The Capital Asset Pricing Model (CAPM) is a key tool in finance for estimating expected returns and assessing risk. It links an asset's expected return to its systematic risk, measured by beta, and the market risk premium.

CAPM helps investors and companies make informed decisions about investments and capital allocation. While it has limitations, CAPM remains widely used for estimating cost of equity, valuing assets, and understanding the risk-return tradeoff in financial markets.

Capital Asset Pricing Model (CAPM)

Assumptions and limitations of CAPM

• Assumes investors are rational and risk-averse, seeking to maximize returns while minimizing risk
• Assumes markets are perfectly competitive and efficient, with all information readily available and reflected in asset prices
• Assumes investors can borrow and lend at the risk-free rate (government bond yields)
• Assumes all investors have the same information and expectations about asset returns and risk
• Assumes there are no transaction costs (brokerage fees) or taxes that impact investment decisions
• Limited by the fact that real-world markets may not always be perfectly efficient (market anomalies, bubbles)
• Limited by the assumption that investors always behave rationally, which may not be the case (emotional investing)
• Relies on historical data to estimate parameters, which may not accurately predict future performance (past returns do not guarantee future results)
• Assumes a single-period time horizon, which may not reflect the reality of long-term investing (multiple holding periods)
• Does not account for unsystematic risk or company-specific factors (management quality, competitive advantage)

Calculating expected return with CAPM

• CAPM equation: $E(R_i) = R_f + \beta_i(E(R_m) - R_f)$
  • $E(R_i)$: Expected return of asset $i$ (individual stock)
  • $R_f$: Risk-free rate (10-year U.S. Treasury bond yield)
  • $\beta_i$: Beta coefficient of asset $i$, measuring its sensitivity to market movements
  • $E(R_m)$: Expected return of the market portfolio (S&P 500 index)
• Risk-free rate ($R_f$) represents the return an investor can earn without taking on any risk (default risk of government bonds)
• Market risk premium ($E(R_m) - R_f$) quantifies the additional return investors demand for bearing market risk (equity risk premium)
• Beta coefficient ($\beta_i$) captures the extent to which an asset's returns are influenced by overall market fluctuations (systematic risk)

Beta coefficient and systematic risk

• Beta coefficient ($\beta_i$) measures the systematic risk of an asset, which cannot be eliminated through diversification (market risk)
• Interpretation of beta values:
  • $\beta = 1$: Asset moves in perfect sync with the market (average risk)
  • $\beta > 1$: Asset amplifies market movements and is more volatile (aggressive stocks)
  • $0 < \beta < 1$: Asset is less responsive to market changes and is less volatile (defensive stocks)
  • $\beta = 0$: Asset's returns are uncorrelated with the market (risk-free assets)
  • $\beta < 0$: Asset moves in the opposite direction of the market (inverse ETFs)
• Higher beta values imply higher systematic risk exposure and, consequently, higher expected returns to compensate investors for the added risk (risk-return tradeoff)

CAPM for cost of equity estimation

• Cost of equity capital represents the required rate of return for a company's equity investors (shareholders)
• CAPM provides a framework to estimate the cost of equity capital:
  • $K_e = R_f + \beta_e(E(R_m) - R_f)$
    • $K_e$: Cost of equity capital (required return for shareholders)
    • $R_f$: Risk-free rate (10-year U.S. Treasury bond yield)
    • $\beta_e$: Beta coefficient of the company's equity (stock)
    • $E(R_m)$: Expected return of the market portfolio (S&P 500 index)
• The estimated cost of equity capital is a crucial input for various corporate finance decisions:
  1. Capital budgeting: Determining the hurdle rate for accepting or rejecting investment projects (NPV, IRR)
  2. Valuation: Discounting future cash flows to estimate the intrinsic value of a company or project (DCF analysis)
  3. Capital structure: Determining the optimal mix of debt and equity financing to minimize the weighted average cost of capital (WACC)