Analytics Vidhya
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Analytics Vidhya

Black-Litterman Model:

The Perspective of Individual Investor

Photo by Stepan Babanin via Unsplash

Do you love fruits? What kind of fruit do you like? Do you like apples? If yes, welcome aboard. Which one do you prefer, a red Gala or a green Granny Smith? Neither? Let me guess you are a big fan of a yellow Golden Delicious. Talk about ripeness, which quite tricky sometimes as color may not indicate the level of ripeness due to natural color of certain apples. However, if you compare two almost perfectly same apples, you are able to distinguish the level of ripeness. You are confident, a darker red Gala means more in ripeness than less red one.

Just like apples, portfolio of asset can be constructed in the same way where you utilize feeling and confidence to determine level of ripeness. In Black-Litterman model, portfolio is permissible to be generated as a product with combination of investor’s view confidence, either absolute or relative view, and market equilibrium. In my previous article, we have discussed about portfolio optimization derived from Markowitz’s Modern Portfolio Theory(MPT). MPT is not flexible, any changes in variance either upside or downside will significantly penalize the weight of asset allocation in our portfolio.

In contrast, Black-Litterman model which developed by Fischer Black and Robert Litterman (1992) generates forecast in Bayesian framework. Bayesian starts with existing ‘prior’ belief to generate ‘posterior’ belief. The Black-Litterman model was developed to make portfolio modeling more useful in practical investment situations (Litterman, 2003).

Let’s get started to get better understanding.

Import Library and Data

Fig-1| Adj. Close
Fig-2| Annualized Covariance
  • Start date from 30 September 2010 and end date at 30 September 2020.
  • Stocks are chosen from Indonesia Stock Exchange(IDX) and data taken from Yahoo.

General Info

Fig-3| General Info
  • Model starts with reverse optimization, where the initial weights and implied returns are calculated based on the market capitalization of the asset.
  • Delta is risk aversion score and tau is a scalar measuring the
    uncertainty of the CAPM prior.
  • P is a matrix of investor’s view and Q is a matrix of investor’s view value

Black-Litterman Model

Fig-4| Black-Litterman Formula

After we input investor’s view matrix and its score, now we get expected return posterior, covariance posterior and weight posterior

Final

Fig-5| Initial vs. Posterior Weight

Investor’s view and score are crucial in the Black-Litterman model as the factors will determine weight posterior, expected return posterior and covariance posterior.

References

  • He, G., & Litterman, R. (2002). The intuition behind Black-Litterman model portfolios.
  • Cheung, W. (2010). The black–litterman model explained. Journal of Asset Management, 11(4), 229–243.
  • Mankert, C. (2006). The Black-Litterman Model: mathematical and behavioral finance approaches towards its use in practice (Doctoral dissertation, KTH).
  • Litterman et. al., (2003) Modern Investment Management- an equilibrium approach, New Jersey: Wiley.

Disclaimer:

This material has been prepared for general informational purposes only and is not intended to be relied upon as professional advice. The information is being presented without consideration of the investment objectives, risk tolerance or financial circumstances .

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Smurpratomo

Smurpratomo

A Data Science learner || Jakarta, ID

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