## What Is the Black-Litterman Model?

The Black-Litterman (BL) Model is an analytical tool used by portfolio managers to optimize asset allocation within an investor’s risk tolerance and market views. Global investors, such as pension funds and insurance companies, need to decide how to allocate their investments across different asset classes and countries.

The BL model starts from a neutral position using modern portfolio theory (MPT), and then takes additional input from investors' views to determine how the ultimate asset allocation should deviate from the initial portfolio weights. It then undergoes a process of mean-variance optimization (MVO) to maximize expected return given one's objective risk tolerance.

### Key Takeaways

- The Black-Litterman Model is a portfolio allocation model that begins with modern portfolio theory (MPT) and adds in investor views of expected returns.
- The MPT model is seen to be limited in that it only incorporates historical market data and then assumes those same returns going forward.
- The BL model lets the investor applies their own views and then optimizes the recommended asset allocation.

## The Basics of the Black-Litterman Model

The Black-Litterman model for portfolio construction is based on modern portfolio theory (MPT). Modern portfolio theory posits that an investment's risk and return characteristics should not be viewed alone, but should be evaluated by how the investment affects the overall portfolio's risk and return. MPT shows that an investor can construct a portfolio of multiple assets that will maximize returns for a given level of risk.

Likewise, given a desired level of expected return, an investor can construct a portfolio with the lowest possible risk. Based on statistical measures such as variance and correlation, an individual investment's performance is less important than how it impacts the entire portfolio.

The BL model was designed to improve on this model since one of the limitations of MPT is that it assumes that past expected returns will continue into the future. Other pricing models—for example, the capital asset pricing model (CAPM)—however, may produce different expectations than that of the past performance. The BL model incorporates observed market data along with investors' projections of future expected returns, based on models like CAPM or others. The model essentially modifies the default MPT allocation by taking into account expectations of future performance.

The BL approach allows any model estimation error to become apparent as allocation choices may magnify poor assumptions.

## Special Considerations

The BL model has been around since 1990, and it receives a great deal of respect from the institutional investment community. It was created by Goldman Sachs economists Fischer Black (of Black-Scholes model fame) and Robert Litterman.

While the BL model is seen to improve the asset allocations provided by MPT by incorporating opinions on future outlook, because these projections are merely opinions or the result of pricing models that rely on subjective inputs, the BL model may result in bias or incorrect assumptions. For instance, an overly-optimistic view of one asset class will result in having greater portfolio weight than MPT would recommend, and if that asset class falters can result in magnified losses. Investors utilizing the Black-Litterman model should be aware of this and update their expectations on a regular basis, rebalancing their portfolio weights accordingly.

## An Example of the Black-Litterman Model

Assume that a portfolio management team at a certain insurance company is extremely bullish on developing country markets in the year ahead. The initial asset allocation to emerging markets resulting from modern portfolio theory is 10%. After confirming their opinions with various pricing models and economic outlooks for the region, they are inclined to overweight emerging markets stocks.

After putting this bullish view into the BL model, they perform mean-variance optimization and allow their portfolio to contain up to 15% emerging markets securities.