value of 11.1% 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:- Compared with the benchmark SPY (18.8%) in the period of the last 5 years, the historical 30 days volatility of 41.8% of Ulta Beauty is higher, thus worse.
- Looking at volatility in of 48% in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (22.4%).

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (13.7%) in the period of the last 5 years, the downside volatility of 29.3% of Ulta Beauty is larger, thus worse.
- Compared with SPY (16.5%) in the period of the last 3 years, the downside risk of 34.6% is larger, thus worse.

'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:- Compared with the benchmark SPY (0.55) in the period of the last 5 years, the ratio of return and volatility (Sharpe) of 0.07 of Ulta Beauty is smaller, thus worse.
- Looking at risk / return profile (Sharpe) in of -0.06 in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (0.38).

'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.'

Which means for our asset as example:- Looking at the downside risk / excess return profile of 0.1 in the last 5 years of Ulta Beauty, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (0.76)
- During the last 3 years, the ratio of annual return and downside deviation is -0.08, which is smaller, thus worse than the value of 0.52 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.'

Which means for our asset as example:- Looking at the Downside risk index of 23 in the last 5 years of Ulta Beauty, we see it is relatively higher, thus worse in comparison to the benchmark SPY (5.78 )
- Looking at Downside risk index in of 24 in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (7.07 ).

'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.'

Using this definition on our asset we see for example:- Looking at the maximum drop from peak to valley of -64.9 days in the last 5 years of Ulta Beauty, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (-33.7 days)
- Looking at maximum reduction from previous high in of -64.9 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'

Using this definition on our asset we see for example:- The maximum days below previous high over 5 years of Ulta Beauty is 364 days, which is larger, thus worse compared to the benchmark SPY (139 days) in the same period.
- Compared with SPY (139 days) in the period of the last 3 years, the maximum time in days below previous high water mark of 300 days is higher, thus worse.

'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 (37 days) in the period of the last 5 years, the average days below previous high of 108 days of Ulta Beauty is larger, thus worse.
- Looking at average days below previous high in of 77 days in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (45 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 Ulta Beauty 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.