'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:- The total return, or increase in value over 5 years of Vanguard Small Cap Value Index Fund is 74%, which is lower, thus worse compared to the benchmark SPY (109.2%) in the same period.
- Compared with SPY (33.3%) in the period of the last 3 years, the total return, or performance of 21.3% 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:- The compounded annual growth rate (CAGR) over 5 years of Vanguard Small Cap Value Index Fund is 11.7%, which is smaller, thus worse compared to the benchmark SPY (15.9%) in the same period.
- Looking at annual return (CAGR) in of 6.7% in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (10.1%).

'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 26.6% of Vanguard Small Cap Value Index Fund is higher, thus worse.
- During the last 3 years, the historical 30 days volatility is 20.4%, which is greater, thus worse than the value of 17.6% from the benchmark.

'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.'

Which means for our asset as example:- The downside deviation over 5 years of Vanguard Small Cap Value Index Fund is 19%, which is higher, thus worse compared to the benchmark SPY (14.9%) in the same period.
- Looking at downside risk in of 14.1% in the period of the last 3 years, we see it is relatively higher, thus worse 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (0.64) in the period of the last 5 years, the Sharpe Ratio of 0.35 of Vanguard Small Cap Value Index Fund is lower, thus worse.
- During the last 3 years, the Sharpe Ratio is 0.2, which is lower, thus worse than the value of 0.43 from the benchmark.

'The Sortino ratio improves upon the Sharpe ratio by isolating downside volatility from total volatility by dividing excess return by the downside deviation. The Sortino ratio is a variation of the Sharpe ratio that differentiates harmful volatility from total overall volatility by using the asset's standard deviation of negative asset returns, called downside deviation. The Sortino ratio takes the asset's return and subtracts the risk-free rate, and then divides that amount by the asset's downside deviation. The ratio was named after Frank A. Sortino.'

Which means for our asset as example:- Compared with the benchmark SPY (0.9) in the period of the last 5 years, the downside risk / excess return profile of 0.49 of Vanguard Small Cap Value Index Fund is smaller, thus worse.
- During the last 3 years, the excess return divided by the downside deviation is 0.29, which is lower, thus worse than the value of 0.62 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.'

Using this definition on our asset we see for example:- The Ulcer Index over 5 years of Vanguard Small Cap Value Index Fund is 12 , which is higher, thus worse compared to the benchmark SPY (9.32 ) in the same period.
- Looking at Ulcer Ratio in of 8.99 in the period of the last 3 years, we see it is relatively lower, thus better in comparison to SPY (10 ).

'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 -45.4 days of Vanguard Small Cap Value Index Fund is lower, thus worse.
- Compared with SPY (-24.5 days) in the period of the last 3 years, the maximum drop from peak to valley of -21.3 days is larger, thus better.

'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 under water of 527 days of Vanguard Small Cap Value Index Fund is larger, thus worse.
- During the last 3 years, the maximum days below previous high is 527 days, which is greater, 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:- 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 147 days of Vanguard Small Cap Value Index Fund is larger, thus worse.
- Compared with SPY (176 days) in the period of the last 3 years, the average days under water of 198 days is higher, thus worse.

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 Small Cap Value Index Fund are hypothetical and do not account for slippage, fees or taxes.