'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 (100.7%) in the period of the last 5 years, the total return, or performance of 222.1% of Regeneron Pharmaceuticals is larger, thus better.
- Compared with SPY (33.2%) in the period of the last 3 years, the total return of 87.6% is higher, thus better.

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (15%) in the period of the last 5 years, the compounded annual growth rate (CAGR) of 26.4% of Regeneron Pharmaceuticals is larger, thus better.
- Looking at compounded annual growth rate (CAGR) in of 23.3% in the period of the last 3 years, we see it is relatively greater, thus better in comparison to SPY (10%).

'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:- Compared with the benchmark SPY (20.9%) in the period of the last 5 years, the volatility of 31% of Regeneron Pharmaceuticals is higher, thus worse.
- Compared with SPY (17.3%) in the period of the last 3 years, the 30 days standard deviation of 27.2% is larger, 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.'

Which means for our asset as example:- Looking at the downside volatility of 19.9% in the last 5 years of Regeneron Pharmaceuticals, we see it is relatively greater, thus worse in comparison to the benchmark SPY (15%)
- Looking at downside risk in of 17.3% in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (12%).

'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:- Compared with the benchmark SPY (0.6) in the period of the last 5 years, the Sharpe Ratio of 0.77 of Regeneron Pharmaceuticals is higher, thus better.
- Compared with SPY (0.44) in the period of the last 3 years, the Sharpe Ratio of 0.77 is larger, 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.'

Which means for our asset as example:- Compared with the benchmark SPY (0.83) in the period of the last 5 years, the excess return divided by the downside deviation of 1.2 of Regeneron Pharmaceuticals is larger, thus better.
- Looking at excess return divided by the downside deviation in of 1.2 in the period of the last 3 years, we see it is relatively greater, thus better in comparison to SPY (0.62).

'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.'

Applying this definition to our asset in some examples:- The Ulcer Index over 5 years of Regeneron Pharmaceuticals is 12 , which is higher, thus worse compared to the benchmark SPY (9.32 ) in the same period.
- Compared with SPY (10 ) in the period of the last 3 years, the Ulcer Index of 8.51 is smaller, thus better.

'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 Regeneron Pharmaceuticals is -32.1 days, which is greater, thus better compared to the benchmark SPY (-33.7 days) in the same period.
- Looking at maximum reduction from previous high in of -25.8 days in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (-24.5 days).

'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 days below previous high over 5 years of Regeneron Pharmaceuticals is 274 days, which is lower, thus better compared to the benchmark SPY (488 days) in the same period.
- Compared with SPY (488 days) in the period of the last 3 years, the maximum days under water of 135 days is smaller, thus better.

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (123 days) in the period of the last 5 years, the average time in days below previous high water mark of 60 days of Regeneron Pharmaceuticals is smaller, thus better.
- During the last 3 years, the average days under water is 39 days, which is lower, thus better than the value of 180 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 Regeneron Pharmaceuticals are hypothetical and do not account for slippage, fees or taxes.