'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (94.9%) in the period of the last 5 years, the total return, or performance of 50.4% of Vanguard Extended Market Index Fund is lower, thus worse.
- Compared with SPY (22.5%) in the period of the last 3 years, the total return, or increase in value of -9.8% is lower, thus worse.

'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.'

Using this definition on our asset we see for example:- Looking at the annual return (CAGR) of 8.5% in the last 5 years of Vanguard Extended Market Index Fund, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (14.3%)
- Looking at compounded annual growth rate (CAGR) in of -3.4% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (7%).

'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.'

Applying this definition to our asset in some examples:- The 30 days standard deviation over 5 years of Vanguard Extended Market Index Fund is 26.5%, which is higher, thus worse compared to the benchmark SPY (20.9%) in the same period.
- Looking at historical 30 days volatility in of 23.2% in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (17.5%).

'The downside volatility is similar to the volatility, or standard deviation, but only takes losing/negative periods into account.'

Which means for our asset as example:- Looking at the downside volatility of 19.3% in the last 5 years of Vanguard Extended Market Index Fund, we see it is relatively higher, thus worse in comparison to the benchmark SPY (15%)
- Looking at downside volatility in of 16.6% in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (12.3%).

'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (0.56) in the period of the last 5 years, the Sharpe Ratio of 0.23 of Vanguard Extended Market Index Fund is smaller, thus worse.
- During the last 3 years, the risk / return profile (Sharpe) is -0.25, which is smaller, thus worse than the value of 0.26 from the benchmark.

'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:- The excess return divided by the downside deviation over 5 years of Vanguard Extended Market Index Fund is 0.31, which is lower, thus worse compared to the benchmark SPY (0.79) in the same period.
- During the last 3 years, the ratio of annual return and downside deviation is -0.36, which is lower, thus worse than the value of 0.37 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:- Looking at the Ulcer Ratio of 19 in the last 5 years of Vanguard Extended Market Index Fund, we see it is relatively greater, thus worse in comparison to the benchmark SPY (9.32 )
- Compared with SPY (10 ) in the period of the last 3 years, the Ulcer Index of 23 is higher, thus worse.

'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 DrawDown of -41.6 days of Vanguard Extended Market Index Fund is smaller, thus worse.
- Compared with SPY (-24.5 days) in the period of the last 3 years, the maximum drop from peak to valley of -36.4 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) in days.'

Using this definition on our asset we see for example:- The maximum days below previous high over 5 years of Vanguard Extended Market Index Fund is 689 days, which is larger, 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 689 days is greater, 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.'

Which means for our asset as example:- The average days below previous high over 5 years of Vanguard Extended Market Index Fund is 216 days, which is greater, thus worse compared to the benchmark SPY (123 days) in the same period.
- Compared with SPY (179 days) in the period of the last 3 years, the average days below previous high of 321 days is larger, thus worse.

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 Vanguard Extended Market Index Fund are hypothetical and do not account for slippage, fees or taxes.