'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.'

Using this definition on our asset we see for example:- Looking at the total return of 538.1% in the last 5 years of lululemon, we see it is relatively greater, thus better in comparison to the benchmark SPY (85.9%)
- During the last 3 years, the total return is 427.6%, which is greater, thus better than the value of 42.4% 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (13.2%) in the period of the last 5 years, the annual performance (CAGR) of 44.9% of lululemon is higher, thus better.
- During the last 3 years, the annual return (CAGR) is 74%, which is larger, thus better than the value of 12.5% 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.'

Using this definition on our asset we see for example:- The volatility over 5 years of lululemon is 39.8%, which is higher, thus worse compared to the benchmark SPY (18.8%) in the same period.
- Compared with SPY (22.5%) in the period of the last 3 years, the 30 days standard deviation of 40.7% 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.'

Applying this definition to our asset in some examples:- The downside risk over 5 years of lululemon is 27.4%, which is greater, thus worse compared to the benchmark SPY (13.7%) in the same period.
- Looking at downside deviation in of 26.9% in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (16.5%).

'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 ratio of return and volatility (Sharpe) over 5 years of lululemon is 1.07, which is larger, thus better compared to the benchmark SPY (0.57) in the same period.
- Compared with SPY (0.44) in the period of the last 3 years, the ratio of return and volatility (Sharpe) of 1.76 is higher, thus better.

'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.'

Using this definition on our asset we see for example:- The excess return divided by the downside deviation over 5 years of lululemon is 1.55, which is greater, thus better compared to the benchmark SPY (0.78) in the same period.
- During the last 3 years, the excess return divided by the downside deviation is 2.65, which is larger, thus better than the value of 0.6 from the benchmark.

'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:- Looking at the Ulcer Ratio of 15 in the last 5 years of lululemon, we see it is relatively higher, thus worse in comparison to the benchmark SPY (5.81 )
- Looking at Ulcer Index in of 10 in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (7.11 ).

'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 reduction from previous high of -47.3 days in the last 5 years of lululemon, we see it is relatively lower, thus worse in comparison to the benchmark SPY (-33.7 days)
- During the last 3 years, the maximum reduction from previous high is -47.3 days, which is smaller, thus worse than the value of -33.7 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). 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:- Looking at the maximum days below previous high of 368 days in the last 5 years of lululemon, we see it is relatively larger, thus worse in comparison to the benchmark SPY (139 days)
- Looking at maximum days below previous high in of 122 days in the period of the last 3 years, we see it is relatively lower, thus better in comparison to SPY (139 days).

'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.'

Applying this definition to our asset in some examples:- Looking at the average days under water of 75 days in the last 5 years of lululemon, we see it is relatively larger, thus worse in comparison to the benchmark SPY (37 days)
- During the last 3 years, the average time in days below previous high water mark is 22 days, which is lower, thus better than the value of 45 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 lululemon 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.