'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 of 59.1% in the last 5 years of Vanguard Total Stock Market Index Fund, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (63%)
- Compared with SPY (33.5%) in the period of the last 3 years, the total return, or performance of 31.6% is lower, thus worse.

'Compound annual growth rate (CAGR) is a business and investing specific term for the geometric progression ratio that provides a constant rate of return over the time period. CAGR is not an accounting term, but it is often used to describe some element of the business, for example revenue, units delivered, registered users, etc. CAGR dampens the effect of volatility of periodic returns that can render arithmetic means irrelevant. It is particularly useful to compare growth rates from various data sets of common domain such as revenue growth of companies in the same industry.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (10.3%) in the period of the last 5 years, the annual performance (CAGR) of 9.7% of Vanguard Total Stock Market Index Fund is lower, thus worse.
- Looking at compounded annual growth rate (CAGR) in of 9.6% in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (10.1%).

'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:- The 30 days standard deviation over 5 years of Vanguard Total Stock Market Index Fund is 22.3%, which is larger, thus worse compared to the benchmark SPY (21.6%) in the same period.
- Compared with SPY (25.1%) in the period of the last 3 years, the historical 30 days volatility of 26% is larger, thus worse.

'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 volatility over 5 years of Vanguard Total Stock Market Index Fund is 16.2%, which is larger, thus worse compared to the benchmark SPY (15.6%) in the same period.
- Compared with SPY (18.1%) in the period of the last 3 years, the downside deviation of 18.8% is higher, thus worse.

'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:- The Sharpe Ratio over 5 years of Vanguard Total Stock Market Index Fund is 0.33, which is lower, thus worse compared to the benchmark SPY (0.36) in the same period.
- Looking at risk / return profile (Sharpe) in of 0.27 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.3).

'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.'

Using this definition on our asset we see for example:- Looking at the excess return divided by the downside deviation of 0.45 in the last 5 years of Vanguard Total Stock Market Index Fund, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (0.5)
- Compared with SPY (0.42) in the period of the last 3 years, the ratio of annual return and downside deviation of 0.38 is smaller, thus worse.

'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (8.88 ) in the period of the last 5 years, the Ulcer Index of 9.48 of Vanguard Total Stock Market Index Fund is larger, thus worse.
- During the last 3 years, the Downside risk index is 12 , which is greater, thus worse than the value of 11 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:- Looking at the maximum reduction from previous high of -35 days in the last 5 years of Vanguard Total Stock Market Index Fund, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (-33.7 days)
- Compared with SPY (-33.7 days) in the period of the last 3 years, the maximum DrawDown of -35 days is smaller, thus worse.

'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.'

Applying this definition to our asset in some examples:- Looking at the maximum days below previous high of 273 days in the last 5 years of Vanguard Total Stock Market Index Fund, we see it is relatively greater, thus worse in comparison to the benchmark SPY (273 days)
- Looking at maximum time in days below previous high water mark in of 273 days in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (273 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.'

Which means for our asset as example:- Compared with the benchmark SPY (57 days) in the period of the last 5 years, the average days under water of 58 days of Vanguard Total Stock Market Index Fund is greater, thus worse.
- Compared with SPY (73 days) in the period of the last 3 years, the average time in days below previous high water mark of 73 days is greater, 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 Total Stock Market 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.