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 41.7%, which is lower, thus worse compared to the benchmark SPY (77.1%) in the same period.
- Looking at total return, or performance in of 31.6% in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (51.7%).

'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.'

Using this definition on our asset we see for example:- Looking at the annual performance (CAGR) of 7.2% 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 9.6%, which is lower, thus worse than the value of 14.9% from the benchmark.

'In finance, volatility (symbol σ) is the degree of variation of a trading price series over time as measured by the standard deviation of logarithmic returns. Historic volatility measures a time series of past market prices. Implied volatility looks forward in time, being derived from the market price of a market-traded derivative (in particular, an option). Commonly, the higher the volatility, the riskier the security.'

Using this definition on our asset we see for example:- Looking at the historical 30 days volatility of 9.7% 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 (13.3%)
- During the last 3 years, the volatility is 8.9%, which is smaller, thus better than the value of 13% from the benchmark.

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

Which means for our asset as example:- Compared with the benchmark SPY (9.6%) in the period of the last 5 years, the downside deviation of 7% of Dr. Bernstein's No Brainer Portfolio is lower, thus better.
- During the last 3 years, the downside risk is 6.4%, which is smaller, thus better than the value of 9.4% from the benchmark.

'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 risk / return profile (Sharpe) over 5 years of Dr. Bernstein's No Brainer Portfolio is 0.49, which is lower, thus worse compared to the benchmark SPY (0.72) in the same period.
- During the last 3 years, the risk / return profile (Sharpe) is 0.8, which is lower, thus worse than the value of 0.96 from the benchmark.

'The Sortino ratio measures the risk-adjusted return of an investment asset, portfolio, or strategy. It is a modification of the Sharpe ratio but penalizes only those returns falling below a user-specified target or required rate of return, while the Sharpe ratio penalizes both upside and downside volatility equally. Though both ratios measure an investment's risk-adjusted return, they do so in significantly different ways that will frequently lead to differing conclusions as to the true nature of the investment's return-generating efficiency. The Sortino ratio is used as a way to compare the risk-adjusted performance of programs with differing risk and return profiles. In general, risk-adjusted returns seek to normalize the risk across programs and then see which has the higher return unit per risk.'

Which means for our asset as example:- The excess return divided by the downside deviation over 5 years of Dr. Bernstein's No Brainer Portfolio is 0.67, which is smaller, thus worse compared to the benchmark SPY (1) in the same period.
- During the last 3 years, the ratio of annual return and downside deviation is 1.11, which is smaller, thus worse than the value of 1.32 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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (3.97 ) in the period of the last 5 years, the Ulcer Ratio of 4.11 of Dr. Bernstein's No Brainer Portfolio is greater, thus worse.
- During the last 3 years, the Ulcer Index is 3.45 , which is lower, thus better than the value of 4.1 from the benchmark.

'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 DrawDown of -15.3 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 (-19.3 days)
- During the last 3 years, the maximum reduction from previous high is -15.3 days, which is higher, thus better than the value of -19.3 days from the benchmark.

'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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (187 days) in the period of the last 5 years, the maximum time in days below previous high water mark of 316 days of Dr. Bernstein's No Brainer Portfolio is greater, thus worse.
- During the last 3 years, the maximum days below previous high is 160 days, which is larger, 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:- Looking at the average days below previous high of 72 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 (42 days)
- Compared with SPY (37 days) in the period of the last 3 years, the average time in days below previous high water mark of 43 days is larger, 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.