'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:- The total return, or performance over 5 years of Vanguard Total International Stock Index Fund is 34.7%, which is lower, thus worse compared to the benchmark SPY (94.9%) in the same period.
- Compared with SPY (22.5%) in the period of the last 3 years, the total return of -1.6% 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (14.3%) in the period of the last 5 years, the annual performance (CAGR) of 6.2% of Vanguard Total International Stock Index Fund is lower, thus worse.
- Compared with SPY (7%) in the period of the last 3 years, the annual return (CAGR) of -0.5% is lower, 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.'

Which means for our asset as example:- Looking at the 30 days standard deviation of 18.3% in the last 5 years of Vanguard Total International Stock Index Fund, we see it is relatively lower, thus better in comparison to the benchmark SPY (20.9%)
- Compared with SPY (17.5%) in the period of the last 3 years, the historical 30 days volatility of 15.2% is smaller, thus better.

'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:- Looking at the downside volatility of 13.4% in the last 5 years of Vanguard Total International Stock Index Fund, we see it is relatively lower, thus better in comparison to the benchmark SPY (15%)
- Looking at downside volatility in of 10.6% in the period of the last 3 years, we see it is relatively lower, thus better in comparison to SPY (12.3%).

'The Sharpe ratio (also known as the Sharpe index, the Sharpe measure, and the reward-to-variability ratio) is a way to examine the performance of an investment by adjusting for its risk. The ratio measures the excess return (or risk premium) per unit of deviation in an investment asset or a trading strategy, typically referred to as risk, named after William F. Sharpe.'

Which means for our asset as example:- Compared with the benchmark SPY (0.56) in the period of the last 5 years, the risk / return profile (Sharpe) of 0.2 of Vanguard Total International Stock Index Fund is smaller, thus worse.
- During the last 3 years, the risk / return profile (Sharpe) is -0.2, which is lower, thus worse than the value of 0.26 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.'

Applying this definition to our asset in some examples:- The excess return divided by the downside deviation over 5 years of Vanguard Total International Stock Index Fund is 0.27, which is smaller, thus worse compared to the benchmark SPY (0.79) in the same period.
- During the last 3 years, the downside risk / excess return profile is -0.29, which is smaller, thus worse than the value of 0.37 from the benchmark.

'The Ulcer Index is a technical indicator that measures downside risk, in terms of both the depth and duration of price declines. The index increases in value as the price moves farther away from a recent high and falls as the price rises to new highs. The indicator is usually calculated over a 14-day period, with the Ulcer Index showing the percentage drawdown a trader can expect from the high over that period. The greater the value of the Ulcer Index, the longer it takes for a stock to get back to the former high.'

Which means for our asset as example:- Compared with the benchmark SPY (9.32 ) in the period of the last 5 years, the Ulcer Index of 12 of Vanguard Total International Stock Index Fund is higher, thus worse.
- Looking at Ulcer Index 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 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.'

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 -34.8 days of Vanguard Total International Stock Index Fund is lower, thus worse.
- During the last 3 years, the maximum reduction from previous high is -29.6 days, which is lower, thus worse than the value of -24.5 days from the benchmark.

'The Maximum 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. It is the length of time the account was in the Max Drawdown. A Max Drawdown measures a retrenchment from when an equity curve reaches a new high. It’s the maximum an account lost during that retrenchment. This method is applied because a valley can’t be measured until a new high occurs. Once the new high is reached, the percentage change from the old high to the bottom of the largest trough is recorded.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (488 days) in the period of the last 5 years, the maximum days below previous high of 734 days of Vanguard Total International Stock Index Fund is higher, thus worse.
- Compared with SPY (488 days) in the period of the last 3 years, the maximum days under water of 674 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.'

Applying this definition to our asset in some examples:- The average time in days below previous high water mark over 5 years of Vanguard Total International Stock Index Fund is 251 days, which is greater, thus worse compared to the benchmark SPY (123 days) in the same period.
- Looking at average days below previous high in of 309 days in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (179 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 and do not account for slippage, fees or taxes.