'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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (60.7%) in the period of the last 5 years, the total return, or increase in value of -2.1% of Vanguard Total International Stock Index Fund is lower, thus worse.
- During the last 3 years, the total return, or increase in value is -2.4%, which is lower, thus worse than the value of 29.5% from the benchmark.

'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 (10%) in the period of the last 5 years, the annual performance (CAGR) of -0.4% of Vanguard Total International Stock Index Fund is lower, thus worse.
- During the last 3 years, the compounded annual growth rate (CAGR) is -0.8%, which is lower, thus worse than the value of 9% 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.'

Which means for our asset as example:- The historical 30 days volatility over 5 years of Vanguard Total International Stock Index Fund is 17.8%, which is lower, thus better compared to the benchmark SPY (20.8%) in the same period.
- During the last 3 years, the 30 days standard deviation is 20.8%, which is lower, thus better than the value of 24% 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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (15.3%) in the period of the last 5 years, the downside volatility of 13.5% of Vanguard Total International Stock Index Fund is lower, thus better.
- Compared with SPY (17.6%) in the period of the last 3 years, the downside deviation of 15.8% is lower, 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.'

Which means for our asset as example:- Compared with the benchmark SPY (0.36) in the period of the last 5 years, the risk / return profile (Sharpe) of -0.16 of Vanguard Total International Stock Index Fund is lower, thus worse.
- During the last 3 years, the risk / return profile (Sharpe) is -0.16, which is lower, thus worse than the value of 0.27 from the benchmark.

'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.'

Which means for our asset as example:- The excess return divided by the downside deviation over 5 years of Vanguard Total International Stock Index Fund is -0.22, which is lower, thus worse compared to the benchmark SPY (0.49) in the same period.
- Looking at downside risk / excess return profile in of -0.21 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.37).

'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:- Looking at the Ulcer Index of 11 in the last 5 years of Vanguard Total International Stock Index Fund, we see it is relatively larger, thus worse in comparison to the benchmark SPY (7.52 )
- Looking at Ulcer Ratio in of 11 in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (8.81 ).

'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:- Compared with the benchmark SPY (-33.7 days) in the period of the last 5 years, the maximum reduction from previous high of -35.9 days of Vanguard Total International Stock Index Fund is smaller, thus worse.
- During the last 3 years, the maximum drop from peak to valley is -34.8 days, which is lower, 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'

Which means for our asset as example:- Compared with the benchmark SPY (182 days) in the period of the last 5 years, the maximum days below previous high of 706 days of Vanguard Total International Stock Index Fund is larger, thus worse.
- Compared with SPY (182 days) in the period of the last 3 years, the maximum time in days below previous high water mark of 323 days is greater, 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.'

Applying this definition to our asset in some examples:- The average days under water over 5 years of Vanguard Total International Stock Index Fund is 257 days, which is higher, thus worse compared to the benchmark SPY (45 days) in the same period.
- Looking at average days below previous high in of 110 days in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (43 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 Total International 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.