Sep
29

## Markowitz's Response Towards Financial Crises

Came across an interesting paper

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Worst-Case Value at Risk of Nonlinear Portfolios

**Does Portfolio Theory Work During Financial Crises?**by Harry M. Markowitz, Mark T. Hebner, Mary E. Brunson, in which the authors defend the Modern Portfolio Theory (MPT) against people's critics due to financial crisis.during any interval of time (day, month, year) the idiosyncratic term of the portfolio during this period is the weighted average of the idiosyncratic terms of the individual securities;

-however, the variance of the idiosyncratic term is not the weighted sum of the securities’ idiosyncratic variances: It is less than that!

Since the securities’ idiosyncratic terms are uncorrelated, they tend to diversify: With a high probability some will do well when others do poorly.

With a sufficiently large, well-diversified portfolio the variance of the portfolio’s idiosyncratic term is negligible.

For example, suppose that all securities in a portfolio have the same alpha: then the portfolio will have that alpha. Also suppose that each security has the same beta: then the portfolio will have the same beta as each of its securities. But if the variances of the idiosyncratic terms of the securities are the same, the variance of the idiosyncratic term for the portfolio will not be the same: It will be smaller than that of each of its securities. The idiosyncratic risks diversify away. The systematic risk (due to beta times the market) does not diversify away.

Generally, asset classes moved roughly in proportion to their historical betas.

At any time we should make our best estimates for “the next spin of the wheel,” and then choose an appropriate point from the implied risk-return trade-off curve.

-however, the variance of the idiosyncratic term is not the weighted sum of the securities’ idiosyncratic variances: It is less than that!

Since the securities’ idiosyncratic terms are uncorrelated, they tend to diversify: With a high probability some will do well when others do poorly.

With a sufficiently large, well-diversified portfolio the variance of the portfolio’s idiosyncratic term is negligible.

For example, suppose that all securities in a portfolio have the same alpha: then the portfolio will have that alpha. Also suppose that each security has the same beta: then the portfolio will have the same beta as each of its securities. But if the variances of the idiosyncratic terms of the securities are the same, the variance of the idiosyncratic term for the portfolio will not be the same: It will be smaller than that of each of its securities. The idiosyncratic risks diversify away. The systematic risk (due to beta times the market) does not diversify away.

Generally, asset classes moved roughly in proportion to their historical betas.

At any time we should make our best estimates for “the next spin of the wheel,” and then choose an appropriate point from the implied risk-return trade-off curve.

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