'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:- Compared with the benchmark SPY (103.4%) in the period of the last 5 years, the total return, or performance of 29.4% of Vanguard Pacific Stock Index Fund is lower, thus worse.
- Looking at total return, or performance in of -4.8% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (33.4%).

'The compound annual growth rate isn't a true return rate, but rather a representational figure. It is essentially a number that describes the rate at which an investment would have grown if it had grown the same rate every year and the profits were reinvested at the end of each year. In reality, this sort of performance is unlikely. However, CAGR can be used to smooth returns so that they may be more easily understood when compared to alternative investments.'

Using this definition on our asset we see for example:- Looking at the compounded annual growth rate (CAGR) of 5.3% in the last 5 years of Vanguard Pacific Stock Index Fund, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (15.3%)
- Looking at annual return (CAGR) in of -1.6% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (10.1%).

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (20.9%) in the period of the last 5 years, the volatility of 17.7% of Vanguard Pacific Stock Index Fund is smaller, thus better.
- Compared with SPY (17.3%) in the period of the last 3 years, the 30 days standard deviation of 15% is lower, thus better.

'The downside volatility is similar to the volatility, or standard deviation, but only takes losing/negative periods into account.'

Applying this definition to our asset in some examples:- The downside risk over 5 years of Vanguard Pacific Stock Index Fund is 12.8%, which is smaller, thus better compared to the benchmark SPY (14.9%) in the same period.
- Compared with SPY (12.1%) in the period of the last 3 years, the downside risk of 10.6% is lower, thus better.

'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.'

Applying this definition to our asset in some examples:- The ratio of return and volatility (Sharpe) over 5 years of Vanguard Pacific Stock Index Fund is 0.16, which is smaller, thus worse compared to the benchmark SPY (0.61) in the same period.
- Looking at ratio of return and volatility (Sharpe) in of -0.28 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.44).

'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.'

Using this definition on our asset we see for example:- The excess return divided by the downside deviation over 5 years of Vanguard Pacific Stock Index Fund is 0.22, which is lower, thus worse compared to the benchmark SPY (0.85) in the same period.
- Compared with SPY (0.63) in the period of the last 3 years, the downside risk / excess return profile of -0.39 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.'

Which means for our asset as example:- The Downside risk index over 5 years of Vanguard Pacific Stock Index Fund is 13 , which is greater, thus worse compared to the benchmark SPY (9.32 ) in the same period.
- Looking at Ulcer Index in of 15 in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (10 ).

'A maximum drawdown is the maximum loss from a peak to a trough of a portfolio, before a new peak is attained. Maximum Drawdown is an indicator of downside risk over a specified time period. It can be used both as a stand-alone measure or as an input into other metrics such as 'Return over Maximum Drawdown' and the Calmar Ratio. Maximum Drawdown is expressed in percentage terms.'

Using this definition on our asset we see for example:- Looking at the maximum drop from peak to valley of -31.3 days in the last 5 years of Vanguard Pacific Stock Index Fund, we see it is relatively greater, thus better in comparison to the benchmark SPY (-33.7 days)
- During the last 3 years, the maximum reduction from previous high is -31.3 days, which is lower, thus worse than the value of -24.5 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) in days.'

Which means for our asset as example:- Looking at the maximum days below previous high of 691 days in the last 5 years of Vanguard Pacific Stock Index Fund, we see it is relatively greater, thus worse in comparison to the benchmark SPY (488 days)
- Compared with SPY (488 days) in the period of the last 3 years, the maximum time in days below previous high water mark of 691 days is greater, 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.'

Which means for our asset as example:- The average days under water over 5 years of Vanguard Pacific Stock Index Fund is 225 days, which is greater, thus worse compared to the benchmark SPY (123 days) in the same period.
- During the last 3 years, the average days under water is 320 days, which is larger, thus worse than the value of 180 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 Pacific Stock Index Fund are hypothetical and do not account for slippage, fees or taxes.