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)

'Total return, when measuring performance, is the actual rate of return of an investment or a pool of investments over a given evaluation period. Total return includes interest, capital gains, dividends and distributions realized over a given period of time. Total return accounts for two categories of return: income including interest paid by fixed-income investments, distributions or dividends and capital appreciation, representing the change in the market price of an asset.'

Applying this definition to our asset in some examples:- The total return, or increase in value over 5 years of Dr. Bernstein's No Brainer Portfolio is 28%, which is lower, thus worse compared to the benchmark SPY (60.9%) in the same period.
- Looking at total return in of 15.2% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (34.2%).

'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:- Compared with the benchmark SPY (10%) in the period of the last 5 years, the compounded annual growth rate (CAGR) of 5.1% of Dr. Bernstein's No Brainer Portfolio is lower, thus worse.
- Looking at annual performance (CAGR) in of 4.8% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (10.3%).

'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:- Compared with the benchmark SPY (18.7%) in the period of the last 5 years, the 30 days standard deviation of 13.4% of Dr. Bernstein's No Brainer Portfolio is lower, thus better.
- Looking at 30 days standard deviation in of 15.1% in the period of the last 3 years, we see it is relatively lower, thus better in comparison to SPY (21.5%).

'Downside risk is the financial risk associated with losses. That is, it is the risk of the actual return being below the expected return, or the uncertainty about the magnitude of that difference. 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.'

Using this definition on our asset we see for example:- The downside deviation over 5 years of Dr. Bernstein's No Brainer Portfolio is 10.1%, which is lower, thus better compared to the benchmark SPY (13.6%) in the same period.
- Compared with SPY (15.7%) in the period of the last 3 years, the downside volatility of 11.5% is lower, thus better.

'The Sharpe ratio is the measure of risk-adjusted return of a financial portfolio. Sharpe ratio is a measure of excess portfolio return over the risk-free rate relative to its standard deviation. Normally, the 90-day Treasury bill rate is taken as the proxy for risk-free rate. A portfolio with a higher Sharpe ratio is considered superior relative to its peers. The measure was named after William F Sharpe, a Nobel laureate and professor of finance, emeritus at Stanford University.'

Applying this definition to our asset in some examples:- The Sharpe Ratio over 5 years of Dr. Bernstein's No Brainer Portfolio is 0.19, which is lower, thus worse compared to the benchmark SPY (0.4) in the same period.
- During the last 3 years, the Sharpe Ratio is 0.16, which is lower, thus worse than the value of 0.36 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 (0.55) in the period of the last 5 years, the downside risk / excess return profile of 0.25 of Dr. Bernstein's No Brainer Portfolio is lower, thus worse.
- During the last 3 years, the downside risk / excess return profile is 0.2, which is smaller, thus worse than the value of 0.5 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.'

Applying this definition to our asset in some examples:- Looking at the Ulcer Index of 5.55 in the last 5 years of Dr. Bernstein's No Brainer Portfolio, we see it is relatively smaller, thus better in comparison to the benchmark SPY (5.82 )
- Looking at Downside risk index in of 6.03 in the period of the last 3 years, we see it is relatively lower, thus better in comparison to SPY (6.86 ).

'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 drop from peak to valley of -28.2 days in the last 5 years of Dr. Bernstein's No Brainer Portfolio, we see it is relatively larger, thus better in comparison to the benchmark SPY (-33.7 days)
- Looking at maximum DrawDown in of -28.2 days in the period of the last 3 years, we see it is relatively larger, thus better in comparison to SPY (-33.7 days).

'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:- The maximum days under water over 5 years of Dr. Bernstein's No Brainer Portfolio is 289 days, which is greater, thus worse compared to the benchmark SPY (187 days) in the same period.
- During the last 3 years, the maximum days below previous high is 160 days, which is higher, thus worse than the value of 139 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:- The average days below previous high over 5 years of Dr. Bernstein's No Brainer Portfolio is 66 days, which is higher, thus worse compared to the benchmark SPY (43 days) in the same period.
- Looking at average time in days below previous high water mark in of 45 days in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (39 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.