# Beta

Beta is a measure of the risk of a stock when it is included in a well-diversified portfolio.

In financial theory, the Capital Asset Pricing Model breaks down expected stock returns into two components. The first is the return that would be expected based on covariance with the movements of the market (for most stocks, when the market as a whole goes up, the price of the stock will also go up). This is considered systematic risk. The second part is the increase in the price of a stock that is not explained by the market (nonsystematic risk). The first part - covariance with the market - is what Beta captures.

When Beta is positive, the stock price tends to move in the same direction as the market, and the magnitude of Beta tells by how much. If a stock's Beta is greater than 1, that means that when the market index goes up 1%, we expect the stock will go up by more than 1%. On the contrary, if the market goes down by 1%, we expect the stock to go down by more than 1%. Negative betas signify a negative correlation. When the market goes up, a stock with a negative beta would be expected to go down.

For readers with a background in regression analysis, Beta is the slope of the linear regression shown in the formula below, where Returns are the return on an individual stock or portfolio, R_f is the risk free rate, R_Market is the return on a market portfolio, and e is an error term.

The following is a table of the benchmark indices used for specific asset classes:

Asset Class | Benchmark Index | Symbol |
---|---|---|

US Equity | S&P 500 Total Return | ^SPXTR |

International Equity | MSCI ACWI ex USA Net Total Return | ^MSACXUSNTR |

Municipal Bond | Bloomberg Municipal Bond Total Return | ^BBMBTR |

Allocation | S&P 500 Total Return | ^SPXTR |

Taxable Bond | Bloomberg US Aggregate Total Return | ^BBUSATR |

Commodities | Bloomberg Commodity Index Total Return | ^BCTR |

Money Market | Bloomberg US Treasury Bills 1-3 Month Total Return | ^BBUTB13MTR |

Sector Equity | MSCI World Net Total Return | ^MSWNTR |

Alternative | MSCI ACWI Net Total Return | ^MSACWINTR |

Canadian Equities | S&P/TSX 60 Index Total Return | ^SPTSX60TR |

Canadian Fixed Income | Bloomberg Global Aggregate CAD Hedged | ^BBGATRCADH |

Beta = Covariance ( Portfolio Return , Benchmark Return) / Variance (Benchmark Return)