VoseTangentPortfolio | Vose Software

# VoseTangentPortfolio

VoseTangentPortfolio(Expected Return,Deviation,Correlation Matrix,Interest Rate, Labels)

Array function that uses the Capital Asset Pricing Model (CAPM) to find the tangent portfolio for a set of assets: the composition of the portfolio that has optimal return rate for minimal variance (i.e. sensitivity for market risk). This portfolio composition is returned as an array of asset weights (that sum to one).

• Expected return - array with the expected return of each asset

• Deviation - array with the standard deviation of each of the assets

• Correlation matrix - array with the matrix of correlation coefficients between the assets

• Interest rate - the risk-free interest rate

• Labels - (optional) array that contains the names of the assets

In the view of the CAPM model, two types of risk are at play for assets:

• The non-systematic risk attached to an individual asset. This can be reduced (to the point where it is neglectable)  by diversifying the portfolio, so this risk is also known as diversifiable risk.

• The systematic risk, caused by the uncertainty of the market. This can be thought of as the risk that is still there when adding the asset to a portfolio that is already well diversified. This type of risk is called the non-diversifiable or market risk.

Sensitivity for the second type of risk (which is the most important, as the first can be diversified away), called the variance of the portfolio, is represented by beta coefficient in finance. An optimal portfolio is one that has the lowest variance - lowest beta coefficient - for a given return. In a variance-return plot, these optimal portfolio combinations make up the efficient frontier.

As total budget to invest is often a constraint when composing a portfolio, the quantities of each asset that comprise it are expressed in weights (proportions of the total budget). The budget constraint is accounted for in the fact that the weights sum to one.

One other component can be incorporated. Rather than investing the entire budget in assets, one might keep part of the budget in cash, earning an (albeit lower) interest at the risk-free return rate. The variance-return relationship of this is linear, and represented as the Security Market Line (SML).

Both components are optimally accounted for in the Tangent Portfolio: where the SML and efficient frontier meet.