'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.'

Using this definition on our asset we see for example:- The total return, or increase in value over 5 years of Vanguard Total Stock Market Index Fund is 94.4%, which is lower, thus worse compared to the benchmark SPY (103%) in the same period.
- During the last 3 years, the total return, or increase in value is 26%, which is smaller, thus worse than the value of 33.6% from the benchmark.

'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:- Compared with the benchmark SPY (15.2%) in the period of the last 5 years, the annual performance (CAGR) of 14.2% of Vanguard Total Stock Market Index Fund is smaller, thus worse.
- Compared with SPY (10.1%) in the period of the last 3 years, the annual return (CAGR) of 8% is lower, 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 volatility over 5 years of Vanguard Total Stock Market Index Fund is 21.7%, which is greater, thus worse compared to the benchmark SPY (20.9%) in the same period.
- Compared with SPY (17.3%) in the period of the last 3 years, the volatility of 17.8% is higher, 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:- Compared with the benchmark SPY (14.9%) in the period of the last 5 years, the downside risk of 15.6% of Vanguard Total Stock Market Index Fund is greater, thus worse.
- Compared with SPY (12.1%) in the period of the last 3 years, the downside deviation of 12.5% is higher, 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:- Looking at the Sharpe Ratio of 0.54 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 (0.61)
- During the last 3 years, the ratio of return and volatility (Sharpe) is 0.31, which is lower, thus worse than the value of 0.44 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.'

Applying this definition to our asset in some examples:- Looking at the ratio of annual return and downside deviation of 0.75 in the last 5 years of Vanguard Total Stock Market Index Fund, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.85)
- Looking at excess return divided by the downside deviation in of 0.44 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.63).

'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:- Compared with the benchmark SPY (9.32 ) in the period of the last 5 years, the Ulcer Ratio of 10 of Vanguard Total Stock Market Index Fund is larger, thus worse.
- Compared with SPY (10 ) in the period of the last 3 years, the Ulcer Index of 12 is larger, thus worse.

'Maximum drawdown is defined as the peak-to-trough decline of an investment during a specific period. It is usually quoted as a percentage of the peak value. The maximum drawdown can be calculated based on absolute returns, in order to identify strategies that suffer less during market downturns, such as low-volatility strategies. However, the maximum drawdown can also be calculated based on returns relative to a benchmark index, for identifying strategies that show steady outperformance over time.'

Which means for our asset as example:- The maximum DrawDown over 5 years of Vanguard Total Stock Market Index Fund is -35 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 reduction from previous high of -25.4 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.'

Applying this definition to our asset in some examples:- Looking at the maximum days under water of 492 days in the last 5 years of Vanguard Total Stock Market Index Fund, we see it is relatively higher, thus worse in comparison to the benchmark SPY (488 days)
- Compared with SPY (488 days) in the period of the last 3 years, the maximum days under water of 492 days is greater, thus worse.

'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.'

Which means for our asset as example:- The average days under water over 5 years of Vanguard Total Stock Market Index Fund is 124 days, which is larger, thus worse compared to the benchmark SPY (123 days) in the same period.
- Compared with SPY (180 days) in the period of the last 3 years, the average days below previous high of 180 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 Total Stock Market Index Fund are hypothetical and do not account for slippage, fees or taxes.