'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 (60.6%) in the period of the last 5 years, the total return, or performance of 152.7% of Costco is larger, thus better.
- Looking at total return, or increase in value in of 71.5% in the period of the last 3 years, we see it is relatively greater, thus better in comparison to SPY (38%).

'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.'

Applying this definition to our asset in some examples:- The annual performance (CAGR) over 5 years of Costco is 20.4%, which is larger, thus better compared to the benchmark SPY (10%) in the same period.
- During the last 3 years, the annual return (CAGR) is 19.7%, which is greater, thus better than the value of 11.3% 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.'

Which means for our asset as example:- The volatility over 5 years of Costco is 24.4%, which is larger, thus worse compared to the benchmark SPY (21.5%) in the same period.
- During the last 3 years, the 30 days standard deviation is 23.8%, which is larger, thus worse than the value of 17.9% from the benchmark.

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

Using this definition on our asset we see for example:- Compared with the benchmark SPY (15.5%) in the period of the last 5 years, the downside volatility of 16.9% of Costco is larger, thus worse.
- During the last 3 years, the downside risk is 16.9%, which is higher, thus worse than the value of 12.5% from the benchmark.

'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.'

Applying this definition to our asset in some examples:- Looking at the risk / return profile (Sharpe) of 0.73 in the last 5 years of Costco, we see it is relatively higher, thus better in comparison to the benchmark SPY (0.35)
- Compared with SPY (0.49) in the period of the last 3 years, the risk / return profile (Sharpe) of 0.72 is larger, thus better.

'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.'

Applying this definition to our asset in some examples:- The downside risk / excess return profile over 5 years of Costco is 1.06, which is greater, thus better compared to the benchmark SPY (0.48) in the same period.
- Compared with SPY (0.71) in the period of the last 3 years, the downside risk / excess return profile of 1.02 is larger, 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:- Looking at the Ulcer Ratio of 10 in the last 5 years of Costco, we see it is relatively greater, thus worse in comparison to the benchmark SPY (9.55 )
- During the last 3 years, the Downside risk index is 12 , which is larger, thus worse than the value of 10 from the benchmark.

'A maximum drawdown is the maximum loss from a peak to a trough of a portfolio, before a new peak is attained. Maximum Drawdown is an indicator of downside risk over a specified time period. It can be used both as a stand-alone measure or as an input into other metrics such as 'Return over Maximum Drawdown' and the Calmar Ratio. Maximum Drawdown is expressed in percentage terms.'

Applying this definition to our asset in some examples:- The maximum drop from peak to valley over 5 years of Costco is -31.4 days, which is greater, thus better compared to the benchmark SPY (-33.7 days) in the same period.
- Compared with SPY (-24.5 days) in the period of the last 3 years, the maximum drop from peak to valley of -31.4 days is lower, thus worse.

'The Maximum 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. It is the length of time the account was in the Max Drawdown. A Max Drawdown measures a retrenchment from when an equity curve reaches a new high. It’s the maximum an account lost during that retrenchment. This method is applied because a valley can’t be measured until a new high occurs. Once the new high is reached, the percentage change from the old high to the bottom of the largest trough is recorded.'

Which means for our asset as example:- Looking at the maximum days under water of 365 days in the last 5 years of Costco, we see it is relatively smaller, thus better in comparison to the benchmark SPY (431 days)
- Compared with SPY (431 days) in the period of the last 3 years, the maximum time in days below previous high water mark of 365 days is smaller, thus better.

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (105 days) in the period of the last 5 years, the average time in days below previous high water mark of 79 days of Costco is smaller, thus better.
- During the last 3 years, the average time in days below previous high water mark is 113 days, which is smaller, thus better than the value of 144 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 Costco 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.