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Why CAPM Betas Change and What Time-Series Betas Measure

Article Quant Q&A · Author: Helper
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Summary

The document distinguishes beta as defined within the Capital Asset Pricing Model from a beta estimated by regressing a stock’s returns on a chosen market index. The question asks how exchange rates, inflation, and interest rates might explain a company’s changing estimated beta. The answer cautions that a regression beta is an empirical time-series estimate and is not automatically the equilibrium beta described by CAPM.

Within the CAPM account presented, beta depends on the market portfolio and equilibrium conditions. Changes in the risk-free rate can alter the tangency portfolio; changes to securities’ payoffs, the set of available securities, investor preferences, or endowments can also change the market portfolio and resulting betas. The exchange does not give a direct causal mapping from a particular macroeconomic move to a beta change, nor does it provide data or an estimation method for testing one.

Key ideas

  • A beta estimated from stock and index returns is not necessarily the equilibrium beta defined by CAPM.
  • In the CAPM framework, beta depends on the market portfolio and equilibrium conditions.
  • Changes in the risk-free rate or available asset payoffs can alter the market portfolio and its betas.
  • Investor preferences and endowments can also affect equilibrium market values and individual betas.
  • A macroeconomic change alone does not establish why a regression beta moved.

Tags

EquitiesStatisticsRisk managementUS markets
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# Question about CAPM Betas - Causes of Beta Movement Query


# Question about CAPM Betas - Causes of Beta Movement Query












CAPM betas are measures of systematic risks, which include things like the exchange rate, inflation, interest rates, etc.

What I'm confused about is described below:

E.g. suppose I'm looking at one company's beta, which has decreased from 0.8 to 0.6 over 1 year, and during that period, the home country's exchange rate decreased which saw an increase in exports and sales revenue for the firm.

How has this exchange rate (amongst other factors) led to the decrease in the beta? Is it because the firm is performing well relative to the market portfolio so is seen as less risky?

Simply: how do factors like exchange rates, inflation and interest rates actually affect the beta? What's the link between them? When I see a change in a variable like exchange rates, how do I link it to the beta?

## Answer by Chen Deng-Ta (score 1)

https://quant.stackexchange.com/a/53714

In CAPM, Beta is not a systemic risk or a characteristic of any security:

- if the risk-free rate changes, the market portfolio changes as the tangent point moves, and beta changes accordingly

- When a security's payoff is changed or a new security is added to the market, the market portfolio must be changed, and the betas should be change

- Changes in investor preferences and endowments will change the equilibrium total market value, thereby affecting the return on the market portfolio and the beta of individual stocks

The beta you mention is a time series beta, the estimator you get from the regression of stock's return on some market index. This beta, is not the beta in CAPM. For more, see CAPM is neither a cross sectional model, nor a time series model

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.