'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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (98.3%) in the period of the last 5 years, the total return of 54.3% of Vanguard Small Cap Index Fund is smaller, thus worse.
- During the last 3 years, the total return, or increase in value is 3.7%, which is lower, thus worse than the value of 27.2% from the benchmark.

'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 (14.7%) in the period of the last 5 years, the annual performance (CAGR) of 9.1% of Vanguard Small Cap Index Fund is smaller, thus worse.
- Looking at compounded annual growth rate (CAGR) in of 1.2% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (8.4%).

'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:- The historical 30 days volatility over 5 years of Vanguard Small Cap Index Fund is 25.6%, which is higher, thus worse compared to the benchmark SPY (20.9%) in the same period.
- During the last 3 years, the 30 days standard deviation is 21.6%, which is greater, thus worse than the value of 17.7% from the benchmark.

'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:- Compared with the benchmark SPY (14.9%) in the period of the last 5 years, the downside volatility of 18.5% of Vanguard Small Cap Index Fund is greater, thus worse.
- Looking at downside volatility in of 15.2% in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (12.4%).

'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:- Compared with the benchmark SPY (0.58) in the period of the last 5 years, the risk / return profile (Sharpe) of 0.26 of Vanguard Small Cap Index Fund is smaller, thus worse.
- During the last 3 years, the risk / return profile (Sharpe) is -0.06, which is lower, thus worse than the value of 0.33 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (0.82) in the period of the last 5 years, the excess return divided by the downside deviation of 0.35 of Vanguard Small Cap Index Fund is lower, thus worse.
- During the last 3 years, the downside risk / excess return profile is -0.08, which is lower, thus worse than the value of 0.47 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 14 in the last 5 years of Vanguard Small Cap Index Fund, we see it is relatively greater, thus worse in comparison to the benchmark SPY (9.32 )
- Looking at Downside risk index in of 15 in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (10 ).

'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:- Looking at the maximum drop from peak to valley of -41.8 days in the last 5 years of Vanguard Small Cap Index Fund, 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 reduction from previous high of -28.2 days is smaller, 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.'

Applying this definition to our asset in some examples:- The maximum days under water over 5 years of Vanguard Small Cap Index Fund is 672 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 time in days below previous high water mark of 672 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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (123 days) in the period of the last 5 years, the average days below previous high of 209 days of Vanguard Small Cap Index Fund is higher, thus worse.
- Compared with SPY (177 days) in the period of the last 3 years, the average days below previous high of 307 days is greater, 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 Small Cap Index Fund are hypothetical and do not account for slippage, fees or taxes.