Arbitrage Pricing Theory

CAPM says one thing drives a stock's required return: how much it moves with the market. That is tidy, but real returns clearly respond to more than one force — inflation surprises, economic growth, interest-rate changes.

Arbitrage Pricing Theory keeps CAPM's core logic (only non-diversifiable risk is rewarded) and allows several sources of that risk. A stock gets a separate beta for each factor, measuring how sensitive it is to that factor.

The price of that flexibility: the theory does not tell you which factors to use.

The workbook lists APT's assumptions:

1. Capital markets are perfectly competitive.
2. Investors always prefer more wealth to less with certainty.
3. Asset returns are generated as a linear function of K factors or indexes.

Just as important is what APT does not assume:

• a market portfolio containing all risky assets that is mean-variance efficient;
• normally distributed security returns.

Like CAPM, APT treats unique risk as independent and diversifiable in a large portfolio. Its main practical challenge, in the workbook's words, is the identification of the risk factors. The examples the workbook gives are inflation, growth in GNP and changes in interest rates.

Written in the linear factor form the workbook uses for multifactor models (Chapter 18):

R_i = a_i + b_i1·F_1 + b_i2·F_2 + … + b_iK·F_K + ε_i

b_ik = sensitivity (beta) of asset i to factor k
F_k  = return or surprise of factor k
ε_i  = unique, diversifiable part of the return

CAPM is the special case with one factor — the market — and one beta.

Illustrative figures — the workbook gives no numerical APT example. An analyst estimates the expected return on a listed auto-component maker using three factors. The risk-free rate is 7%.

Expected return = 7% + 5.1% = 12.1%. On a ₹10 lakh holding, that is ₹1.21 lakh a year.

Now suppose a single-factor CAPM view gave the same stock a market beta of 1.1 and a market risk premium of 6%: 7% + 1.1 × 6% = 13.6%. The two models disagree by 1.5 percentage points because APT has separated why the stock is risky. A manager who expects inflation to cool can see that only 1.0% of this stock's premium comes from inflation exposure — something the single CAPM beta cannot show.

Chapter 16 (Introduction to Capital Market Theory), section 16.11, introduces APT as the main multifactor alternative to CAPM. Questions are conceptual: who developed it (Stephen Ross), how many betas it uses, which CAPM assumptions it drops, and its main weakness. Chapter 18 (Equity Portfolio Management Strategies) extends the same linear factor idea to macroeconomic, fundamental and statistical factor models.

• APT does not assume normal returns and does not need a market portfolio. Questions phrase these as assumptions to see if you tick them. Both are CAPM features.
• APT still says unique risk is diversifiable — it does not reward company-specific risk any more than CAPM does.
• Many betas, not one. Each beta measures sensitivity to a different factor.
• The factors are not specified by the theory. Inflation, GNP growth and interest rates are the workbook's examples, not a fixed list. Identifying factors is the model's main practical difficulty.
• Do not confuse APT with arbitrage in the derivatives sense (cash-futures price differences, Chapter 18). Same word, different idea.