'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 (72.5%) in the period of the last 5 years, the total return, or performance of 31.4% of Vanguard Pacific Stock Index Fund is lower, thus worse.
- Looking at total return, or increase in value in of 2% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (34.1%).

'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:- The compounded annual growth rate (CAGR) over 5 years of Vanguard Pacific Stock Index Fund is 5.6%, which is lower, thus worse compared to the benchmark SPY (11.5%) in the same period.
- During the last 3 years, the compounded annual growth rate (CAGR) is 0.7%, which is lower, thus worse than the value of 10.3% from the benchmark.

'Volatility is a statistical measure of the dispersion of returns for a given security or market index. Volatility can either be measured by using the standard deviation or variance between returns from that same security or market index. Commonly, the higher the volatility, the riskier the security. In the securities markets, volatility is often associated with big swings in either direction. For example, when the stock market rises and falls more than one percent over a sustained period of time, it is called a 'volatile' market.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (18.9%) in the period of the last 5 years, the 30 days standard deviation of 16.4% of Vanguard Pacific Stock Index Fund is smaller, thus better.
- Looking at historical 30 days volatility in of 18.4% in the period of the last 3 years, we see it is relatively lower, thus better in comparison to SPY (22.6%).

'Downside risk is the financial risk associated with losses. That is, it is the risk of the actual return being below the expected return, or the uncertainty about the magnitude of that difference. 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 12% 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 (13.8%)
- During the last 3 years, the downside risk is 13.8%, which is smaller, thus better than the value of 16.7% from the benchmark.

'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 Pacific Stock Index Fund is 0.19, which is smaller, thus worse compared to the benchmark SPY (0.48) in the same period.
- Looking at Sharpe Ratio in of -0.1 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.34).

'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.'

Applying this definition to our asset in some examples:- The excess return divided by the downside deviation over 5 years of Vanguard Pacific Stock Index Fund is 0.26, which is smaller, thus worse compared to the benchmark SPY (0.65) in the same period.
- Compared with SPY (0.47) in the period of the last 3 years, the ratio of annual return and downside deviation of -0.13 is lower, thus worse.

'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:- The Ulcer Index over 5 years of Vanguard Pacific Stock Index Fund is 9.73 , which is larger, thus worse compared to the benchmark SPY (5.83 ) in the same period.
- During the last 3 years, the Downside risk index is 12 , which is higher, thus worse than the value of 7.13 from the benchmark.

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (-33.7 days) in the period of the last 5 years, the maximum reduction from previous high of -33.9 days of Vanguard Pacific Stock Index Fund is lower, thus worse.
- During the last 3 years, the maximum reduction from previous high is -33.9 days, which is smaller, thus worse than the value of -33.7 days from the benchmark.

'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'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (139 days) in the period of the last 5 years, the maximum days below previous high of 696 days of Vanguard Pacific Stock Index Fund is larger, thus worse.
- Looking at maximum time in days below previous high water mark in of 696 days in the period of the last 3 years, we see it is relatively larger, 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.'

Which means for our asset as example:- The average days below previous high over 5 years of Vanguard Pacific Stock Index Fund is 219 days, which is larger, thus worse compared to the benchmark SPY (37 days) in the same period.
- Compared with SPY (45 days) in the period of the last 3 years, the average days under water of 332 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 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.