'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.'

Which means for our asset as example:- The total return, or performance over 5 years of Walgreens is -73.9%, which is smaller, thus worse compared to the benchmark SPY (94.9%) in the same period.
- Looking at total return in of -73.1% in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (22.5%).

'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:- Compared with the benchmark SPY (14.3%) in the period of the last 5 years, the annual performance (CAGR) of -23.6% of Walgreens is lower, thus worse.
- During the last 3 years, the compounded annual growth rate (CAGR) is -35.5%, which is smaller, thus worse than the value of 7% 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.'

Using this definition on our asset we see for example:- Looking at the historical 30 days volatility of 37% in the last 5 years of Walgreens, we see it is relatively larger, thus worse in comparison to the benchmark SPY (20.9%)
- During the last 3 years, the historical 30 days volatility is 35.2%, which is greater, thus worse than the value of 17.5% from the benchmark.

'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:- The downside risk over 5 years of Walgreens is 27.6%, which is greater, thus worse compared to the benchmark SPY (15%) in the same period.
- Looking at downside risk in of 27.8% in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (12.3%).

'The Sharpe ratio (also known as the Sharpe index, the Sharpe measure, and the reward-to-variability ratio) is a way to examine the performance of an investment by adjusting for its risk. The ratio measures the excess return (or risk premium) per unit of deviation in an investment asset or a trading strategy, typically referred to as risk, named after William F. Sharpe.'

Using this definition on our asset we see for example:- Looking at the risk / return profile (Sharpe) of -0.71 in the last 5 years of Walgreens, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.56)
- Compared with SPY (0.26) in the period of the last 3 years, the risk / return profile (Sharpe) of -1.08 is smaller, thus worse.

'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:- Compared with the benchmark SPY (0.79) in the period of the last 5 years, the downside risk / excess return profile of -0.94 of Walgreens is lower, thus worse.
- Compared with SPY (0.37) in the period of the last 3 years, the downside risk / excess return profile of -1.37 is smaller, thus worse.

'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.'

Which means for our asset as example:- The Downside risk index over 5 years of Walgreens is 36 , which is larger, thus worse compared to the benchmark SPY (9.32 ) in the same period.
- During the last 3 years, the Downside risk index is 40 , which is higher, 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.'

Using this definition on our asset we see for example:- Looking at the maximum DrawDown of -78.5 days in the last 5 years of Walgreens, we see it is relatively lower, thus worse in comparison to the benchmark SPY (-33.7 days)
- Compared with SPY (-24.5 days) in the period of the last 3 years, the maximum DrawDown of -77.3 days is smaller, thus worse.

'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 time in days below previous high water mark over 5 years of Walgreens is 1190 days, which is larger, thus worse compared to the benchmark SPY (488 days) in the same period.
- During the last 3 years, the maximum time in days below previous high water mark is 645 days, which is larger, thus worse 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.'

Which means for our asset as example:- The average time in days below previous high water mark over 5 years of Walgreens is 568 days, which is larger, thus worse compared to the benchmark SPY (123 days) in the same period.
- Looking at average days below previous high in of 285 days in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (179 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 Walgreens are hypothetical and do not account for slippage, fees or taxes.