'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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (99.9%) in the period of the last 5 years, the total return of 29.5% of Take-Two Interactive is smaller, thus worse.
- Compared with SPY (35%) in the period of the last 3 years, the total return, or performance of -11% 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:- Looking at the annual performance (CAGR) of 5.3% in the last 5 years of Take-Two Interactive, we see it is relatively lower, thus worse in comparison to the benchmark SPY (14.9%)
- Looking at compounded annual growth rate (CAGR) in of -3.8% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (10.5%).

'In finance, volatility (symbol σ) is the degree of variation of a trading price series over time as measured by the standard deviation of logarithmic returns. Historic volatility measures a time series of past market prices. Implied volatility looks forward in time, being derived from the market price of a market-traded derivative (in particular, an option). Commonly, the higher the volatility, the riskier the security.'

Which means for our asset as example:- Looking at the volatility of 34.7% in the last 5 years of Take-Two Interactive, we see it is relatively higher, thus worse in comparison to the benchmark SPY (20.9%)
- Compared with SPY (17.3%) in the period of the last 3 years, the volatility of 33.6% 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.'

Which means for our asset as example:- Looking at the downside deviation of 24.8% in the last 5 years of Take-Two Interactive, we see it is relatively higher, thus worse in comparison to the benchmark SPY (15%)
- Compared with SPY (12%) in the period of the last 3 years, the downside risk of 24.1% is higher, thus worse.

'The Sharpe ratio is the measure of risk-adjusted return of a financial portfolio. Sharpe ratio is a measure of excess portfolio return over the risk-free rate relative to its standard deviation. Normally, the 90-day Treasury bill rate is taken as the proxy for risk-free rate. A portfolio with a higher Sharpe ratio is considered superior relative to its peers. The measure was named after William F Sharpe, a Nobel laureate and professor of finance, emeritus at Stanford University.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (0.59) in the period of the last 5 years, the risk / return profile (Sharpe) of 0.08 of Take-Two Interactive is lower, thus worse.
- Looking at risk / return profile (Sharpe) in of -0.19 in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (0.47).

'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.'

Using this definition on our asset we see for example:- The ratio of annual return and downside deviation over 5 years of Take-Two Interactive is 0.11, which is lower, thus worse compared to the benchmark SPY (0.83) in the same period.
- During the last 3 years, the excess return divided by the downside deviation is -0.26, which is smaller, thus worse than the value of 0.67 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.'

Applying this definition to our asset in some examples:- The Ulcer Ratio over 5 years of Take-Two Interactive is 28 , which is higher, thus worse compared to the benchmark SPY (9.32 ) in the same period.
- Looking at Ulcer Index in of 29 in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (10 ).

'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.'

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 -56.1 days of Take-Two Interactive is smaller, thus worse.
- During the last 3 years, the maximum reduction from previous high is -51.5 days, which is lower, 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 866 days of Take-Two Interactive is greater, thus worse.
- Looking at maximum days under water in of 678 days in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (488 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.'

Which means for our asset as example:- Compared with the benchmark SPY (124 days) in the period of the last 5 years, the average days below previous high of 326 days of Take-Two Interactive is larger, thus worse.
- Looking at average time in days below previous high water mark in of 311 days in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (181 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 Take-Two Interactive are hypothetical and do not account for slippage, fees or taxes.