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 is the amount of value an investor earns from a security over a specific period, typically one year, when all distributions are reinvested. Total return is expressed as a percentage of the amount invested. For example, a total return of 20% means the security increased by 20% of its original value due to a price increase, distribution of dividends (if a stock), coupons (if a bond) or capital gains (if a fund). Total return is a strong measure of an investment’s overall performance.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (106.8%) in the period of the last 5 years, the total return, or performance of 58.1% of Dr. Bernstein's No Brainer Portfolio is smaller, thus worse.
- Compared with SPY (71.9%) in the period of the last 3 years, the total return of 41.2% is smaller, thus worse.

'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.'

Which means for our asset as example:- The compounded annual growth rate (CAGR) over 5 years of Dr. Bernstein's No Brainer Portfolio is 9.6%, which is smaller, thus worse compared to the benchmark SPY (15.7%) in the same period.
- Compared with SPY (19.8%) in the period of the last 3 years, the annual performance (CAGR) of 12.2% 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:- Looking at the volatility of 13.6% 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 (18.9%)
- Looking at volatility in of 16% in the period of the last 3 years, we see it is relatively lower, thus better in comparison to SPY (21.9%).

'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 volatility over 5 years of Dr. Bernstein's No Brainer Portfolio is 10.2%, which is lower, thus better compared to the benchmark SPY (13.8%) in the same period.
- Looking at downside volatility in of 12% in the period of the last 3 years, we see it is relatively smaller, thus better in comparison to SPY (15.9%).

'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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (0.69) in the period of the last 5 years, the Sharpe Ratio of 0.52 of Dr. Bernstein's No Brainer Portfolio is lower, thus worse.
- Looking at Sharpe Ratio in of 0.61 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.79).

'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:- The ratio of annual return and downside deviation over 5 years of Dr. Bernstein's No Brainer Portfolio is 0.7, which is smaller, thus worse compared to the benchmark SPY (0.95) in the same period.
- Compared with SPY (1.09) in the period of the last 3 years, the ratio of annual return and downside deviation of 0.81 is lower, thus worse.

'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 (5.61 ) in the period of the last 5 years, the Ulcer Ratio of 4.95 of Dr. Bernstein's No Brainer Portfolio is smaller, thus better.
- Compared with SPY (6.08 ) in the period of the last 3 years, the Ulcer Index of 5.44 is lower, thus better.

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

'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 160 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 (139 days)
- Looking at maximum time in days below previous high water mark in of 136 days in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (119 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.'

Applying this definition to our asset in some examples:- Looking at the average days under water of 38 days in the last 5 years of Dr. Bernstein's No Brainer Portfolio, we see it is relatively larger, thus worse in comparison to the benchmark SPY (32 days)
- Compared with SPY (22 days) in the period of the last 3 years, the average days under water of 26 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 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.