'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:- Compared with the benchmark SPY (103.4%) in the period of the last 5 years, the total return, or increase in value of 229.1% of Alphabet is larger, thus better.
- Compared with SPY (33.4%) in the period of the last 3 years, the total return, or increase in value of 41.3% is higher, thus better.

'Compound annual growth rate (CAGR) is a business and investing specific term for the geometric progression ratio that provides a constant rate of return over the time period. CAGR is not an accounting term, but it is often used to describe some element of the business, for example revenue, units delivered, registered users, etc. CAGR dampens the effect of volatility of periodic returns that can render arithmetic means irrelevant. It is particularly useful to compare growth rates from various data sets of common domain such as revenue growth of companies in the same industry.'

Applying this definition to our asset in some examples:- The compounded annual growth rate (CAGR) over 5 years of Alphabet is 26.9%, which is higher, thus better compared to the benchmark SPY (15.3%) in the same period.
- Compared with SPY (10.1%) in the period of the last 3 years, the annual return (CAGR) of 12.2% is greater, thus better.

'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.'

Using this definition on our asset we see for example:- The historical 30 days volatility over 5 years of Alphabet is 32%, which is higher, 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 volatility of 31.7% is larger, 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.'

Which means for our asset as example:- Looking at the downside deviation of 21.8% in the last 5 years of Alphabet, we see it is relatively larger, thus worse in comparison to the benchmark SPY (14.9%)
- Looking at downside volatility in of 22% in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (12.1%).

'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:- Looking at the Sharpe Ratio of 0.76 in the last 5 years of Alphabet, we see it is relatively higher, thus better in comparison to the benchmark SPY (0.61)
- Looking at Sharpe Ratio in of 0.31 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.44).

'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 downside risk / excess return profile of 1.12 of Alphabet is higher, thus better.
- Looking at downside risk / excess return profile in of 0.44 in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (0.63).

'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:- Looking at the Ulcer Ratio of 16 in the last 5 years of Alphabet, we see it is relatively higher, thus worse in comparison to the benchmark SPY (9.32 )
- Looking at Ulcer Index in of 20 in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (10 ).

'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:- Looking at the maximum drop from peak to valley of -44.6 days in the last 5 years of Alphabet, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (-33.7 days)
- Compared with SPY (-24.5 days) in the period of the last 3 years, the maximum DrawDown of -44.6 days is lower, thus worse.

'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:- Looking at the maximum days below previous high of 546 days in the last 5 years of Alphabet, we see it is relatively greater, thus worse in comparison to the benchmark SPY (488 days)
- During the last 3 years, the maximum time in days below previous high water mark is 546 days, which is larger, 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.'

Which means for our asset as example:- Looking at the average time in days below previous high water mark of 142 days in the last 5 years of Alphabet, we see it is relatively greater, thus worse in comparison to the benchmark SPY (123 days)
- Looking at average days under water in of 212 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 Alphabet are hypothetical and do not account for slippage, fees or taxes.