Finding The Beta For A Portfolio Isn't Obvious: An Educational Example

When a portfolio is not actively managed to maintain a fixed investment percentage in each asset but rather maintains a fixed number of shares for each asset, the portfolio weights will change over time because the market returns of the different assets will not be the same.  Consequently, portfolio betas computed as a linear combination of asset betas, which is the usual practice, will be different from betas computed using regression techniques on portfolio returns as is done when evaluating individual assets and mutual funds.  The alternative approaches can result in quite different beta statistics and, consequently, inconsistent decisions depending on which method is used.