There may not be a formula for the efficient frontier. In this course, I will emphasize using a maximization program to solve for the efficient frontier. More specifically, we will use the excel program SOLVER to find the points on the efficient frontier. SOLVER is an excel add-in package. To find solver, click on tools on the menu bar.
We can see that the chart formed an arch at the top of the portfolios which I marked with the black pen. This line is essentially pointing at the portfolios that are the most efficient. This line is known as the efficient frontier. The efficient frontier is a set of portfolios that give us the highest return for the lowest possible risk.
If we find two efficient portfolios, we can plot the entire efficient frontier by varying the weight of capital applied to each of these portfolios. I can use Excel’s Solver to find two efficient portfolios; the way I choose to do this is to maximize the value of the portfolio mean by changing the portfolio weights, subject to the constraint.
Sep 18, 2018 Graphing the efficient frontier for a two-stock portfolio in Excel - Duration: 12:23. CFA/FRM: How to Build Efficient Frontier in Excel - Part 1 (of 2) - Duration: 20:07.
The efficient frontier is the set of portfolios that gets us the highest expected return for any given risk level. Or from another perspective, the minimum amount of risk for an expected return. To trace this line, we can define a variable frontiery. Going back to the chart above, we can see the maximum return doesn’t go much higher than 0.3.
The concept of Efficient Frontier was first introduced by Harry Markowitz in his paper on Portfolio Selection (1952 Journal of Finance).
The portfolio theory considers a universe of risky investments and explores these possible investments in order to find the optimum portfolio. So, for a given amount of risk, MTP explains how select a portfolio with maximum returns, and with a given amount of return, MTP explains how to select a portfolio with minimum risk.
Suppose you have all the required data (expected returns, volatility, and correlations) for all the investments you are considering. Using this data, you can create various portfolios with different portfolio risk and return profiles.
Among all these portfolios, choose the optimal portfolios in either of the following way:
Identify all the portfolios that have the same risk (volatility). From this sub-set of portfolios, choose the one that has the highest return.
Identify all the portfolios that have the same returns. From this sub-set of portfolios, choose the one that has the lowest risk.
How To Graph Efficient Frontier In Excel For Mac Free
Both the methods will product a set of optimal portfolios. This set of optimal portfolios is called the efficient frontier. (Later in this post, we will learn how to construct an efficient frontier in Excel)
If you plot all the portfolios that you could make using the universe of risky securities that you have, the graph will look something like the one below:
Each red dot represents the mean and standard deviation of a portfolio. The blue line is the efficient frontier. The efficient frontier has all the optimal portfolios we selected above. Portfolios on the efficient frontier have maximum return for a given level of risk or, alternatively, minimum risk for a given level of return. Clearly, a rational investor will select a portfolio on the efficient frontier.
Dominated Portfolio
In the above graph, you see that for the same level of risk there are multiple portfolios providing different levels of return. A portfolio is said to be dominated, if there is atleast one portfolio that has higher return and lower standard deviation. In other words, a portfolio is dominated if there is any other portfolio to its north-west. So, in the above graph, all portfolios other than those on the efficient frontier are dominated.
Typically, the portfolios that make the efficient frontier are the most diversified ones. Less diversified portfolios tend to be closer to the middle of the achievable region.
Constructing an Efficient Frontier in Excel
How To Plot Efficient Frontier In Excel
The attached PDF file shows you how you can construct an efficient frontier using excel.
Constructing Efficient Frontier in Excel
This Excel workbook illustrates how to use Excel’s matrix functions to find unconstrained frontier portfolios, from a global minimum variance portfolio up to a tangency portfolio. It uses no macros or VBA, nor does it require you to enable Solver.
(Version 3 corrects the volatility estimate for FrontierPort4.)
The workbook is “flexible” in that it accommodates any number of assets up to 50. It is simple to use.
Disclaimer This workbook and the results it produces do not constitute investment advice.
The workbook and its contents serve to illustrate how to generate an efficient frontier without any return assumptions. While that topic may be of interest to students or instructors of finance, it does not pertain to investment choices made by most people. If you are not well-versed in the mathematics of modern portfolio theory (MPT) or the Capital Asset Pricing Model (CAPM), and you think you understand this workbook, you are probably mistaken.
The frontier generated spans the GMV portfolio (using simple matrix math) and the tangency portfolio (applying CAPM assumptions and the assumption that the risk-free rate is zero). Points between are fractionally equidistant in weight.
You should not use this workbook to make investment decisions.
1. Enter the names, volatilities, and correlations on the DataEntry sheet.
The sheet is populated with 9 assets’ data in rows 2 – 10. To add more assets, simply type in their data in rows 11 and below. To examine more or fewer than 9, delete data in the rows you don’t need or add data in the rows you do need, and write the number of assets in cell A2
2. See the resulting frontier portfolios on the Frontier sheet.
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If you have no stray data in the DataEntry sheet, the Frontier sheet displays allocations from Global Minimum Variance (GMV) in Column B to Tangency in Column L. In the 9-sector example, notice how the allocations migrate from a long-short GMV portfolio to a long-only Tangency portfolio, in which reward/risk is maximized. In a world with a zero risk-free rate, the Tangency portfolio should be the market portfolio, assuming all assets are represented. It is interesting to note that the weights of the Tangency portfolio are a respectably close approximation of the actual sector weights in the S&P 500, when the data for this workbook were estimated.
Regardless of whether you believe in CAPM, you have to admit that the math is elegant – which is probably a significant reason so many still cling to CAPM.