Post Modern Portfolio Theory

Shiller and his colleagues have given the more open-minded members of the finance establishment examples that bring into question many of the assumptions of modern portfolio theory. Some have begun to chart a new course, aka, post-modern portfolio theory. We leave this as an exercise to the reader. One place to start is the Wikipedia article cited below.

Case Study Exercise

  1. Calculate the annualized means and variance for the 10 equity positions (GE, MSFT, PG, etc.).  Plot them on means-variance plane.

  2. Calculate the respective beta for each of the 10 given equities versus the S&P 500.

  3. Calculate the beta for the initial equity portfolio versus the S&P 500.

  4. Using the betas calculated above, and assuming a 10 year T-bill rate of 3.5%, calculate the expected returns of the individual equities as well as that of the initial equity portfolio.

  5. The guys in marketing have asked you to develop a portfolio asset allocation risk assessment tool for wealthy clients and potential clients – including individuals, institutions, foundations, and endowments. These clients have existing portfolios containing only vanilla stocks and/or bonds. You should create a tool that plots a portfolio on the Markowitz means-variance plane and then creates the efficient frontier, demonstrating how the client could use asset allocation either to increase return without increasing risk, or to reduce risk without decreasing return. You have the following asset categories at your disposal.

Asset Class

Index Proxy

US Large Cap equities

S&P 500 index

US Small Cap equities

Russell 2000

US investment grade bonds

Lehman Aggregate index

International Equity

MSCI World

Hedge Funds

HFRX Global Hedge Fund Index

US Real estate

FTSE NAREIT US Real Estate Index



We have given you the monthly return streams for each of these indexes. Your tool will take as input the client’s current allocation to each of these asset classes. Based on the mean-variance data at your disposal, you will calculate the following.

 

Bonus question: calculate the VAR (Value at Risk) of the client’s portfolios before and after diversification.


Acknowledgements

I would like to thank my risk colleagues, Pat Moran and David Mael, for their assistance in providing the index data (Pat) and reviewing these notes and exercises (David). I also have borrowed liberally from Stalla CFA test preparation materials to develop these notes and the exercises.

References



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