Dr. William Bernstein is a physician and neurologist as well as a financial adviser to high net worth individuals. This one's so simple: Allocate 25% in each of four index funds diversified across basic categories.

The no-brainer portfolio comprises the following fund allocation:

25% in Vanguard 500 Index VFINX (NYSEARCA:IVW)

25% in Vanguard Small Cap NAESX or VTMSX (NYSEARCA:VB)

25% in Vanguard Total International VGTSX or VTMGX (EFA, VEA)

25% in Vanguard Total Bond VBMFX or VBISX (NASDAQ:BND)

'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 performance over 5 years of Dr. Bernstein's No Brainer Portfolio is 37.8%, which is lower, thus worse compared to the benchmark SPY (77.4%) in the same period.
- Compared with SPY (43.3%) in the period of the last 3 years, the total return, or performance of 20.9% is smaller, 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.'

Applying this definition to our asset in some examples:- Looking at the annual performance (CAGR) of 6.6% in the last 5 years of Dr. Bernstein's No Brainer Portfolio, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (12.1%)
- During the last 3 years, the annual return (CAGR) is 6.5%, which is lower, thus worse than the value of 12.7% from the benchmark.

'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:- The volatility over 5 years of Dr. Bernstein's No Brainer Portfolio is 13.7%, which is lower, thus better compared to the benchmark SPY (19%) in the same period.
- Compared with SPY (22%) in the period of the last 3 years, the historical 30 days volatility of 15.6% is lower, thus better.

'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.'

Applying this definition to our asset in some examples:- Looking at the downside deviation of 10.4% in the last 5 years of Dr. Bernstein's No Brainer Portfolio, we see it is relatively lower, thus better in comparison to the benchmark SPY (13.9%)
- Compared with SPY (16.2%) in the period of the last 3 years, the downside deviation of 11.9% is smaller, thus better.

'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:- The ratio of return and volatility (Sharpe) over 5 years of Dr. Bernstein's No Brainer Portfolio is 0.3, which is lower, thus worse compared to the benchmark SPY (0.51) in the same period.
- Compared with SPY (0.46) in the period of the last 3 years, the risk / return profile (Sharpe) of 0.26 is lower, thus worse.

'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 downside risk / excess return profile of 0.4 in the last 5 years of Dr. Bernstein's No Brainer Portfolio, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.7)
- During the last 3 years, the ratio of annual return and downside deviation is 0.34, which is lower, thus worse than the value of 0.63 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.'

Which means for our asset as example:- Compared with the benchmark SPY (5.87 ) in the period of the last 5 years, the Ulcer Ratio of 5.44 of Dr. Bernstein's No Brainer Portfolio is lower, thus better.
- During the last 3 years, the Ulcer Index is 6.21 , which is lower, thus better than the value of 7.01 from the benchmark.

'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.'

Using this definition on our asset we see for example:- Looking at the maximum reduction from previous high of -28.2 days in the last 5 years of Dr. Bernstein's No Brainer Portfolio, we see it is relatively greater, thus better 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 -28.2 days is greater, thus better.

'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'

Using this definition on our asset we see for example:- The maximum days below previous high over 5 years of Dr. Bernstein's No Brainer Portfolio is 242 days, which is larger, thus worse compared to the benchmark SPY (139 days) in the same period.
- During the last 3 years, the maximum time in days below previous high water mark is 160 days, which is higher, thus worse than the value of 139 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.'

Applying this definition to our asset in some examples:- Looking at the average time in days below previous high water mark of 59 days in the last 5 years of Dr. Bernstein's No Brainer Portfolio, we see it is relatively greater, thus worse in comparison to the benchmark SPY (37 days)
- Looking at average days under water in of 51 days in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (45 days).

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 Dr. Bernstein's No Brainer Portfolio 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.