Capital Market Theory

Quick Answer

Modern portfolio theory (MPT) builds the efficient frontier by combining assets with low correlation. The capital asset pricing model (CAPM) prices a security off its systematic risk (beta): E(R) = Rf + beta x (Rm - Rf). Alpha is return above CAPM. The efficient market hypothesis (EMH) comes in weak, semi-strong, and strong forms.

The whole unit on one sheet: MPT and the efficient frontier, CAPM with beta and alpha, the security market line, and the three forms of market efficiency.

The One-Liners That Win Points

  • Modern portfolio theory (MPT) maximizes expected return for a given level of risk; total risk is measured by standard deviation.
  • Combining assets that are not perfectly correlated reduces portfolio risk; the benefit starts at any correlation below +1.0, not just negative.
  • The efficient frontier is the set of optimal portfolios (highest return for each risk level). Nothing plots above it; individual securities plot inside (below and to the right) because they still carry unsystematic risk.
  • Adding the risk-free asset to the frontier creates the capital market line (CML).
  • Beta measures systematic risk only (sensitivity to the market); the market portfolio's beta is 1.0 by definition. Portfolio beta = weighted average of asset betas.
  • Alpha is return above the CAPM-expected return: positive = manager added value, negative = destroyed value.
  • Standard deviation = total risk; beta = systematic risk only.
  • R-squared shows how reliable beta is; below 0.70 beta is unreliable, so use standard deviation instead.
  • Security market line (SML): above the line = undervalued (buy, positive alpha); below = overvalued (sell, negative alpha).
  • Efficient market hypothesis (EMH) supports passive management / index funds; active management assumes markets are NOT fully efficient.

Numbers to Lock In

  • CAPM formula: E(R)=Rf+β×(Rm−Rf)E(R) = R_f + \beta \times (R_m - R_f) where RfR_f = risk-free rate (typically the 91-day T-bill yield), (Rm−Rf)(R_m - R_f) = market risk premium.
  • Alpha formula: α=Actual Return−[Rf+β×(Rm−Rf)]\alpha = \text{Actual Return} - [R_f + \beta \times (R_m - R_f)]
  • Worked CAPM: Rf 3%, Rm 10%, beta 1.2 gives 3% + (1.2 x 7%) = 11.4%. If the portfolio actually returned 14%, alpha = 14% - 11.4% = +2.6%.
  • Beta reference points: > 1.0 aggressive (moves more than the market), = 1.0 moves with the market, between 0 and 1.0 defensive, = 0 no correlation (cash, T-bills), negative moves opposite (rare).
  • Correlation (r): ranges -1.0 to +1.0; +1.0 = zero diversification benefit, -1.0 = maximum benefit.
  • Standard deviation ranges: ~68% of returns within 1 SD, ~95% within 2 SD, ~99.7% within 3 SD.

Top Gotchas

  • CAPM only compensates for systematic risk (beta), not total risk. If asked what return an investor should expect, use beta, not standard deviation.
  • Alpha is NOT portfolio return minus market return. Calculate the CAPM-expected return with the portfolio's beta first, THEN subtract.
  • Above the SML = undervalued (buy). "Above = overvalued" is the classic wrong answer.
  • CML uses standard deviation and applies to efficient portfolios only; SML uses beta and applies to any security. This is the highest-frequency trap.
  • Three forms of EMH: weak = past prices in price (technical analysis useless, fundamental may work); semi-strong = all public info in price (technical AND fundamental useless, only insider info helps), the most tested form; strong = all info including insider in price (nothing works).
  • Insider trading regulations are evidence AGAINST the strong form (insiders DO have an edge).

One-Breath Recap

Modern portfolio theory builds the efficient frontier by combining assets that are not perfectly correlated, reducing risk at any correlation below +1.0; individual securities plot inside the frontier because they carry unsystematic risk, and nothing plots above it. CAPM prices a security off systematic risk alone with E(R) = Rf + beta x (Rm - Rf), and alpha is the return above that expected value. Standard deviation is total risk, beta is systematic risk, and R-squared tells you when beta is trustworthy. The security market line flags undervalued (above) versus overvalued (below), the capital market line uses standard deviation for efficient portfolios only, and the efficient market hypothesis (weak, semi-strong, strong) points toward passive index investing.

Need more than the recap? This is a condensed summary. If it is not enough, read the full Capital Market Theory unit for the complete lesson.