'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (67.3%) in the period of the last 5 years, the total return of 340.8% of Take-Two Interactive Software is higher, thus better.
- Looking at total return in of 175.5% in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (46.1%).

'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:- Compared with the benchmark SPY (10.9%) in the period of the last 5 years, the annual return (CAGR) of 34.6% of Take-Two Interactive Software is larger, thus better.
- Compared with SPY (13.5%) in the period of the last 3 years, the annual performance (CAGR) of 40.2% is higher, thus better.

'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.'

Which means for our asset as example:- Looking at the 30 days standard deviation of 34.2% in the last 5 years of Take-Two Interactive Software, we see it is relatively higher, thus worse in comparison to the benchmark SPY (13.2%)
- Compared with SPY (12.4%) in the period of the last 3 years, the volatility of 35.4% is higher, 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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (14.6%) in the period of the last 5 years, the downside deviation of 33.8% of Take-Two Interactive Software is larger, thus worse.
- During the last 3 years, the downside volatility is 36.1%, which is higher, thus worse than the value of 14% from the benchmark.

'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:- Looking at the ratio of return and volatility (Sharpe) of 0.94 in the last 5 years of Take-Two Interactive Software, we see it is relatively higher, thus better in comparison to the benchmark SPY (0.63)
- During the last 3 years, the Sharpe Ratio is 1.07, which is greater, thus better than the value of 0.88 from the benchmark.

'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.'

Which means for our asset as example:- Looking at the ratio of annual return and downside deviation of 0.95 in the last 5 years of Take-Two Interactive Software, we see it is relatively greater, thus better in comparison to the benchmark SPY (0.57)
- During the last 3 years, the downside risk / excess return profile is 1.05, which is larger, thus better than the value of 0.79 from the benchmark.

'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:- The Ulcer Index over 5 years of Take-Two Interactive Software is 10 , which is greater, thus better compared to the benchmark SPY (3.95 ) in the same period.
- Looking at Ulcer Index in of 12 in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (4 ).

'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:- Looking at the maximum drop from peak to valley of -38.7 days in the last 5 years of Take-Two Interactive Software, we see it is relatively lower, thus worse in comparison to the benchmark SPY (-19.3 days)
- Looking at maximum reduction from previous high in of -38.7 days in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (-19.3 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:- Looking at the maximum time in days below previous high water mark of 119 days in the last 5 years of Take-Two Interactive Software, we see it is relatively smaller, thus better in comparison to the benchmark SPY (187 days)
- Compared with SPY (131 days) in the period of the last 3 years, the maximum days under water of 117 days is smaller, thus better.

'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:- Looking at the average days below previous high of 28 days in the last 5 years of Take-Two Interactive Software, we see it is relatively lower, thus better in comparison to the benchmark SPY (39 days)
- During the last 3 years, the average days below previous high is 28 days, which is lower, thus better than the value of 33 days from the benchmark.

Historical returns have been extended using synthetic data.
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- "Year" returns in the table above are not equal to the sum of monthly returns due to compounding.
- Performance results of Take-Two Interactive Software are hypothetical, do not account for slippage, fees or taxes, and are based on backtesting, which has many inherent limitations, some of which are described in our Terms of Use.