# Expected Return And Variance For A Two Asset Portfolio

In other words, you always need the variance of returns for each asset, the covariance between each pair of assets, and the investment weights. Portfolio variance is a measurement of risk, of how the aggregate actual returns of a set of securities making up a portfolio fluctuate over time. This portfolio variance statistic is calculated using the standard deviations of each security in the portfolio as well as the correlations of each security pair in the portfolio.

### When to Use bagging vs boosting?

Bagging is usually applied where the classifier is unstable and has a high variance. Boosting is usually applied where the classifier is stable and simple and has high bias.

This can be done by dividing the total value of each stock by the total portfolio value. Buttons- Press theCalculatebutton to calculate the Expected Return, Variance and Standard Deviation on portfolios formed from Stocks 1 and 2. Anderson is CPA, doctor of accounting, and an accounting and finance professor who has been working in the accounting and finance industries for more than 20 years. Her expertise covers a wide range of accounting, corporate finance, taxes, lending, and personal finance areas. The Structured Query Language comprises several different data types that allow it to store different types of information… Free Financial Modeling Guide A Complete Guide to Financial Modeling This resource is designed to be the best free guide to financial modeling! Learn financial modeling and valuation in Excel the easy way, with step-by-step training.

## How Can I Measure Portfolio Variance?

Note that σ12means the variance of asset 1, which is nothing but the covariance of the asset with itself. This formula is not really scalable to real life situations where a portfolio may consist of tens or hundreds of securities.

Asset 1 makes up 41% of a portfolio and has an expected return of 23% and volatility of 13%. Variance is a measurement of the spread between numbers in a data set. Investors use the variance equation to evaluate a portfolio’s asset allocation.

Fred wants to assess the risk of the portfolio using portfolio variance and portfolio standard deviation. As the number of assets in the portfolio grows, the terms in the formula for variance increase exponentially.

## Portfolio Standard Deviation In Excel

For Asset 1, enter the variance of Asset 1 (σ12), the covariance between Asset 1 and Asset 2 (σ12), and the covariance between Asset 1 and Asset 3 (σ13). Understand why covariance matters when considering the risk of a portfolio. Regression analysis is a set of statistical methods used to estimate relationships between a dependent variable and one or more independent variables. First, he needs to determine the weights of each stock in the portfolio.

The level of risk in a portfolio is often measured using standard deviation, which is calculated as the square root of the variance. If data points are far away from the mean, the variance is high, and the overall level of risk in the portfolio is high as well. Standard deviation is a key measure of risk used by portfolio managers, financial advisors, and institutional investors. Asset managers routinely include standard deviation in their performance reports. The most important quality of portfolio variance is that its value is a weighted combination of the individual variances of each of the assets adjusted by their covariances. This means that the overall portfolio variance is lower than a simple weighted average of the individual variances of the stocks in the portfolio. The short tutorial below implements the standard matrix multiplication algorithm for determining expected portfolio variance and standard deviation .

## Easily Calculate Portfolio Volatility Standard Deviation Using Excel

Two assets a perfectly negatively correlated provide the maximum diversification benefit and hence minimize the risk. We learned about how to calculate the standard deviation of a single asset. Let’s now look at how to calculate the standard deviation of a portfolio with two or more assets. Keep in mind that this is the calculation for portfolio variance. If a test question asks for the standard deviation then you will need to take the square root of the variance calculation. Percentage values can be used in this formula for the variances, instead of decimals. Wherewiis the investment weight for asset i,wjis the investment weight for asset j, and σij is the covariance between assets i and j.

For example, a three-asset portfolio has six terms in the variance calculation, while a five-asset portfolio has 15. The portfolio variance is equivalent to the portfolio standard deviation squared. Portfolio variance takes into account the weights and variances of each asset in a portfolio as well as their covariances. A better way is to use the variance-covariance matrix to find portfolio variance.

## Financial Calculators

This tutorial looks at how portfolio risk calculations can be modeled within Excel. You are unlikely to be asked to do this in the exam, in fact the multiple choice format is very poorly suited to testing such knowledge. Yet this is useful should you wish to see how this really would work in practice, or wish to test some additional ideas, for example, the impact of changing correlations on portfolio volatility. Risk is lowered in MPT portfolios by investing in non-correlated assets. Assets that might be risky on their own can actually lower the overall risk of a portfolio by introducing an investment that will rise when other investments fall.

