'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 over 5 years of Vanguard European Stock Index Fund is 48.9%, which is lower, thus worse compared to the benchmark SPY (111.3%) in the same period.
- Compared with SPY (39.3%) in the period of the last 3 years, the total return, or performance of 16.5% is smaller, thus worse.

'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 annual performance (CAGR) of 8.3% in the last 5 years of Vanguard European Stock Index Fund, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (16.2%)
- Compared with SPY (11.7%) in the period of the last 3 years, the annual return (CAGR) of 5.2% is smaller, thus worse.

'Volatility is a rate at which the price of a security increases or decreases for a given set of returns. Volatility is measured by calculating the standard deviation of the annualized returns over a given period of time. It shows the range to which the price of a security may increase or decrease. Volatility measures the risk of a security. It is used in option pricing formula to gauge the fluctuations in the returns of the underlying assets. Volatility indicates the pricing behavior of the security and helps estimate the fluctuations that may happen in a short period of time.'

Applying this definition to our asset in some examples:- The historical 30 days volatility over 5 years of Vanguard European Stock Index Fund is 21.1%, which is larger, thus worse compared to the benchmark SPY (20.9%) in the same period.
- During the last 3 years, the volatility is 18.3%, which is higher, thus worse 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:- Looking at the downside volatility of 15.4% in the last 5 years of Vanguard European Stock Index Fund, we see it is relatively higher, thus worse in comparison to the benchmark SPY (14.9%)
- Compared with SPY (12.2%) in the period of the last 3 years, the downside deviation of 12.5% is larger, thus worse.

'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 (0.66) in the period of the last 5 years, the Sharpe Ratio of 0.28 of Vanguard European Stock Index Fund is smaller, thus worse.
- Compared with SPY (0.53) in the period of the last 3 years, the Sharpe Ratio of 0.15 is lower, thus worse.

'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:- Compared with the benchmark SPY (0.92) in the period of the last 5 years, the ratio of annual return and downside deviation of 0.38 of Vanguard European Stock Index Fund is lower, thus worse.
- Looking at excess return divided by the downside deviation in of 0.22 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.75).

'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:- The Ulcer Index over 5 years of Vanguard European Stock Index Fund is 11 , which is higher, thus worse compared to the benchmark SPY (9.32 ) in the same period.
- Compared with SPY (10 ) in the period of the last 3 years, the Downside risk index of 12 is larger, thus worse.

'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 DrawDown of -36.6 days in the last 5 years of Vanguard European Stock Index Fund, we see it is relatively lower, thus worse in comparison to the benchmark SPY (-33.7 days)
- During the last 3 years, the maximum reduction from previous high is -32.5 days, which is smaller, 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). 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:- Looking at the maximum days below previous high of 619 days in the last 5 years of Vanguard European Stock 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 576 days, which is greater, thus worse than the value of 488 days from the benchmark.

'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.'

Using this definition on our asset we see for example:- Looking at the average time in days below previous high water mark of 189 days in the last 5 years of Vanguard European Stock Index Fund, we see it is relatively higher, thus worse in comparison to the benchmark SPY (124 days)
- During the last 3 years, the average time in days below previous high water mark is 233 days, which is higher, 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 European Stock Index Fund are hypothetical and do not account for slippage, fees or taxes.