Addressing MVO Criticisms: Black–Litterman Model

On 31 December 1975, Jack Bogle introduced the first index fund that tracked a standard market index. He had seen an opportunity to change the old way of investing by making a simple modification to the common investing model that has produced significant benefits and had a huge impact on how people invest. A small change can have a big impact, but it must be done right. For example, making a similar modification to the mean–variance optimization approach won't work very well. Why is changing an input to this model so dangerous?

Yes. Making a small change to the mean–variance optimization model can lead to extreme changes to the outputs. So just like Jack Bogle's investment vehicle modification, a small change will produce dramatic results. But unfortunately, this won't always be the best approach to maximizing the investor's utility, so there needs to be another way to complete the process and allow you to influence the inputs into the model without causing harm.

No, actually. Changing inputs could actually reduce trading costs, depending on the change.

For example, you may believe that Indian equities are going to outperform relative to the equities of other countries, so you'd naturally want to allocate more assets to them. How do you think the Black–Litterman model impacts your asset allocation's risk?

That's not it. You'd be improving returns with your extra allocation to Indian equities.

That's right! Risk should decrease if returns are being increased due to your personal forecast. That also means that the Sharpe Ratio should increase as a measure of risk-adjusted returns. So the Black–Litterman model improves the consistency between each asset class's expected return and its contribution to systematic risk.

No. Making asset allocation decisions definitely impacts risk.

The model itself can receive your personal inputs in one of two ways: as an absolute return forecast for a given asset class, or as a return differential of an asset as given relative to another asset. Unfortunately, the inner details of the model's calculations and algorithms have been captured in software, so analysts use the Black–Litterman model as an application through a computer.

No. It's not a constraint to change an input.

To sum it up: [[summary]]

That's where the __Black–Litterman Model__ comes in. It starts with returns in excess of the risk-free rate produced from the reverse optimization and uses a technique to alter the reverse optimization expected returns to incorporate your own personal views on asset returns. It can be used in an unconstrained or constrained optimization setting to improve the overall asset allocations. Or if you do not have market views, it can analyze the assumed market weights.

It adds another constraint to the portfolio

It can result in extreme changes to the outputs

It increases the rebalancing costs of the portfolio

It increases it

It decreases it

There's no impact

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