'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, or performance over 5 years of Vanguard Developed Markets Index Fund is 37.9%, which is lower, thus worse compared to the benchmark SPY (94.8%) in the same period.
- Looking at total return, or performance in of 7.5% in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (31.6%).

'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:- Looking at the annual performance (CAGR) of 6.7% in the last 5 years of Vanguard Developed Markets Index Fund, we see it is relatively lower, thus worse in comparison to the benchmark SPY (14.3%)
- Looking at compounded annual growth rate (CAGR) in of 2.4% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (9.6%).

'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 (20.9%) in the period of the last 5 years, the historical 30 days volatility of 19% of Vanguard Developed Markets Index Fund is smaller, thus better.
- Looking at volatility in of 16% in the period of the last 3 years, we see it is relatively lower, thus better in comparison to SPY (17.3%).

'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%) in the period of the last 5 years, the downside risk of 13.8% of Vanguard Developed Markets Index Fund is lower, thus better.
- Compared with SPY (12.1%) in the period of the last 3 years, the downside volatility of 11% is lower, thus better.

'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.'

Using this definition on our asset we see for example:- Looking at the Sharpe Ratio of 0.22 in the last 5 years of Vanguard Developed Markets Index Fund, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.56)
- During the last 3 years, the Sharpe Ratio is 0, which is smaller, thus worse than the value of 0.41 from the benchmark.

'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.'

Which means for our asset as example:- The excess return divided by the downside deviation over 5 years of Vanguard Developed Markets Index Fund is 0.3, which is lower, thus worse compared to the benchmark SPY (0.79) in the same period.
- Compared with SPY (0.59) in the period of the last 3 years, the ratio of annual return and downside deviation of -0.01 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:- Looking at the Ulcer Index of 11 in the last 5 years of Vanguard Developed Markets Index Fund, we see it is relatively greater, thus worse in comparison to the benchmark SPY (9.33 )
- During the last 3 years, the Ulcer Ratio is 12 , which is higher, thus worse than the value of 10 from the benchmark.

'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:- The maximum reduction from previous high over 5 years of Vanguard Developed Markets Index Fund is -35.1 days, which is lower, thus worse compared to the benchmark SPY (-33.7 days) in the same period.
- Compared with SPY (-24.5 days) in the period of the last 3 years, the maximum DrawDown of -29.7 days is lower, thus worse.

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (488 days) in the period of the last 5 years, the maximum days below previous high of 627 days of Vanguard Developed Markets Index Fund is greater, thus worse.
- Looking at maximum time in days below previous high water mark in of 627 days in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (488 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (123 days) in the period of the last 5 years, the average time in days below previous high water mark of 191 days of Vanguard Developed Markets Index Fund is larger, thus worse.
- During the last 3 years, the average time in days below previous high water mark is 271 days, which is larger, thus worse than the value of 179 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 Developed Markets 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.