Personal Finance

How do you draw an efficient frontier?

By: Mohammad DayyanUpdated: January 03, 2021


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    August 12, 2022
Constructing an Efficient Frontier
  1. Identify all the portfolios that have the same risk (volatility). From this sub-set of portfolios, choose the one that has the highest return.
  2. Identify all the portfolios that have the same returns. From this sub-set of portfolios, choose the one that has the lowest risk.

Correspondingly, why is efficient frontier concave?

According to Markowitz, for every point on the efficient frontier, there is at least one portfolio that can be constructed from all available investments that has the expected risk and return corresponding to that point. The efficient frontier is curved because there is a diminishing marginal return to risk.

Can Efficient Frontier be a straight line?

Efficient Frontier. The hyperbola is sometimes referred to as the 'Markowitz Bullet', and its upward sloped portion is the efficient frontier if no risk-free asset is available. With a risk-free asset, the straight line is the efficient frontier.

How is the efficient frontier determined?

The efficient frontier is the set of optimal portfolios that offer the highest expected return for a defined level of risk or the lowest risk for a given level of expected return. Portfolios that lie below the efficient frontier are sub-optimal because they do not provide enough return for the level of risk.

What is efficient frontier graph?

An efficient frontier is a graph that plots the expected return on a portfolio of investments on the y-axis and its risk as measured by its standard deviation on the x-axis. The efficient frontier plots portfolios that yields the same risk-return tradeoff.


Why is the efficient frontier a hyperbola?

The efficient frontier is the upper leg of the hyperbola originating from the minimum variance portfolio (MVP) in case of n risky assets. This means that only line AT dominates all other combinations and, therefore, it is the efficient frontier in this case.

What is efficient frontier analysis?

The efficient frontier is a portfolio analysis concept designed to assess risk vs. return for an investment portfolio. The line, which is the efficient frontier itself, represents the highest level of expected return for any given level of risk for any possible combination of assets for the portfolio.

Why is the efficient frontier a parabola?

Keep adding more of the riskier asset, you get more returns and consequently more risk too. Thus the top half of the parabola is full of points which have either the most returns for any risk, or the least risk for any return. This is called the efficient frontier.

What makes a portfolio efficient?

An efficient portfolio is either a portfolio that offers the highest expected return for a given level of risk, or one with the lowest level of risk for a given expected return. The efficient frontier represents that set of portfolios that has the maximum rate of return for every given level of risk.

What is a good Sharpe ratio?

So what is considered a good Sharpe ratio that indicates a high degree of expected return for a relatively low amount of risk? Usually, any Sharpe ratio greater than 1.0 is considered acceptable to good by investors. A ratio higher than 2.0 is rated as very good. A ratio of 3.0 or higher is considered excellent.

What is the minimum variance portfolio?

A minimum variance portfolio is a collection of securities that combine to minimize the price volatility of the overall portfolio. Volatility is a statistical measure of a particular security's price movement (ups and downs). An investment's volatility is interchangeable in meaning with “market risk”.

How do you calculate tangency portfolio?

If you want to calculate the tangency portfolio, you need to maximize the Sharpe ratio, by varying the weights of the assets in the portfolio. This is relatively simple in a portfolio with 2 or 3 assets, but becomes more complex, and requires optimization algorithms, as you increase the number of assets.

How do you calculate portfolio weight?

Portfolio weight is the percentage of an investment portfolio that a particular holding or type of holding comprises. The most basic way to determine the weight of an asset is by dividing the dollar value of a security by the total dollar value of the portfolio.

How do you calculate expected return?

It is calculated by multiplying potential outcomes by the chances of them occurring and then totaling these results. For example, if an investment has a 50% chance of gaining 20% and a 50% chance of losing 10%, the expected return is 5% (50% x 20% + 50% x -10% = 5%).

What is the slope of the capital allocation line?

Capital allocation line (CAL) is a graph created by investors to measure the risk of risky and risk-free assets. The graph displays the return to be made by taking on a certain level of risk. Its slope is known as the "reward-to-variability ratio".

Where is Excel Solver?

After you load the Solver Add-in, the Solver command is available in the Analysis group on the Data tab.
  1. On the Tools menu, select Excel Add-Ins.
  2. In the Add-Ins available box, select the Solver Add-In check box, and then click OK.

How do you calculate portfolio variance in Excel?

Examples of Portfolio Variance Formula (With Excel Template)
  1. Variance= (20%^2*2.3%^2)+(35%^2*3.5%^2)+(45%^2*4%^2)+(2*(20%*35%*2.3%*3.5*0.6))+(2*(20%*45%*2.3%*4%*0.8))+(2*(35%*45%*3.5%*4%*0.5))
  2. Variance = 0.000916.

How do you calculate the variance?

To calculate the variance follow these steps: Work out the Mean (the simple average of the numbers) Then for each number: subtract the Mean and square the result (the squared difference). Then work out the average of those squared differences.

How do I use Solver in Excel?

In Excel for Mac 2011: Click the Data tab, under Analysis, click Solver. After you define a problem, in the Solver Parameters dialog box, click Options. Select the Show Iteration Results check box to see the values of each trial solution, and then click OK. In the Solver Parameters dialog box, click Solve.

Is the market portfolio on the efficient frontier?

The capital market line (CML) represents portfolios that optimally combine risk and return. CML is a special case of the CAL where the risk portfolio is the market portfolio. The intercept point of CML and efficient frontier would result in the most efficient portfolio called the tangency portfolio.

Which portfolio Cannot lie on the efficient frontier?

Answer and Explanation:
Asset Y cannot be on the efficient frontier. For all the assets on the efficient frontier, their returns are maximized for the amount of risk they