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:- Looking at the total return, or increase in value of 25.6% 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 (60.6%)
- Looking at total return in of 18% in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (38%).

'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:- Compared with the benchmark SPY (10%) in the period of the last 5 years, the compounded annual growth rate (CAGR) of 4.7% of Dr. Bernstein's No Brainer Portfolio is smaller, thus worse.
- Looking at annual performance (CAGR) in of 5.7% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (11.3%).

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (21.5%) in the period of the last 5 years, the historical 30 days volatility of 15.8% of Dr. Bernstein's No Brainer Portfolio is smaller, thus better.
- During the last 3 years, the volatility is 13.9%, which is lower, thus better than the value of 17.9% from the benchmark.

'The downside volatility is similar to the volatility, or standard deviation, but only takes losing/negative periods into account.'

Using this definition on our asset we see for example:- Looking at the downside volatility of 11.6% 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 (15.5%)
- Looking at downside volatility in of 9.7% in the period of the last 3 years, we see it is relatively lower, thus better in comparison to SPY (12.5%).

'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.'

Using this definition on our asset we see for example:- Looking at the ratio of return and volatility (Sharpe) of 0.14 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 (0.35)
- During the last 3 years, the ratio of return and volatility (Sharpe) is 0.23, which is smaller, thus worse than the value of 0.49 from the benchmark.

'The Sortino ratio, a variation of the Sharpe ratio only factors in the downside, or negative volatility, rather than the total volatility used in calculating the Sharpe ratio. The theory behind the Sortino variation is that upside volatility is a plus for the investment, and it, therefore, should not be included in the risk calculation. Therefore, the Sortino ratio takes upside volatility out of the equation and uses only the downside standard deviation in its calculation instead of the total standard deviation that is used in calculating the Sharpe ratio.'

Using this definition on our asset we see for example:- The ratio of annual return and downside deviation over 5 years of Dr. Bernstein's No Brainer Portfolio is 0.19, which is lower, thus worse compared to the benchmark SPY (0.48) in the same period.
- Looking at downside risk / excess return profile in of 0.33 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.71).

'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.'

Applying this definition to our asset in some examples:- The Ulcer Ratio over 5 years of Dr. Bernstein's No Brainer Portfolio is 9.42 , which is lower, thus better compared to the benchmark SPY (9.55 ) in the same period.
- During the last 3 years, the Ulcer Index is 11 , which is greater, thus worse than the value of 10 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:- Compared with the benchmark SPY (-33.7 days) in the period of the last 5 years, the maximum reduction from previous high of -28.2 days of Dr. Bernstein's No Brainer Portfolio is higher, thus better.
- Compared with SPY (-24.5 days) in the period of the last 3 years, the maximum drop from peak to valley of -24.4 days is higher, thus better.

'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 469 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 (431 days)
- During the last 3 years, the maximum days below previous high is 469 days, which is larger, thus worse than the value of 431 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:- The average time in days below previous high water mark over 5 years of Dr. Bernstein's No Brainer Portfolio is 118 days, which is larger, thus worse compared to the benchmark SPY (105 days) in the same period.
- During the last 3 years, the average time in days below previous high water mark is 167 days, which is higher, thus worse than the value of 144 days from the benchmark.

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.