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)

'The total return on a portfolio of investments takes into account not only the capital appreciation on the portfolio, but also the income received on the portfolio. The income typically consists of interest, dividends, and securities lending fees. This contrasts with the price return, which takes into account only the capital gain on an investment.'

Which means for our asset as example:- The total return, or performance over 5 years of Dr. Bernstein's No Brainer Portfolio is 75.5%, which is lower, thus worse compared to the benchmark SPY (122%) in the same period.
- During the last 3 years, the total return, or increase in value is 38.9%, which is smaller, thus worse than the value of 61% from the benchmark.

'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 compounded annual growth rate (CAGR) of 11.9% 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 (17.3%)
- During the last 3 years, the annual return (CAGR) is 11.6%, which is lower, thus worse than the value of 17.2% 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.'

Applying this definition to our asset in some examples:- Looking at the historical 30 days 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 (18.8%)
- Compared with SPY (22.5%) in the period of the last 3 years, the 30 days standard deviation of 16.1% is lower, thus better.

'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:- Looking at the downside volatility of 10.2% 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 (13.6%)
- During the last 3 years, the downside risk is 12.1%, which is lower, thus better than the value of 16.3% 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (0.79) in the period of the last 5 years, the ratio of return and volatility (Sharpe) of 0.69 of Dr. Bernstein's No Brainer Portfolio is lower, thus worse.
- Compared with SPY (0.65) in the period of the last 3 years, the Sharpe Ratio of 0.56 is lower, thus worse.

'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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (1.09) in the period of the last 5 years, the excess return divided by the downside deviation of 0.92 of Dr. Bernstein's No Brainer Portfolio is smaller, thus worse.
- During the last 3 years, the downside risk / excess return profile is 0.75, which is smaller, thus worse than the value of 0.9 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (5.58 ) in the period of the last 5 years, the Ulcer Index of 4.92 of Dr. Bernstein's No Brainer Portfolio is lower, thus better.
- Looking at Downside risk index in of 6.07 in the period of the last 3 years, we see it is relatively lower, thus better in comparison to SPY (6.83 ).

'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.'

Applying this definition to our asset in some examples:- The maximum DrawDown over 5 years of Dr. Bernstein's No Brainer Portfolio is -28.2 days, which is higher, thus better compared to the benchmark SPY (-33.7 days) in the same period.
- Compared with SPY (-33.7 days) in the period of the last 3 years, the maximum DrawDown of -28.2 days is larger, 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.'

Using this definition on our asset we see for example:- The maximum days below previous high over 5 years of Dr. Bernstein's No Brainer Portfolio is 160 days, which is higher, thus worse compared to the benchmark SPY (139 days) in the same period.
- During the last 3 years, the maximum time in days below previous high water mark 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.'

Which means for our asset as example:- Looking at the average days below previous high of 38 days in the last 5 years of Dr. Bernstein's No Brainer Portfolio, we see it is relatively higher, thus worse in comparison to the benchmark SPY (33 days)
- Compared with SPY (34 days) in the period of the last 3 years, the average days under water of 41 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.