In investment portfolio construction, an investor or analyst is faced with determining which

asset classes In finance, an asset class is a group of financial instruments that have similar financial characteristics and behave similarly in the marketplace. We can often break these instruments into those having to do with real assets and those having ...

, such as domestic

fixed income Fixed income refers to any type of investment under which the borrower or issuer is obliged to make payments of a fixed amount on a fixed schedule. For example, the borrower may have to pay interest at a fixed rate once a year and repay the prin ...

, domestic

equity Equity may refer to: Finance, accounting and ownership * Equity (finance), ownership of assets that have liabilities attached to them ** Stock, equity based on original contributions of cash or other value to a business ** Home equity, the dif ...

, foreign fixed income, and foreign equity, to invest in and what proportion of the total portfolio should be of each asset class.

Harry Markowitz Harry Max Markowitz (born August 24, 1927) is an American economist who received the 1989 John von Neumann Theory Prize and the 1990 Nobel Memorial Prize in Economic Sciences. Markowitz is a professor of finance at the Rady School of Management ...

(1959) first described a method for constructing a portfolio with optimal

risk In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty about the effects/implications of an activity with respect to something that humans value (such as health, well-being, wealth, property or the environme ...

return Return may refer to: In business, economics, and finance * Return on investment (ROI), the financial gain after an expense. * Rate of return, the financial term for the profit or loss derived from an investment * Tax return, a blank document or t ...

characteristics. His portfolio optimization method finds the minimum risk portfolio with a given expected return. Because the Markowitz or Mean-Variance Efficient Portfolio is calculated from the

sample mean and covariance The sample mean (or "empirical mean") and the sample covariance are statistics computed from a sample of data on one or more random variables. The sample mean is the average value (or mean value) of a sample of numbers taken from a larger po ...

, which are likely different from the population

mean There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value (magnitude and sign) of a given data set. For a data set, the ''arithme ...

and

covariance In probability theory and statistics, covariance is a measure of the joint variability of two random variables. If the greater values of one variable mainly correspond with the greater values of the other variable, and the same holds for the les ...

, the resulting

investment portfolio In finance, a portfolio is a collection of investments. Definition The term “portfolio” refers to any combination of financial assets such as stocks, bonds and cash. Portfolios may be held by individual investors or managed by financial pro ...

may allocate too much weight to assets with better estimated than true risk/return characteristics. To account for the

uncertainty Uncertainty refers to epistemic situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown. Uncertainty arises in partially observable or ...

of the sample estimates, a financial analyst can create many alternative efficient frontiers based on resampled versions of the data. Each resampled dataset will result in a different set of Markowitz efficient portfolios. These efficient frontiers of portfolios can then be averaged to create a resampled efficient frontier. The appropriate compromise between the investor's

Risk aversion In economics and finance, risk aversion is the tendency of people to prefer outcomes with low uncertainty to those outcomes with high uncertainty, even if the average outcome of the latter is equal to or higher in monetary value than the more ce ...

and desired return will then guide the financial analyst to choose a portfolio from the set of resampled efficient frontier portfolios. Since such a portfolio is different from the Markowitz efficient portfolio it will have suboptimal risk/return characteristics with respect to the sample mean and covariance, but optimal characteristics when averaged over the many possible values of the unknown true mean and covariance. (Michaud, 1998) Resampled Efficiency is covered by U. S.

patent A patent is a type of intellectual property that gives its owner the legal right to exclude others from making, using, or selling an invention for a limited period of time in exchange for publishing an enabling disclosure of the invention."A p ...

#6,003,018, patent pending worldwide. New Frontier Advisors, LLC, has exclusive worldwide licensing rights.

References

* Markowitz, H. 1959. ''Portfolio Selection: Efficient Diversification of Investments.'' New York: Wiley, 2nd ed. Cambridge, MA: Basil Blackwell, 1991. *Michaud, R., and Michaud, R. 1998. ''Efficient Asset Management: A practical Guide to Stock Portfolio Optimization and Asset Allocation.'' Boston: Harvard Business School Press. 2nd ed. Oxford: Oxford University Press, 2008. . *Sharpe, W. et al. (2009). ''CFA Portfolio Management, Level III'', Volume 3, pages 261 & 262. Pearson Publishing. . {{DEFAULTSORT:Resampled Efficient Frontier Investment