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Efficient Frontier and Mean Variance Optimization for CFA Level 3



For the CFA Level 3 exam study session 9, Principles of Asset Allocation, we begin with the actual process of building a strategic asset allocation plan, the first step of which is to map out the universe of efficient portfolios you might invest in.

Put simply, first we generate what options are theoretically ideal from a risk/reward perspective and then we decide how to place our bets. In previous levels this has focused on mean variance optimization (MVO).

For CFA Level 3 we start with MVO but then look at three other alternatives that address some of MVO’s shortcomings. For the exam know the pros/cons of each approach and their implications for portfolio concentrations and rebalancing concerns. 

Generating and Interpreting the Efficient Frontier

The entire process of asset allocation involves a portfolio manager selecting a specified return on an efficient frontier and using historical data for asset class returns, standard deviations, and correlations to run various simulations to create a set of mean-variance portfolios.

There are a variety of approaches of estimating this efficient frontier, each with their advantages and drawbacks.

For the CFA Level 3 exam you need to know:

  • Mean Variance Optimization (MVO)
  • Reverse Optimization
  • The Black Litterman Model

This post is concerned with mean variance optimization (both constrained and unconstrained). 

Understanding Mean Variance Optimization

Mean Variance Optimization, or MVO, involves taking the expected return of each asset, the standard deviation of each asset, and the correlation between assets to create an efficient frontier, or set of portfolios with the lowest risk for any given level of return.

Broadly speaking, the process looks like this:

Mean Variance Optimization (MVO) CFA Exam

There are two types of MVO: constrained and unconstrained.

  • Unconstrained MVO allows for short-selling
  • Constrained MVO is long-only

In both approaches the combined weight of all assets = 1 (100%). 

In theory, MVO should generate a list of minimum variance portfolios to select from based on desired risk and return characteristics:

Minimum Variance Frontier - CFA

From the global minimum variance portfolio we can add in a risk free asset to get the CML/CAL depicted below. Portfolios on the CML/CAL dominate the EF.

Capital Allocation Line (CAL) - CFA Exam

Positives and Negatives of Mean Variance Optimization (MVO)

Mean variance optimization has many advantages and disadvantages. For the CFA Level 3 exam you will want to be very comfortable comparing MVO to both the Black Litterman and reverse optimization approaches to creating a market efficient portfolio. 

Positives of MVO

MVO is inexpensive, widely understood, and lets us identify portfolios with the best risk/return tradeoff (e.g. highest Sharpe ratio).

Negatives of MVO

There are many drawbacks to MVO including that it:

  • Is a static single-period model
  • GIGO – Garbage In, Garbage Out. MVO is VERY sensitive to the model inputs. Small changes in estimated returns, variances, or correlations will greatly alter the results. This can lead to estimation and input bias
  • Often leads to concentrated portfolios and requires frequent rebalancing
  • Ignores skewness and kurtosis of a portfolio, i.e. the mean and variance aren’t the only thing that matters
  • Ignores liabilities (or that portfolios may need to be used to pay for something in the future)
  • MVO identifies whether an asset allocation is diversified across asset classes but not necessarily the sources of risk / common risk factors