'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 (60.6%) in the period of the last 5 years, the total return of 74% of Paychex is greater, thus better.
- Compared with SPY (38%) in the period of the last 3 years, the total return, or increase in value of 59.9% is greater, thus better.

'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.'

Using this definition on our asset we see for example:- Looking at the annual return (CAGR) of 11.7% in the last 5 years of Paychex, we see it is relatively higher, thus better in comparison to the benchmark SPY (10%)
- Compared with SPY (11.3%) in the period of the last 3 years, the annual return (CAGR) of 17% is larger, thus better.

'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.'

Which means for our asset as example:- Looking at the historical 30 days volatility of 29.2% in the last 5 years of Paychex, we see it is relatively greater, thus worse in comparison to the benchmark SPY (21.5%)
- Compared with SPY (17.9%) in the period of the last 3 years, the historical 30 days volatility of 23.5% is higher, thus worse.

'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.'

Using this definition on our asset we see for example:- Looking at the downside volatility of 20.6% in the last 5 years of Paychex, we see it is relatively larger, thus worse in comparison to the benchmark SPY (15.5%)
- Looking at downside risk in of 16.1% in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (12.5%).

'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 ratio of return and volatility (Sharpe) over 5 years of Paychex is 0.32, which is smaller, thus worse compared to the benchmark SPY (0.35) in the same period.
- During the last 3 years, the ratio of return and volatility (Sharpe) is 0.62, which is higher, thus better than the value of 0.49 from the benchmark.

'The Sortino ratio improves upon the Sharpe ratio by isolating downside volatility from total volatility by dividing excess return by the downside deviation. The Sortino ratio is a variation of the Sharpe ratio that differentiates harmful volatility from total overall volatility by using the asset's standard deviation of negative asset returns, called downside deviation. The Sortino ratio takes the asset's return and subtracts the risk-free rate, and then divides that amount by the asset's downside deviation. The ratio was named after Frank A. Sortino.'

Using this definition on our asset we see for example:- Looking at the excess return divided by the downside deviation of 0.45 in the last 5 years of Paychex, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (0.48)
- During the last 3 years, the excess return divided by the downside deviation is 0.9, which is greater, thus better than the value of 0.71 from the benchmark.

'The ulcer index is a stock market risk measure or technical analysis indicator devised by Peter Martin in 1987, and published by him and Byron McCann in their 1989 book The Investors Guide to Fidelity Funds. It's designed as a measure of volatility, but only volatility in the downward direction, i.e. the amount of drawdown or retracement occurring over a period. Other volatility measures like standard deviation treat up and down movement equally, but a trader doesn't mind upward movement, it's the downside that causes stress and stomach ulcers that the index's name suggests.'

Which means for our asset as example:- Looking at the Downside risk index of 12 in the last 5 years of Paychex, we see it is relatively greater, thus worse in comparison to the benchmark SPY (9.55 )
- During the last 3 years, the Ulcer Ratio is 11 , which is larger, thus worse than the value of 10 from the benchmark.

'Maximum drawdown measures the loss in any losing period during a fund’s investment record. It is defined as the percent retrenchment from a fund’s peak value to the fund’s valley value. The drawdown is in effect from the time the fund’s retrenchment begins until a new fund high is reached. The maximum drawdown encompasses both the period from the fund’s peak to the fund’s valley (length), and the time from the fund’s valley to a new fund high (recovery). It measures the largest percentage drawdown that has occurred in any fund’s data record.'

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 -44.2 days of Paychex is lower, thus worse.
- During the last 3 years, the maximum DrawDown is -23.4 days, which is higher, thus better than the value of -24.5 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'

Applying this definition to our asset in some examples:- Looking at the maximum time in days below previous high water mark of 366 days in the last 5 years of Paychex, we see it is relatively lower, thus better in comparison to the benchmark SPY (431 days)
- Looking at maximum days below previous high in of 366 days in the period of the last 3 years, we see it is relatively lower, thus better in comparison to SPY (431 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.'

Applying this definition to our asset in some examples:- The average days under water over 5 years of Paychex is 92 days, which is smaller, thus better compared to the benchmark SPY (105 days) in the same period.
- Looking at average days below previous high in of 107 days in the period of the last 3 years, we see it is relatively lower, thus better in comparison to SPY (144 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.