'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (111.3%) in the period of the last 5 years, the total return of 26.7% of Take-Two Interactive is lower, thus worse.
- During the last 3 years, the total return, or performance is -9.2%, which is lower, thus worse than the value of 39.3% from the benchmark.

'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.'

Applying this definition to our asset in some examples:- The annual return (CAGR) over 5 years of Take-Two Interactive is 4.9%, which is lower, thus worse compared to the benchmark SPY (16.2%) in the same period.
- Looking at compounded annual growth rate (CAGR) in of -3.2% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (11.7%).

'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.'

Applying this definition to our asset in some examples:- The historical 30 days volatility over 5 years of Take-Two Interactive is 34.4%, which is greater, thus worse compared to the benchmark SPY (20.9%) in the same period.
- During the last 3 years, the volatility is 33.5%, 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.'

Using this definition on our asset we see for example:- Looking at the downside volatility of 24.6% in the last 5 years of Take-Two Interactive, we see it is relatively greater, thus worse in comparison to the benchmark SPY (14.9%)
- Looking at downside deviation in of 23.9% in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (12.2%).

'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.'

Which means for our asset as example:- The risk / return profile (Sharpe) over 5 years of Take-Two Interactive is 0.07, which is lower, thus worse compared to the benchmark SPY (0.66) in the same period.
- Looking at ratio of return and volatility (Sharpe) in of -0.17 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.53).

'The Sortino ratio measures the risk-adjusted return of an investment asset, portfolio, or strategy. It is a modification of the Sharpe ratio but penalizes only those returns falling below a user-specified target or required rate of return, while the Sharpe ratio penalizes both upside and downside volatility equally. Though both ratios measure an investment's risk-adjusted return, they do so in significantly different ways that will frequently lead to differing conclusions as to the true nature of the investment's return-generating efficiency. The Sortino ratio is used as a way to compare the risk-adjusted performance of programs with differing risk and return profiles. In general, risk-adjusted returns seek to normalize the risk across programs and then see which has the higher return unit per risk.'

Which means for our asset as example:- Compared with the benchmark SPY (0.92) in the period of the last 5 years, the ratio of annual return and downside deviation of 0.1 of Take-Two Interactive is smaller, thus worse.
- Compared with SPY (0.75) in the period of the last 3 years, the downside risk / excess return profile of -0.24 is smaller, 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (9.32 ) in the period of the last 5 years, the Downside risk index of 29 of Take-Two Interactive is greater, thus worse.
- During the last 3 years, the Ulcer Index is 29 , 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.'

Which means for our asset as example:- Compared with the benchmark SPY (-33.7 days) in the period of the last 5 years, the maximum DrawDown of -56.1 days of Take-Two Interactive 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 -51.5 days is lower, thus worse.

'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:- The maximum time in days below previous high water mark over 5 years of Take-Two Interactive is 925 days, which is greater, thus worse 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 below previous high of 737 days is larger, thus worse.

'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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (124 days) in the period of the last 5 years, the average days under water of 358 days of Take-Two Interactive is higher, thus worse.
- Looking at average time in days below previous high water mark in of 365 days in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (179 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.