Civil Rights
Movements, leaders, victories and the continuing fight for equality.
q2K BHP
Black History Portal
THE BHP WIRE —
HIDDEN TRUTHS
What's New!
Explore the people, places, events, achievements, struggles and stories that shaped our journey.
Movements, leaders, victories and the continuing fight for equality.
Innovation, patents, science, technology and world-changing contributions.
Pioneers, champions, Negro Leagues, records, activism and excellence.
Meet the people whose lives, choices and achievements shaped the journey.
Black towns, communities, institutions and places where history happened.
Moments that changed communities, movements, institutions and the nation.
Mansa Musa was the ruler of the Mali Empire in West Africa. Details recorded here should be sourced; unknown information is left blank.
MORE →Reflects the personal views, recollections, and perspective of the author, Mike Davis.
This is a personal recollection on the Move fire on May 13, 1985
In modern portfolio theory, the efficient frontier (or portfolio frontier) is an investment portfolio which occupies the "efficient" parts of the risk–return spectrum. Formally, it is the set of portfolios which satisfy the condition that no other portfolio exists with a higher expected return but with the same standard deviation of return (i.e., the risk).[1] The efficient frontier was first formulated by Harry Markowitz in 1952;[2] see Markowitz model.
A combination of assets, i.e. a portfolio, is referred to as "efficient" if it has the best possible expected level of return for its level of risk (which is represented by the standard deviation of the portfolio's return).[3] Here, every possible combination of risky assets can be plotted in risk–expected return space, and the collection of all such possible portfolios defines a region in this space. In the absence of the opportunity to hold a risk-free asset, this region is the opportunity set (the feasible set). The positively sloped (upward-sloped) top boundary of this region is a portion of a hyperbola,[4] and is called the "efficient frontier".
If a risk-free asset is also available, the opportunity set is larger, and its upper boundary, the efficient frontier, is a straight line segment emanating from the vertical axis at the value of the risk-free asset's return and tangent to the risky-assets-only opportunity set. All portfolios between the risk-free asset and the tangency portfolio are portfolios composed of risk-free assets and the tangency portfolio, while all portfolios on the linear frontier above and to the right of the tangency portfolio are generated by borrowing at the risk-free rate and investing the proceeds into the tangency portfolio.
On the efficient frontier, the portfolio with the lowest possible risk is known as the minimum-variance portfolio. Corporate Finance Institute describes the minimum-variance portfolio as the combination of risky assets that minimizes standard deviation, and identifies it as the point where the efficient frontier begins.[5]
When a risk-free asset is introduced, the efficient set is no longer limited to the upper portion of the Markowitz frontier. In that case, the relevant portfolio of risky assets is the 'tangency portfolio, which is the portfolio where the capital allocation line is tangent to the efficient frontier. The same source describes this portfolio as the optimal market portfolio in the standard MPT framework.[6]
Source: Wikipedia. Article content is retrieved live through the MediaWiki API.
In modern portfolio theory, the efficient frontier (or portfolio frontier) is an investment portfolio which occupies the "efficient" parts of the risk–return spectrum. Formally, it is the set of portfolios which satisfy the condition that no other portfolio exists with a higher expected return but with the same standard deviation of return (i.e., the risk). The efficient frontier was first formulated by Harry Markowitz in 1952; see Markowitz model.
Resampled efficient frontier is a technique in investment portfolio construction under modern portfolio theory to use a set of portfolios and then average them to create an effective portfolio. This will not necessarily be the optimal portfolio, but a portfolio that is more balanced between risk and the rate of return. It is used when an investor or analyst is faced with determining which asset classes, such as domestic fixed income, domestic equity, foreign fixed income, and foreign equity, to invest in and what proportion of the total portfolio should be of each asset class.
Anil Kamath is a web and technology entrepreneur. He is the founder of eBoodle.com and of Efficient Frontier. Kamath holds the patent on use of modern portfolio theory to the field of online advertising. He is on the board of Commerce.com (Nasdaq: CMRC) formerly known as BigCommerce.
In multi-objective optimization, the Pareto frontier (also called the Pareto front, Pareto set, Pareto boundary or Pareto curve) is the set of all Pareto efficient solutions. Informally, this means when there are many distinct objectives to consider in an optimization problem, a Pareto front represents the set of solutions where no solution outperforms any other solution due to trade-offs among the objectives, and that set excludes the remaining solutions which are outperformed. That is to say, the frontier is the set of choices where it is impossible to choose another option that is better in some way without being worse in another. Outperforming is called Pareto dominance: a solution A dominates (outperforms) B if A is no worse than B in every objective, and better than B in at least one objective. The concept is widely used in engineering. It allows the designer to restrict attention to the set of efficient choices, and to make tradeoffs within this set, rather than considering the full range of every parameter.
Before the 1921 destruction of Tulsa’s Greenwood District, Black residents had created a remarkable center of business and community life. The district included stores, professional offices, entertainment venues and homes owned by Black citizens. Understanding Greenwood means learning what was built—not only what was burned.
MORE →Brown v. Board of Education in 1954.
