'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, or performance of 29.8% in the last 5 years of Vanguard Extended Market Index Fund, we see it is relatively lower, thus worse in comparison to the benchmark SPY (61.3%)
- Compared with SPY (31.6%) in the period of the last 3 years, the total return, or performance of 16.7% is smaller, 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:- Compared with the benchmark SPY (10%) in the period of the last 5 years, the compounded annual growth rate (CAGR) of 5.4% of Vanguard Extended Market Index Fund is lower, thus worse.
- During the last 3 years, the annual return (CAGR) is 5.3%, which is smaller, thus worse than the value of 9.6% from the benchmark.

'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:- Looking at the historical 30 days volatility of 25.3% 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 (20.8%)
- Looking at volatility in of 30% in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (24%).

'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:- Looking at the downside deviation of 18.8% 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 (15.3%)
- Looking at downside volatility in of 22.3% in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (17.6%).

'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.'

Which means for our asset as example:- The risk / return profile (Sharpe) over 5 years of Vanguard Extended Market Index Fund is 0.11, which is lower, thus worse compared to the benchmark SPY (0.36) in the same period.
- During the last 3 years, the ratio of return and volatility (Sharpe) is 0.09, which is smaller, thus worse than the value of 0.3 from the benchmark.

'The Sortino ratio measures the risk-adjusted return of an investment asset, portfolio, or strategy. It is a modification of the Sharpe ratio but penalizes only those returns falling below a user-specified target or required rate of return, while the Sharpe ratio penalizes both upside and downside volatility equally. Though both ratios measure an investment's risk-adjusted return, they do so in significantly different ways that will frequently lead to differing conclusions as to the true nature of the investment's return-generating efficiency. The Sortino ratio is used as a way to compare the risk-adjusted performance of programs with differing risk and return profiles. In general, risk-adjusted returns seek to normalize the risk across programs and then see which has the higher return unit per risk.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (0.49) in the period of the last 5 years, the ratio of annual return and downside deviation of 0.15 of Vanguard Extended Market Index Fund is lower, thus worse.
- During the last 3 years, the downside risk / excess return profile is 0.12, which is lower, thus worse than the value of 0.4 from the benchmark.

'The Ulcer Index is a technical indicator that measures downside risk, in terms of both the depth and duration of price declines. The index increases in value as the price moves farther away from a recent high and falls as the price rises to new highs. The indicator is usually calculated over a 14-day period, with the Ulcer Index showing the percentage drawdown a trader can expect from the high over that period. The greater the value of the Ulcer Index, the longer it takes for a stock to get back to the former high.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (7.61 ) in the period of the last 5 years, the Ulcer Ratio of 12 of Vanguard Extended Market Index Fund is higher, thus worse.
- Compared with SPY (8.93 ) in the period of the last 3 years, the Ulcer Index of 15 is greater, 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.'

Which means for our asset as example:- The maximum drop from peak to valley over 5 years of Vanguard Extended Market Index Fund is -41.6 days, which is smaller, thus worse compared to the benchmark SPY (-33.7 days) in the same period.
- During the last 3 years, the maximum DrawDown is -41.6 days, which is smaller, thus worse than the value of -33.7 days from the benchmark.

'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.'

Using this definition on our asset we see for example:- The maximum days under water over 5 years of Vanguard Extended Market Index Fund is 309 days, which is greater, thus worse compared to the benchmark SPY (185 days) in the same period.
- Compared with SPY (185 days) in the period of the last 3 years, the maximum time in days below previous high water mark of 223 days is larger, thus worse.

'The Average 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. 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 79 days 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 (46 days)
- During the last 3 years, the average days under water is 57 days, which is larger, thus worse than the value of 44 days from the benchmark.

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, 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.