CFA L1 / PM / M2. CAPM
Module 2 · Portfolio Management

Portfolio Risk and Return — Part II (CAPM)

EN: CAPM, beta, Security Market Line, performance metrics.
VN: CAPM, beta, SML, các chỉ số đánh giá hiệu quả.

1. Capital Asset Pricing Model (CAPM) Core

About: E(R) = Rf + β·(Rm − Rf). Required return = risk-free + beta × market risk premium. Single-factor model — workhorse of equity cost of capital.Tóm tắt: E(R) = Rf + β(Rm − Rf). Required return = risk-free + β × MRP.
\[ E(R_i) = R_f + \beta_i \cdot [E(R_m) - R_f] \]

Components

  • Rf Risk-free rate.
  • E(Rm) − Rf Equity risk premium / market risk premium.
  • βi Beta — sensitivity of asset i to market.
Practice problem

Rf = 3%, E(Rm) = 10%, β = 1.4. Required return?

Show solution
E(R) = 3% + 1.4(10% − 3%) = 3% + 9.8%
= 12.8%

2. Beta Core

About: Sensitivity of asset return to market return. Captures only systematic (market) risk — diversifiable risk doesn't earn a premium. Foundation of CAPM.Tóm tắt: Độ nhạy của tài sản với thị trường. Chỉ bắt rủi ro hệ thống — risk đa dạng hóa được không có premium.
Market return Rm Asset return Ri β = 1 β < 1 β = 0 β > 1
Slope of the regression line of asset return on market return = beta.
\[ \beta_i = \frac{\text{Cov}(R_i, R_m)}{\sigma_m^{2}} = \rho_{i,m} \cdot \frac{\sigma_i}{\sigma_m} \]

Interpretation

  • β = 1 Same risk as market.
  • β > 1 Aggressive — moves more than market.
  • β < 1 Defensive.
  • β = 0 Uncorrelated with market.
  • β < 0 Hedge against market.
Practice problem

Cov(Ri, Rm) = 0.012, σm² = 0.04. Compute β.

Show solution
β = 0.012/0.04
β = 0.30

3. Security Market Line (SML) Core

About: Graphical CAPM. Above SML = undervalued (positive α). Below SML = overvalued. The tool to identify mispriced equities.Tóm tắt: Đồ thị CAPM. Trên SML = undervalued (α dương). Dưới SML = overvalued.

Graphical version of CAPM — relationship between expected return and beta. All correctly priced assets lie on the SML. Above SML = undervalued (positive alpha); Below = overvalued.

4. Performance Metrics Core

About: Sharpe (total risk), Treynor (systematic), Jensen's α (risk-adjusted excess), M² (Sharpe in return units), IR (active return per active risk).Tóm tắt: Sharpe (tổng), Treynor (hệ thống), Jensen's α, M², IR.
\[ \text{Sharpe} = \frac{R_p - R_f}{\sigma_p} \quad \text{(total risk)} \] \[ \text{Treynor} = \frac{R_p - R_f}{\beta_p} \quad \text{(systematic risk)} \] \[ \alpha_p = R_p - [R_f + \beta_p (R_m - R_f)] \quad \text{(Jensen's alpha)} \] \[ M^{2} = (R_p - R_f) \cdot \frac{\sigma_m}{\sigma_p} - (R_m - R_f) \quad \text{(M-squared)} \] \[ \text{Information ratio} = \frac{R_p - R_b}{\sigma(R_p - R_b)} \]

Sharpe and M² use total risk; Treynor and Jensen's α use systematic risk only — appropriate for well-diversified portfolios.

Practice problem

Rp = 12%, σp = 16%, βp = 1.1, Rm = 9%, Rf = 3%. Compute Sharpe, Treynor, Jensen's α.

Show solution
Sharpe = (12 − 3)/16 ≈ 0.563
Treynor = (12 − 3)/1.1 ≈ 8.18
α = 12 − [3 + 1.1(9 − 3)] = 12 − 9.6 = 2.4
Sharpe 0.563; Treynor 8.18; α = +2.4%