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 performance over 5 years of Dr. Bernstein's No Brainer Portfolio is 27.8%, which is lower, thus worse compared to the benchmark SPY (62.6%) in the same period.
- Compared with SPY (32.1%) in the period of the last 3 years, the total return, or increase in value of 13.5% is smaller, thus worse.

'The compound annual growth rate (CAGR) is a useful measure of growth over multiple time periods. It can be thought of as the growth rate that gets you from the initial investment value to the ending investment value if you assume that the investment has been compounding over the time period.'

Applying this definition to our asset in some examples:- Looking at the annual return (CAGR) of 5% 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 (10.2%)
- During the last 3 years, the annual return (CAGR) is 4.3%, which is smaller, thus worse than the value of 9.7% from the benchmark.

'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 (21.5%) in the period of the last 5 years, the 30 days standard deviation of 15.6% of Dr. Bernstein's No Brainer Portfolio is lower, thus better.
- Compared with SPY (24.8%) in the period of the last 3 years, the 30 days standard deviation of 18.3% 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.'

Using this definition on our asset we see for example:- Looking at the downside deviation of 11.6% 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 (15.6%)
- Looking at downside deviation in of 13.6% in the period of the last 3 years, we see it is relatively lower, thus better in comparison to SPY (17.9%).

'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:- Compared with the benchmark SPY (0.36) in the period of the last 5 years, the Sharpe Ratio of 0.16 of Dr. Bernstein's No Brainer Portfolio is lower, thus worse.
- Looking at ratio of return and volatility (Sharpe) in of 0.1 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.29).

'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:- Compared with the benchmark SPY (0.5) in the period of the last 5 years, the downside risk / excess return profile of 0.22 of Dr. Bernstein's No Brainer Portfolio is smaller, thus worse.
- During the last 3 years, the ratio of annual return and downside deviation is 0.13, which is lower, thus worse than the value of 0.4 from the benchmark.

'The ulcer index is a stock market risk measure or technical analysis indicator devised by Peter Martin in 1987, and published by him and Byron McCann in their 1989 book The Investors Guide to Fidelity Funds. It's designed as a measure of volatility, but only volatility in the downward direction, i.e. the amount of drawdown or retracement occurring over a period. Other volatility measures like standard deviation treat up and down movement equally, but a trader doesn't mind upward movement, it's the downside that causes stress and stomach ulcers that the index's name suggests.'

Which means for our asset as example:- Looking at the Ulcer Ratio of 8.25 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 (8.52 )
- Looking at Ulcer Ratio in of 10 in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (10 ).

'Maximum drawdown measures the loss in any losing period during a fund’s investment record. It is defined as the percent retrenchment from a fund’s peak value to the fund’s valley value. The drawdown is in effect from the time the fund’s retrenchment begins until a new fund high is reached. The maximum drawdown encompasses both the period from the fund’s peak to the fund’s valley (length), and the time from the fund’s valley to a new fund high (recovery). It measures the largest percentage drawdown that has occurred in any fund’s data record.'

Using this definition on our asset we see for 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 higher, thus better.
- Compared with SPY (-33.7 days) in the period of the last 3 years, the maximum drop from peak to valley 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) in days.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (235 days) in the period of the last 5 years, the maximum days under water of 273 days of Dr. Bernstein's No Brainer Portfolio is larger, thus worse.
- Looking at maximum days under water in of 273 days in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (235 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (55 days) in the period of the last 5 years, the average days under water of 67 days of Dr. Bernstein's No Brainer Portfolio is higher, thus worse.
- Compared with SPY (59 days) in the period of the last 3 years, the average days under water of 74 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 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.