'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:- The total return over 5 years of Paychex is 97.1%, which is larger, thus better compared to the benchmark SPY (88%) in the same period.
- Looking at total return, or increase in value in of 43.2% in the period of the last 3 years, we see it is relatively larger, thus better in comparison to SPY (39.5%).

'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:- Looking at the annual performance (CAGR) of 14.5% in the last 5 years of Paychex, we see it is relatively higher, thus better in comparison to the benchmark SPY (13.5%)
- Compared with SPY (11.7%) in the period of the last 3 years, the annual return (CAGR) of 12.7% is greater, thus better.

'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 30 days standard deviation of 26.3% in the last 5 years of Paychex, we see it is relatively greater, thus worse in comparison to the benchmark SPY (18.8%)
- Looking at historical 30 days volatility in of 31.1% in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (22.3%).

'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:- Compared with the benchmark SPY (13.7%) in the period of the last 5 years, the downside deviation of 18.7% of Paychex is larger, thus worse.
- Looking at downside deviation in of 22.3% 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 (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.'

Applying this definition to our asset in some examples:- The risk / return profile (Sharpe) over 5 years of Paychex is 0.46, which is lower, thus worse compared to the benchmark SPY (0.58) in the same period.
- Compared with SPY (0.41) in the period of the last 3 years, the ratio of return and volatility (Sharpe) of 0.33 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:- Looking at the ratio of annual return and downside deviation of 0.64 in the last 5 years of Paychex, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (0.8)
- Compared with SPY (0.56) in the period of the last 3 years, the downside risk / excess return profile of 0.46 is lower, 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 Ulcer Index over 5 years of Paychex is 8.98 , which is larger, thus worse compared to the benchmark SPY (5.79 ) in the same period.
- Compared with SPY (7.08 ) in the period of the last 3 years, the Ulcer Ratio of 11 is higher, thus worse.

'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:- The maximum reduction from previous high over 5 years of Paychex is -44.2 days, which is smaller, thus worse compared to the benchmark SPY (-33.7 days) in the same period.
- During the last 3 years, the maximum DrawDown is -44.2 days, which is lower, 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) in days.'

Applying this definition to our asset in some examples:- Looking at the maximum days below previous high of 152 days in the last 5 years of Paychex, we see it is relatively larger, thus worse in comparison to the benchmark SPY (139 days)
- During the last 3 years, the maximum days below previous high is 152 days, which is larger, thus worse than the value of 139 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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (37 days) in the period of the last 5 years, the average time in days below previous high water mark of 48 days of Paychex is higher, thus worse.
- Looking at average days below previous high in of 53 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 Paychex 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.