Do you have a vague idea of how to measure it but find the implementation daunting? What we generally get is the correlation matrix, which gives us the correlation between any two of the assets in the portfolio in the form of a matrix. Where w1to wnare the weights of assets 1 to n in the portfolio, and σxyis the covariance between assets x and y.

## Expected Return For A Two Asset Portfolio

The modern portfolio theory looks at how risk-averse investors can build portfolios to maximize expected return based on a given level of risk. People have long known that diversification mitigates risk, not in just finacial markets, but in nearly every aspect of life. But, have you ever wondered how diverisfication works on investments?

### How do you calculate portfolio volatility?

Volatility for a portfolio may be calculated using the statistical formula for the variance of the sum of two or more random variables which is then square rooted. Alternatively, the volatility for a portfolio may be calculated based on the weighted average return series calculated for the portfolio.

Investors seek what is called an efficient frontier, or the lowest level of risk and volatility at which a target return can be achieved. The expected return of a portfolio is equal to the weighted average of the returns on individual assets in the portfolio. The variance of a portfolio of correlated assets can be written as WTvW, where W is a column vector containing the weights of different assets in the portfolio. V is the covariance matrix, and WTis the transpose of the matrix W.

## Expected Variance For A Two Asset Portfolio

Besides his extensive derivative trading expertise, Adam is an expert in economics and behavioral finance. Adam received his master’s in economics from The New School for Social Research and his Ph.D. from the University of Wisconsin-Madison in sociology.

• The returns of the portfolio were simply the weighted average of returns of all assets in the portfolio.
• Buttons- Press theCalculatebutton to calculate the Expected Return, Variance and Standard Deviation on portfolios formed from Stocks 1 and 2.
• Her expertise covers a wide range of accounting, corporate finance, taxes, lending, and personal finance areas.
• Also, if you have any questions or suggestions, you are more than welcome to leave a comment below.
• Asset 1 makes up 41% of a portfolio and has an expected return of 23% and volatility of 13%.
• Note that σ12means the variance of asset 1, which is nothing but the covariance of the asset with itself.
• We often say that risk and return are two sides of the same coin.

While portfolio return is a weighted average of each asset’s return, the variance of portfolio returns is not a weighted average of each asset’s variance of returns. This is because the interactions between pairs of assets, captured by covariances, affect portfolio risk as well. His pioneering work on the modern portfolio theory led to a share of a Nobel prize in 1990.

## Portfolio Variance

This reduced correlation can reduce the variance of a theoretical portfolio. For calculation of variance of a portfolio, we need a matrix of mutual correlation of all the constituent assets of the portfolio . The exact formula differs depending on the number of assets in the portfolio. In general as the correlation reduces, the risk of the portfolio reduces due to the diversification benefits.

This can be accomplished in Excel with MMULT and TRANSPOSE array functions.This tutorial makes use of a COVARIANCE matrix. Alternatively a portfolio variance can be calculated using a CORRELATION matrix, but using the COVARIANCE may be more intuitive. Variance of a portfolio measures the dispersion of average returns of a portfolio from its mean. It is calculated based on the individual variances of the portfolio investments and their mutual correlation. This formula is very useful in forming an intuitive understanding of how correlation affects risk, and examining various concepts relating to portfolio construction. Modern portfolio theory is a framework for constructing an investment portfolio. MPT takes as its central premise the idea that rational investors want to maximize returns while also minimizing risk, sometimes measured using volatility.

He is a CFA charterholder as well as holding FINRA Series 7 & 63 licenses. He currently researches and teaches at the Hebrew University in Jerusalem. If you found this post helpful, feel free to share it on social media. Also, if you have any questions or suggestions, you are more than welcome to leave a comment below. Gain the confidence you need to move up the ladder in a high powered corporate finance career path. Volatility measures how much the price of a security, derivative, or index fluctuates.

However, the calculation of the risk/standard deviation is not the same. While calculating the variance, we also need to consider the covariance between the assets in the portfolio. If the assets are perfectly correlated, then the simple weighted average of variances will work. However, when we have to account for the covariance, the equation will change.

See the calculations in action – here is asample spreadsheetwith 6 assets for which the standard deviations and correlations are known. We can calculate the portfolio volatility for any set of weights, and also calculate the Sharpe Ratio. We can look at the effect of changing different variables on risk and return, and even calculate the efficient portfolio . The returns of the portfolio were simply the weighted average of returns of all assets in the portfolio.