'The total return on a portfolio of investments takes into account not only the capital appreciation on the portfolio, but also the income received on the portfolio. The income typically consists of interest, dividends, and securities lending fees. This contrasts with the price return, which takes into account only the capital gain on an investment.'

Applying this definition to our asset in some examples:- The total return over 5 years of Vanguard Pacific Stock Index Fund is 6.4%, which is smaller, thus worse compared to the benchmark SPY (68.1%) in the same period.
- Compared with SPY (47%) in the period of the last 3 years, the total return, or performance of 20.1% is lower, thus worse.

'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 (11%) in the period of the last 5 years, the annual performance (CAGR) of 1.2% of Vanguard Pacific Stock Index Fund is smaller, thus worse.
- Looking at annual performance (CAGR) in of 6.3% in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (13.7%).

'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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (21.4%) in the period of the last 5 years, the 30 days standard deviation of 17.6% of Vanguard Pacific Stock Index Fund is lower, thus better.
- During the last 3 years, the volatility is 15.7%, which is lower, thus better than the value of 18.7% from the benchmark.

'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.'

Using this definition on our asset we see for example:- The downside deviation over 5 years of Vanguard Pacific Stock Index Fund is 12.9%, which is lower, thus better compared to the benchmark SPY (15.4%) in the same period.
- Looking at downside deviation in of 11% in the period of the last 3 years, we see it is relatively lower, thus better in comparison to SPY (13.3%).

'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:- The Sharpe Ratio over 5 years of Vanguard Pacific Stock Index Fund is -0.07, which is lower, thus worse compared to the benchmark SPY (0.4) in the same period.
- Compared with SPY (0.6) in the period of the last 3 years, the Sharpe Ratio of 0.24 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:- Compared with the benchmark SPY (0.55) in the period of the last 5 years, the excess return divided by the downside deviation of -0.1 of Vanguard Pacific Stock Index Fund is lower, thus worse.
- Looking at downside risk / excess return profile in of 0.34 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.84).

'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 12 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 (9.45 )
- Looking at Ulcer Ratio in of 13 in the period of the last 3 years, we see it is relatively greater, 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.'

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 drop from peak to valley of -31.3 days of Vanguard Pacific Stock Index Fund is higher, thus better.
- Looking at maximum DrawDown in of -31.3 days in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (-24.5 days).

'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:- Compared with the benchmark SPY (351 days) in the period of the last 5 years, the maximum days below previous high of 427 days of Vanguard Pacific Stock Index Fund is larger, thus worse.
- Compared with SPY (351 days) in the period of the last 3 years, the maximum days below previous high of 427 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (78 days) in the period of the last 5 years, the average time in days below previous high water mark of 160 days of Vanguard Pacific Stock Index Fund is greater, thus worse.
- Compared with SPY (101 days) in the period of the last 3 years, the average days below previous high of 140 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.