Portfolio variance formula excel mmult
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The curly braces in the formula bar indicate an array formula.
➤ To get the variance-covariance matrix divide each element of the transpose matrix with the total number of observations.
Or,
➤ Auto-fill the formula to the rest of the cells.
➤ Set the weights arbitrarily.
To maximize the benefit of diversification more securities are needed, making the textbook method of calculation tedious and prone to error. Thanks to Excel's covariance matrix and array functionality, we can easily calculate the variance and standard deviation for a portfolio of as many securities as we want. To determine which weights in the portfolio produce the minimum variance, you can use Excel’s Solver Add-in to calculate the covariance matrix of returns.
Using 123 daily return observations, we’ll determine the minimum variance portfolio weights for the five assets.
All the weights must add up to one
➤ Weight transpose matrix:
➤ Portfolio variance:
➤ Enable Solver: File >> Options >> Excel Add-ins >> Solver Add-in.
➤ Solver: Set objective >> Min >> By Changing Variable Cells >> Constraints >> Solve.
In this article, we’ll learn to make a minimum variance portfolio in Excel using MMULT and TRANSPOSE functions and the Solver Add-in.
Download Practice Workbook
What is a Minimum Variance Portfolio?
A portfolio with the lowest volatility for a particular group of assets is known as the Minimum Variance Portfolio.
When constructing an investment portfolio, reducing risk is as important as increasing returns. However, the total must be equal to one.
➤ Check that the total weights equal one.
➤ Multiply the transpose of the weights with the variance-covariance matrix to get the weight transpose sigma array. For example, we’ll add the constraints that the sum of all the weights must equal one and the weight for NVDA should be at least zero.
Other constraints include all the weights must be greater than zero or that some weights should be negative (shorting stocks).
➤ The sum of the weights equals one: Select AB7 cell >> Choose equal to >> enter 1 >> Add.
➤ The weight for NVDA should be at least zero: Select AB5 cell >> Choose greater than equal to >> Enter 0 >> OK.
➤ Check all the inputs and hit the Solve button.
➤ Check Keep Solver Solution >> OK.
Based on the Solver results our portfolio should have the following weights for each stock:
➤ Toyota Motor Corporation: 10%
➤ Walmart Inc.: 35%
➤ Chevron Corporation: 29%
➤ Nvidia Corporation: 2%
➤ Microsoft Corporation: 23%
➤ For each of the five assets, you will obtain a different weight.
The risk in SML is beta or systematic risk.
What is the minimum variance curve of a portfolio?
The minimum variance curve or minimum variance frontier represents a set of portfolios with the least variance (risk) for each level of expected return.
How to calculate returns from the adjusted close price?
Returns:
Wrapping Up
In this tutorial, we’ve learned about the minimum variance portfolio and the steps to calculate minimum variance portfolio in Excel using the functions and the Solver add-in.
So please ask me a question if anything is unclear.
Many thanks for your time and help. Feel free to download the practice file and share your thoughts and suggestions.
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How to Calculate Portfolio Variance in Excel
For versions of Excel: Excel for Office 365, Excel for Office 365 for Mac, Excel 2016, Excel 2016 for Mac, Excel 2013, Excel 2011 for Mac, Excel 2010, Excel 2008 for Mac, Excel 2007
Diversification in Excel Using Multiple Securities
People have long known that diversification mitigates risk, not in just finacial markets, but in nearly every aspect of life.
This blog post explores the minimum variance portfolio and explains how to make a minimum variance portfolio in Excel using simple steps.
➤ A minimum variance portfolio offers the lowest risk for a given expected return.
➤ Excess returns:
➤ Transpose matrix:
➤ Variance-covariance matrix:
➤ Set weights arbitrarily.
It uses the covariance matrix of asset returns to assign weights that minimize the variance of the entire portfolio.
Why Use a Minimum Variance Portfolio?
➤ Uses diversification to lower portfolio risk.
➤ Only the historical return data is needed.
➤ A typical place to start in the Modern Portfolio Theory (MPT)
Making a Minimum Variance Portfolio in Excel
In this dataset, we have the returns from 1st January 2024 to 30th June 2024 for five stocks:
➤ Toyota Motor Corporation (TM)
➤ Walmart Inc.
(WMT)
➤ Chevron Corporation (CVX)
➤ Nvidia Corporation (NVDA)
➤ Microsoft Corporation (MSFT)
There are 123 observations and the returns have been calculated from Yahoo Finance based on the adjusted close price.
Suppose you are in charge of a portfolio of these five assets and want to reduce the total volatility.
Learn how in seven minutes!
The short tutorial below implements the standard matrix multiplication algorithm for determining expected portfolio variance and standard deviation (volatility). So before doing the matrix multiplication, the variance-covariance matrix must be filtered first.
Below are snips of my power bi and my example calculation in excel using MMULT and Transpose functions (see the formula bar on the snip).
It's probably confusing.
For risk averse investors, it is particularly useful since it can be used as a benchmark before using strategies.
Steps:
➤ Select the output cell (G3) and enter the formula. There is a correlation of 0.85 between the two stocks. But, have you ever wondered how diverisfication works on investments?
➤ Drag the Fill Handle tool to copy the formula for the rest of the columns and rows.
➤ Since there are 5 firms, select the cells for the 5 by 5 matrix >> Select all the excess returns >> Press Ctrl + Shift + Enter .
Note: Remember to press the Ctrl + Shift + Enter keys, otherwise you’ll get an error.
This can be accomplished in Excel with MMULT and TRANSPOSE array functions.This tutorial makes use of a COVARIANCE matrix. The value of stock A is $60,000, and its standard deviation is 15%, while the value of stock B is $90,000, and its standard deviation is 10%.