'The total return on a portfolio of investments takes into account not only the capital appreciation on the portfolio, but also the income received on the portfolio. The income typically consists of interest, dividends, and securities lending fees. This contrasts with the price return, which takes into account only the capital gain on an investment.'

Using this definition on our asset we see for example:- Looking at the total return of 21.8% in the last 5 years of CoStar Group, we see it is relatively lower, thus worse in comparison to the benchmark SPY (94.9%)
- Compared with SPY (22.5%) in the period of the last 3 years, the total return of -14% is smaller, thus worse.

'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:- Compared with the benchmark SPY (14.3%) in the period of the last 5 years, the compounded annual growth rate (CAGR) of 4% of CoStar Group is lower, thus worse.
- During the last 3 years, the annual performance (CAGR) is -4.9%, 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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (20.9%) in the period of the last 5 years, the volatility of 35.4% of CoStar Group is larger, thus worse.
- During the last 3 years, the historical 30 days volatility is 34.1%, which is larger, 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 volatility over 5 years of CoStar Group is 23.8%, which is higher, thus worse compared to the benchmark SPY (15%) in the same period.
- Looking at downside volatility in of 23.1% 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 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:- Compared with the benchmark SPY (0.56) in the period of the last 5 years, the risk / return profile (Sharpe) of 0.04 of CoStar Group is lower, thus worse.
- Looking at risk / return profile (Sharpe) in of -0.22 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.26).

'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.'

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 ratio of annual return and downside deviation of 0.06 of CoStar Group is lower, thus worse.
- Looking at downside risk / excess return profile in of -0.32 in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (0.37).

'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:- The Downside risk index over 5 years of CoStar Group is 20 , which is higher, thus worse compared to the benchmark SPY (9.32 ) in the same period.
- During the last 3 years, the Ulcer Index is 24 , 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:- Compared with the benchmark SPY (-33.7 days) in the period of the last 5 years, the maximum drop from peak to valley of -46.6 days of CoStar Group is smaller, thus worse.
- Compared with SPY (-24.5 days) in the period of the last 3 years, the maximum reduction from previous high of -46.6 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) in days.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (488 days) in the period of the last 5 years, the maximum time in days below previous high water mark of 698 days of CoStar Group is greater, thus worse.
- Compared with SPY (488 days) in the period of the last 3 years, the maximum days below previous high of 698 days is greater, thus worse.

'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.'

Using this definition on our asset we see for example:- Looking at the average time in days below previous high water mark of 222 days in the last 5 years of CoStar Group, we see it is relatively larger, thus worse in comparison to the benchmark SPY (123 days)
- Compared with SPY (179 days) in the period of the last 3 years, the average days below previous high of 330 days is greater, thus worse.

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 CoStar Group are hypothetical and do not account for slippage, fees or taxes.