'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:- Looking at the total return of 0% in the last 5 years of Celgene, we see it is relatively lower, thus worse in comparison to the benchmark SPY (103.3%)
- During the last 3 years, the total return is -10.5%, which is lower, thus worse than the value of 37.7% from the benchmark.

'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.'

Which means for our asset as example:- Looking at the annual performance (CAGR) of 0% in the last 5 years of Celgene, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (15.3%)
- During the last 3 years, the annual return (CAGR) is -3.6%, which is lower, thus worse than the value of 11.3% 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 30 days standard deviation of 30.9% of Celgene is higher, thus worse.
- Compared with SPY (17.3%) in the period of the last 3 years, the 30 days standard deviation of 29.2% is greater, thus worse.

'The downside volatility is similar to the volatility, or standard deviation, but only takes losing/negative periods into account.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (14.9%) in the period of the last 5 years, the downside risk of 21.6% of Celgene is greater, thus worse.
- Compared with SPY (12%) in the period of the last 3 years, the downside risk of 21% is higher, thus worse.

'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:- The risk / return profile (Sharpe) over 5 years of Celgene is -0.08, which is lower, thus worse compared to the benchmark SPY (0.61) in the same period.
- Compared with SPY (0.51) in the period of the last 3 years, the ratio of return and volatility (Sharpe) of -0.21 is smaller, thus worse.

'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (0.85) in the period of the last 5 years, the ratio of annual return and downside deviation of -0.12 of Celgene is lower, thus worse.
- Compared with SPY (0.73) in the period of the last 3 years, the excess return divided by the downside deviation of -0.29 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:- Compared with the benchmark SPY (9.32 ) in the period of the last 5 years, the Ulcer Ratio of 28 of Celgene is greater, thus worse.
- During the last 3 years, the Ulcer Ratio is 32 , which is higher, thus worse than the value of 10 from the benchmark.

'Maximum drawdown is defined as the peak-to-trough decline of an investment during a specific period. It is usually quoted as a percentage of the peak value. The maximum drawdown can be calculated based on absolute returns, in order to identify strategies that suffer less during market downturns, such as low-volatility strategies. However, the maximum drawdown can also be calculated based on returns relative to a benchmark index, for identifying strategies that show steady outperformance over time.'

Applying this definition to our asset in some examples:- The maximum DrawDown over 5 years of Celgene is -59.6 days, which is lower, thus worse compared to the benchmark SPY (-33.7 days) in the same period.
- During the last 3 years, the maximum reduction from previous high is -59.6 days, which is smaller, thus worse than the value of -24.5 days from the benchmark.

'The Maximum 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. It is the length of time the account was in the Max Drawdown. A Max Drawdown measures a retrenchment from when an equity curve reaches a new high. It’s the maximum an account lost during that retrenchment. This method is applied because a valley can’t be measured until a new high occurs. Once the new high is reached, the percentage change from the old high to the bottom of the largest trough is recorded.'

Which means for our asset as 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 537 days of Celgene is larger, thus worse.
- During the last 3 years, the maximum days under water is 537 days, which is higher, 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.'

Applying this definition to our asset in some examples:- The average days under water over 5 years of Celgene is 237 days, which is higher, thus worse compared to the benchmark SPY (123 days) in the same period.
- Compared with SPY (181 days) in the period of the last 3 years, the average days below previous high of 206 days is larger, 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 Celgene are hypothetical and do not account for slippage, fees or taxes.