'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.'

Which means for our asset as example:- Looking at the total return, or increase in value of 41.9% 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 (97.7%)
- Looking at total return, or increase in value in of 3.1% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (26%).

'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 compounded annual growth rate (CAGR) of 7.3% 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 (14.6%)
- Compared with SPY (8%) in the period of the last 3 years, the annual return (CAGR) of 1% is smaller, thus worse.

'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (20.9%) in the period of the last 5 years, the volatility of 19.1% of Vanguard Developed Markets Index Fund is lower, thus better.
- During the last 3 years, the 30 days standard deviation is 16.1%, which is lower, thus better than the value of 17.5% from the benchmark.

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

Which means for our asset as example:- The downside deviation over 5 years of Vanguard Developed Markets Index Fund is 13.9%, which is lower, thus better compared to the benchmark SPY (15%) in the same period.
- Looking at downside volatility in of 11.2% in the period of the last 3 years, we see it is relatively smaller, thus better in comparison to SPY (12.3%).

'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.'

Using this definition on our asset we see for example:- Looking at the risk / return profile (Sharpe) of 0.25 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 (0.58)
- During the last 3 years, the risk / return profile (Sharpe) is -0.09, which is lower, thus worse than the value of 0.32 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.'

Using this definition on our asset we see for example:- Looking at the ratio of annual return and downside deviation of 0.34 in the last 5 years of Vanguard Developed Markets Index Fund, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (0.81)
- During the last 3 years, the excess return divided by the downside deviation is -0.13, which is lower, thus worse than the value of 0.45 from the benchmark.

'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:- The Downside risk index over 5 years of Vanguard Developed Markets Index Fund is 11 , which is higher, thus worse compared to the benchmark SPY (9.32 ) in the same period.
- Looking at Ulcer Index in of 12 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.'

Applying this definition to our asset in some examples:- The maximum drop from peak to valley 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.
- During the last 3 years, the maximum DrawDown is -29.7 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.'

Using this definition on our asset we see for example:- Looking at the maximum days below previous high of 627 days 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 (488 days)
- During the last 3 years, the maximum time in days below previous high water mark is 627 days, which is larger, thus worse than the value of 488 days from the benchmark.

'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 days under water over 5 years of Vanguard Developed Markets Index Fund is 191 days, which is greater, thus worse compared to the benchmark SPY (123 days) in the same period.
- Compared with SPY (179 days) in the period of the last 3 years, the average days under water of 270 days is higher, thus worse.

Historical returns have been extended using synthetic data.
[Show Details]

- 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 and do not account for slippage, fees or taxes.