'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:- The total return, or performance over 5 years of Vanguard Pacific Stock Index Fund is 2.6%, which is smaller, thus worse compared to the benchmark SPY (46.1%) in the same period.
- Compared with SPY (23.5%) in the period of the last 3 years, the total return, or increase in value of -2.2% 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.'

Applying this definition to our asset in some examples:- The annual performance (CAGR) over 5 years of Vanguard Pacific Stock Index Fund is 0.5%, which is smaller, thus worse compared to the benchmark SPY (7.9%) in the same period.
- Compared with SPY (7.3%) in the period of the last 3 years, the annual return (CAGR) of -0.7% is smaller, thus worse.

'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 historical 30 days volatility over 5 years of Vanguard Pacific Stock Index Fund is 16.4%, which is smaller, thus better compared to the benchmark SPY (18.3%) in the same period.
- Compared with SPY (20.8%) in the period of the last 3 years, the volatility of 16.9% is lower, thus better.

'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 volatility of 12.3% in the last 5 years of Vanguard Pacific Stock Index Fund, we see it is relatively lower, thus better in comparison to the benchmark SPY (13.4%)
- Compared with SPY (15.4%) in the period of the last 3 years, the downside deviation of 12.9% is smaller, thus better.

'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 risk / return profile (Sharpe) of -0.12 in the last 5 years of Vanguard Pacific Stock Index Fund, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.29)
- Compared with SPY (0.23) in the period of the last 3 years, the ratio of return and volatility (Sharpe) of -0.19 is lower, thus worse.

'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:- The downside risk / excess return profile over 5 years of Vanguard Pacific Stock Index Fund is -0.16, which is lower, thus worse compared to the benchmark SPY (0.4) in the same period.
- During the last 3 years, the ratio of annual return and downside deviation is -0.25, which is smaller, thus worse than the value of 0.31 from the benchmark.

'The ulcer index is a stock market risk measure or technical analysis indicator devised by Peter Martin in 1987, and published by him and Byron McCann in their 1989 book The Investors Guide to Fidelity Funds. It's designed as a measure of volatility, but only volatility in the downward direction, i.e. the amount of drawdown or retracement occurring over a period. Other volatility measures like standard deviation treat up and down movement equally, but a trader doesn't mind upward movement, it's the downside that causes stress and stomach ulcers that the index's name suggests.'

Applying this definition to our asset in some examples:- The Ulcer Ratio over 5 years of Vanguard Pacific Stock Index Fund is 11 , which is greater, thus worse compared to the benchmark SPY (5.27 ) in the same period.
- During the last 3 years, the Downside risk index is 11 , which is greater, thus worse than the value of 6.08 from the benchmark.

'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.'

Applying this definition to our asset in some examples:- The maximum reduction from previous high over 5 years of Vanguard Pacific Stock Index Fund is -33.9 days, which is smaller, thus worse compared to the benchmark SPY (-33.7 days) in the same period.
- Compared with SPY (-33.7 days) in the period of the last 3 years, the maximum drop from peak to valley of -33.9 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.'

Which means for our asset as example:- The maximum days under water over 5 years of Vanguard Pacific Stock Index Fund is 553 days, which is greater, thus worse compared to the benchmark SPY (187 days) in the same period.
- Looking at maximum time in days below previous high water mark in of 553 days in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (139 days).

'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 220 days in the last 5 years of Vanguard Pacific Stock Index Fund, we see it is relatively higher, thus worse in comparison to the benchmark SPY (42 days)
- Looking at average days under water in of 224 days in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (36 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 Vanguard Pacific Stock 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.