CAPM Lecture Notes

What is the slope of the Capital Allocation Line (CAL)?
- A. Idiosyncratic Risk
- B. Sharpe Ratio
- C. Global Minimum Variance Portfolio
Is a portfolio with a steeper Capital Allocation Line (CAL) generally preferred?
- A. Yes
- B. No
If allocating between two risky assets, what correlation leads to zero portfolio risk (standard deviation)?
- A. $<br>ho = 1$
- B. $<br>ho = -1$
- C. $<br>ho = -0.3$
- D. $<br>ho = 0$
For risky assets A and B with correlation $ho = -1$ and standard deviations 5 and 10, respectively, what weight on A gives you a zero-risk portfolio?
- A. 0.1
- B. 0.67
- C. 0.4
- D. 0.8

One Risky Asset and a Risk-Free Asset:
- Expected Return:
- $E(r)$ = .1028
- Portfolio Expected Return: $E(r_p) = .15$
- Risk-Free Rate: $r_1 = .07$
- Utility Values:\n - $U = .094$ \n - $U = .08653$ \n - $U = .078$ \n - Standard deviation: $ext{σ} = .0902$ \n - Portfolio standard deviation: $ext{σ}_p = .22$
Two Risky Assets:
- Expected Returns (%):
- Points plotted: 14, 13, 12, 11, 10, with proportions impacting the risk-return tradeoff.
Two Risky Assets and a Risk-Free Asset:
- Expected Returns plotted against Standard Deviation with distinct figures showing CAL.
Many Risky Assets:
- Formation of the Efficient Frontier and Minimum Variance Portfolio concepts.
Many Risky Assets and a Risk-Free Asset:
- Efficient Frontier and various capital allocation lines illustrated.

Purpose of CAPM: To price assets within portfolios based on an equilibrium model.
Establishes how risks influence pricing in financial markets.

Key Contributors:
- Harry Markowitz: Portfolio allocation in the 1950s.
- William Sharpe: Demonstrated equilibrium asset prices in 1964.
- Additional contributors: Jack Treynor, Jan Mossin, John Lintner.

Decomposition of Security Risk:
- $ext{Security Risk} = ext{Systematic Risk} + ext{Nonsystematic Risk}$
Pricing of Risk:
- Only systematic risk is priced; nonsystematic risk can be diversified away.

Equilibrium Definition:
- All assets are priced such that aggregate demand equals supply across all investors.

Investor Behavior:
- Rational, mean-variance optimizers with a single-period planning horizon.
- Homogeneous expectations—investment assumptions based on publicly available information.
Market Structure:
- All publicly traded assets; free borrowing/lending at a common risk-free rate.
- Assumes no taxes or transaction costs.
- Discussion prompted on the feasibility of these assumptions in real-world scenarios.

Uniform Portfolio Holding: All investors hold the same risky portfolio (the tangency portfolio).
This optimal risky portfolio also represents the market portfolio, comprising all assets in proportion to market value.

Illustrative Figure: Depicts the relationship between expected return and risk for efficient portfolios (CML).

Determining Risk Premium:
- E(r_M) - r_f ext{ is proportional to } ar{A} ext{σ}^2_M where σ²_M is variance of the market portfolio and ar A is average risk aversion.

Pricing Relationship:
- The ratio of risk premium to covariance with the market must be constant across assets:
- For assets $i$ and $j$ :
$rac{E(r_i) - r_f}{Cov(r_i, r_M)} = rac{E(r_j) - r_f}{Cov(r_j, r_M)}$
Substituting for the market portfolio:
- $E(r_i) - r_f = Cov(r_i, r_M) rac{E(r_M) - r_f}{ ext{σ}^2_M}$

Expected Return Formula:
- E(r_i) = r_f + eta_i(E(r_M) - r_f)
  - Where eta_i = rac{Cov(r_i, r_M)}{ ext{σ}^2_M}
- Risk Premium Concept: Only systematic risk (market risk) is compensated by a return premium.
- Idiosyncratic risk: regardless of volatility or variance, if uncorrelated with market, does not earn a premium.

Example 1:
- Market return = 10%, Risk-free rate = 2%, Google Beta = 2. Calculate expected returns.
Example 2: Nike with correlation to market specified to analyze expected return comprehension.
Example 3: Excel file comparing stocks Ford, GM, and Tesla, evaluating actual vs predicted returns.

Exploring the practical application of the CAPM.
Introduction to Multifactor Models (Avenues for broader risk assessment beyond CAPM).