'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.'

Which means for our asset as example:- Looking at the total return of 25.6% in the last 5 years of Activision Blizzard, we see it is relatively lower, thus worse in comparison to the benchmark SPY (103%)
- During the last 3 years, the total return, or increase in value is 19%, which is lower, thus worse than the value of 33.6% 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:- Compared with the benchmark SPY (15.2%) in the period of the last 5 years, the annual return (CAGR) of 4.7% of Activision Blizzard is lower, thus worse.
- Compared with SPY (10.1%) in the period of the last 3 years, the annual performance (CAGR) of 6% is lower, thus worse.

'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.'

Using this definition on our asset we see for example:- The volatility over 5 years of Activision Blizzard is 33.9%, which is larger, thus worse compared to the benchmark SPY (20.9%) in the same period.
- Compared with SPY (17.3%) in the period of the last 3 years, the historical 30 days volatility of 28.7% is larger, 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (14.9%) in the period of the last 5 years, the downside volatility of 23.7% of Activision Blizzard is larger, thus worse.
- Compared with SPY (12.1%) in the period of the last 3 years, the downside deviation of 18.2% is larger, thus worse.

'The Sharpe ratio (also known as the Sharpe index, the Sharpe measure, and the reward-to-variability ratio) is a way to examine the performance of an investment by adjusting for its risk. The ratio measures the excess return (or risk premium) per unit of deviation in an investment asset or a trading strategy, typically referred to as risk, named after William F. Sharpe.'

Using this definition on our asset we see for example:- The risk / return profile (Sharpe) over 5 years of Activision Blizzard is 0.06, which is smaller, thus worse compared to the benchmark SPY (0.61) in the same period.
- Compared with SPY (0.44) in the period of the last 3 years, the ratio of return and volatility (Sharpe) of 0.12 is lower, thus worse.

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (0.85) in the period of the last 5 years, the excess return divided by the downside deviation of 0.09 of Activision Blizzard is smaller, thus worse.
- During the last 3 years, the excess return divided by the downside deviation is 0.19, which is lower, thus worse than the value of 0.63 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.'

Applying this definition to our asset in some examples:- The Downside risk index over 5 years of Activision Blizzard is 25 , which is higher, thus worse compared to the benchmark SPY (9.32 ) in the same period.
- Compared with SPY (10 ) in the period of the last 3 years, the Ulcer Index of 21 is larger, thus worse.

'Maximum drawdown measures the loss in any losing period during a fund’s investment record. It is defined as the percent retrenchment from a fund’s peak value to the fund’s valley value. The drawdown is in effect from the time the fund’s retrenchment begins until a new fund high is reached. The maximum drawdown encompasses both the period from the fund’s peak to the fund’s valley (length), and the time from the fund’s valley to a new fund high (recovery). It measures the largest percentage drawdown that has occurred in any fund’s data record.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (-33.7 days) in the period of the last 5 years, the maximum reduction from previous high of -49.1 days of Activision Blizzard is lower, thus worse.
- During the last 3 years, the maximum drop from peak to valley is -44.6 days, which is lower, thus worse than the value of -24.5 days from the benchmark.

'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'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (488 days) in the period of the last 5 years, the maximum days below previous high of 668 days of Activision Blizzard is greater, thus worse.
- Compared with SPY (488 days) in the period of the last 3 years, the maximum days below previous high of 668 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:- Looking at the average time in days below previous high water mark of 260 days in the last 5 years of Activision Blizzard, we see it is relatively larger, thus worse in comparison to the benchmark SPY (123 days)
- Looking at average time in days below previous high water mark in of 306 days in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (180 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 Activision Blizzard are hypothetical and do not account for slippage, fees or taxes.