'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (63%) in the period of the last 5 years, the total return, or performance of 137.3% of Ulta Beauty is higher, thus better.
- During the last 3 years, the total return, or increase in value is 89.4%, which is greater, thus better than the value of 33.5% from the benchmark.

'The compound annual growth rate isn't a true return rate, but rather a representational figure. It is essentially a number that describes the rate at which an investment would have grown if it had grown the same rate every year and the profits were reinvested at the end of each year. In reality, this sort of performance is unlikely. However, CAGR can be used to smooth returns so that they may be more easily understood when compared to alternative investments.'

Applying this definition to our asset in some examples:- The annual performance (CAGR) over 5 years of Ulta Beauty is 18.9%, which is larger, thus better compared to the benchmark SPY (10.3%) in the same period.
- During the last 3 years, the compounded annual growth rate (CAGR) is 23.7%, which is larger, thus better than the value of 10.1% from the benchmark.

'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.'

Applying this definition to our asset in some examples:- Looking at the volatility of 43.5% in the last 5 years of Ulta Beauty, we see it is relatively higher, thus worse in comparison to the benchmark SPY (21.6%)
- During the last 3 years, the historical 30 days volatility is 46.8%, which is greater, thus worse than the value of 25.1% 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.'

Which means for our asset as example:- Looking at the downside volatility of 30.7% in the last 5 years of Ulta Beauty, we see it is relatively higher, thus worse in comparison to the benchmark SPY (15.6%)
- Compared with SPY (18.1%) in the period of the last 3 years, the downside deviation of 31.4% is greater, thus worse.

'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.'

Which means for our asset as example:- Looking at the risk / return profile (Sharpe) of 0.38 in the last 5 years of Ulta Beauty, we see it is relatively higher, thus better in comparison to the benchmark SPY (0.36)
- Looking at Sharpe Ratio in of 0.45 in the period of the last 3 years, we see it is relatively larger, thus better in comparison to SPY (0.3).

'The Sortino ratio, a variation of the Sharpe ratio only factors in the downside, or negative volatility, rather than the total volatility used in calculating the Sharpe ratio. The theory behind the Sortino variation is that upside volatility is a plus for the investment, and it, therefore, should not be included in the risk calculation. Therefore, the Sortino ratio takes upside volatility out of the equation and uses only the downside standard deviation in its calculation instead of the total standard deviation that is used in calculating the Sharpe ratio.'

Applying this definition to our asset in some examples:- The downside risk / excess return profile over 5 years of Ulta Beauty is 0.53, which is larger, thus better compared to the benchmark SPY (0.5) in the same period.
- Compared with SPY (0.42) in the period of the last 3 years, the ratio of annual return and downside deviation of 0.68 is greater, thus better.

'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.'

Using this definition on our asset we see for example:- The Ulcer Index over 5 years of Ulta Beauty is 20 , which is greater, thus worse compared to the benchmark SPY (8.88 ) in the same period.
- Compared with SPY (11 ) in the period of the last 3 years, the Downside risk index of 16 is higher, 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.'

Using this definition on our asset we see for example:- 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.
- Looking at maximum reduction from previous high in of -57.4 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) in days.'

Which means for our asset as example:- Compared with the benchmark SPY (273 days) in the period of the last 5 years, the maximum days below previous high of 521 days of Ulta Beauty is larger, thus worse.
- Looking at maximum time in days below previous high water mark in of 227 days in the period of the last 3 years, we see it is relatively lower, thus better in comparison to SPY (273 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (57 days) in the period of the last 5 years, the average time in days below previous high water mark of 128 days of Ulta Beauty is larger, thus worse.
- During the last 3 years, the average days under water is 55 days, which is lower, thus better than the value of 73 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, 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.