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Capital Asset Pricing Model (CAPM)

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Financial Mathematics

Definition

The Capital Asset Pricing Model (CAPM) is a financial model that describes the relationship between systematic risk and expected return for assets, particularly stocks. It establishes a framework for evaluating the expected return on an investment given its risk in relation to the market as a whole, connecting crucial concepts like risk premiums, diversification, and efficient portfolios.

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5 Must Know Facts For Your Next Test

  1. The CAPM formula is expressed as: $$E(R_i) = R_f + \beta_i (E(R_m) - R_f)$$ where $$E(R_i)$$ is the expected return on asset i, $$R_f$$ is the risk-free rate, $$\beta_i$$ is the asset's beta, and $$E(R_m)$$ is the expected return of the market.
  2. CAPM assumes that investors are rational and risk-averse, seeking to maximize their expected returns while minimizing risk through diversification.
  3. The model emphasizes the importance of systematic risk (market risk), which cannot be eliminated through diversification, unlike unsystematic risk (specific to individual assets).
  4. CAPM provides a benchmark for assessing portfolio performance and making informed investment decisions based on the expected returns relative to their risks.
  5. The validity of CAPM has been debated among financial scholars, particularly regarding its assumptions and its applicability in real-world scenarios.

Review Questions

  • How does the Capital Asset Pricing Model help investors understand the trade-off between risk and return?
    • The Capital Asset Pricing Model helps investors understand that higher levels of systematic risk are associated with higher expected returns. By quantifying this relationship through beta and comparing it with the risk-free rate and market returns, investors can evaluate whether an asset offers a fair return given its level of risk. This understanding aids in making informed investment decisions while managing portfolio exposure to market fluctuations.
  • Discuss how CAPM contributes to mean-variance analysis and the construction of an efficient frontier.
    • CAPM plays a key role in mean-variance analysis by providing a method to assess the expected return for assets based on their systematic risk. When constructing an efficient frontier, CAPM helps identify optimal portfolios that yield the highest returns for given levels of risk. This model reinforces the idea that efficient portfolios should lie on the efficient frontier, maximizing return relative to risk while considering the trade-offs outlined by CAPM.
  • Evaluate how CAPM relates to the Efficient Market Hypothesis and its implications for active portfolio management strategies.
    • CAPM relates closely to the Efficient Market Hypothesis (EMH) by asserting that all available information is reflected in asset prices, suggesting that it is difficult to consistently outperform the market through active management. If markets are efficient, then CAPM implies that no excess returns can be gained without taking on additional risk. This challenges active portfolio management strategies since they may struggle to outperform passive strategies that align with CAPM expectations, leading investors to favor index funds over actively managed portfolios.
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