Addressing MVO Criticisms: Reverse Optimization

In a report dated 26 January 2001, two financial analysts rated Enron a "buy" at USD 98, when the stock was trading at USD 79. One year later, it was trading at less than USD 1. Knowing this, it should come as no surprise that the analysts' predictions were built on earnings estimates of Enron's fake subsidiaries. The estimates that built their prediction were wrong. Clearly, it wasn't a good situation, but it might have been avoidable if the forecast wasn't built on unrealistic estimates or if the analysts took their assumed Enron value and broke it down. Suppose you were in charge of breaking down their forecast. What inputs would you work towards?

No. That's not breaking something down; it's building it up.

Not quite. That's not getting all the way to the heart of the issue.

Exactly! You'd break down the valuation into specific individual businesses so that the overall valuation can be analyzed from a different viewpoint. This could help address issues by changing the frame of reference. For mean–variance optimizations (MVO), there's a similar approach because, just like the Enron forecast, MVO relies on estimated inputs. So breaking down the optimization can be really helpful.

Which of these inputs do you think is based on an optimal risk/reward?

No. Covariances will measure just the risk portion of the inputs.

Not quite. Although it's an estimate, it's not going to factor in returns.

What portfolio should guide your asset allocation weights?

That's right! The world market portfolio is a great place to start developing the asset allocation opportunity set because it includes all investable assets for the client. Plus, it doesn't overlap. So the world market portfolio's market capitalization will be the foundation of the optimal asset allocation weightings. For example, in practice you can develop an all-inclusive market portfolio based on the securities found in traditional stock and bond index funds. These funds will typically capture most of the market size or capitalization, so they are essentially a proxy for the global market portfolio.

That's not it. There are some benefits to including global equities in diversification.

No, actually. Fixed-income investments would be excluded in this approach.

What type of risk is the focus of this reverse optimization process?

That's it! The reverse optimization process is going to capture systematic risk because it's linking the asset class's expected return directly to its systematic risk or beta. That's really a benefit of using a well-rounded asset allocation mix because it captures this overall portfolio risk. But you'll need to be careful in changing any of the expected returns for a particular asset class, because just like the mean–variance optimization, changing a specific input will lead to significant changes in the asset allocations.

No. Diversification among a global opportunity set limits non-systematic risk.

That's not it. A specific company would only be a very small fraction of this global portfolio.

To summarize: [[summary]]

The process is called __reverse optimization__, which takes asset allocation weights, covariances, and the risk-aversion coefficient and solves for the expected return. So while this process can help you identify which portfolios will meet your expected return requirement, it also must contain assumptions to achieve the necessary output at the best risk/reward ratio between the various asset classes.

That's it! Those asset allocation weights must be optimal or be on the efficient frontier in order to solve for the expected return. So that's one difficult assumption about reverse optimization and the reason why reverse optimization returns are referred to as implied or imputed returns. To start the reverse optimization process, you'll want to begin by establishing the optimal asset allocation weights by developing asset classes that form the opportunity set for the investor. These asset classes shouldn't overlap, so a broad approach is the starting point for developing a globally diversified opportunity set.

Once you have these indexes, you can use the capital asset pricing model to find the expected return of each asset class by using a risk-free rate and beta. The final step is then using your market capitalization weights to find the sum of the overall portfolio's expected return. You can see from this approach that consistency in applying betas to the market risk premiums of every asset class captures a more stable expected return because it incorporates global risk and also increases diversification.

The overall valuation of Enron

The sub-valuations of each major sector of Enron

The individual valuations of each part of Enron's business

Covariances

Investor risk coefficient

Asset allocation weights

The world market portfolio

The domestic equity index

The global equity market portfolio

Systematic risk

Non-systematic risk

Company-specific risk

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