Portfolio variance formula excel mmult
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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%. 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.
However, some accounts only have a couple of products. This method works well if you want to lower portfolio risk without depending on projected returns. The risk in CML is the standard deviation of returns or the total risk.
SML indicates the market’s risk and returns at a specific point in time and the expected returns of each asset.
➤ 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.
The total weight adds up to 1.
➤ Based on past data, these weights will return the lowest portfolio standard deviation.
➤ Note how diversification among assets with weak or negative correlations helps to lower total volatility.
➤ The minimum variance portfolio configuration can be used as a standard against which other portfolios (such as equal weighted or max Sharpe) can be compared.
FAQ
What is portfolio variance?
Portfolio variance measures the risk of a portfolio based on the variance of each asset in that portfolio.
How to minimize portfolio variance?
Portfolio variance can be minimized by selecting stocks with negative or low correlation.
What is the difference between CML and SML?
CML shows the rate of return for a certain portfolio.
We want to minimize the portfolio variance.
➤ For the By Changing Variable Cells field choose the weights (AB2:AB6).
➤ Click Add to add constraints.
You can add multiple constraints. 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.
Portfolio Variance Formula
Let us take the example of a portfolio that consists of two stocks.
Excess return is calculated by subtracting the average returns from the firm’s return.
Note: Press the F4 key twice to lock only the rows. Alternatively a portfolio variance can be calculated using a CORRELATION matrix, but using the COVARIANCE may be more intuitive.
You may also be interested in:
Portfolio Optimization with Excel
Value at Risk with Excel
You can download the Excel file used in the video here.
Portfolio Standard Deviation in Excel
Using 123 daily return observations, we’ll determine the minimum variance portfolio weights for the five assets.
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.
But, have you ever wondered how diverisfication works on investments? 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. 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.
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.
This tutorial covers how to quickly and accurately calculate portfolio volitility for any number of securities.The tutorial is useful for anyone trying to understand diversification of risk, and is a must know for any aspiring Professional Risk Manager(PRM).
Easily Calculate Portfolio Volatility (Standard Deviation) Using Excel
Finance textbooks demonstrate how to calculate variance of a portfolio with two securities, a fairly complex algorithm meant to demonstrate the idea of diversification, however not very realistic.
Determine the variance.
Given,
- The standard deviation of stock A, ơA = 15%
- The standard deviation of stock B, ơB = 10%
Correlation, ρA,B = 0.85
Below is data for the calculation of the portfolio variance of two stocks.
Weightage of Stock A, wA = $60,000 / ($60,000 + $90,000) * 100%
Weightage of Stock A = 40% or 0.40
Weightage of Stock B, wB = $90,000 / ($60,000 + $90,000) * 100%
Weightage of Stock B= 60% or 0.60
Therefore, the portfolio variance calculation will be as follows,
Variance = wA2 * ơA2 + wB2 * ơB2 + 2 * ρA,B * wA * wB * ơA * ơB
= 0.4^2* (0.15)2 + 0.6 ^2* (0.10)2 + 2 * 0.85 * 0.4 * 0.6 * 0.15 * 0.10
Therefore, the variance is 1.33%.
When constructing an investment portfolio, reducing risk is as important as increasing returns.
➤ You’ll get the transpose matrix. 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.
Feel free to download the practice file and share your thoughts and suggestions.
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Hi guys,
Need your help.
I have a portfolio with various accounts each of which has some products (called risk_curve_month_name in my datasets).
My goal is to be able to calculate portfolio variance based on what accounts were selected (one or a few).
Portfolio variance is calculated through the multiplication of the transposed vector of asset weights by the variance-covariance matrix and multiplied by the vector of asset weights again (this time not transposed).
The weights of assets are already calculated in my power bi: quantity (called exposure in my dataset) * price * variance.
The tricky part is that the variance-covariance matrix consists of all possible combinations of the products.