APT Flashcards
What is the risk adjusted interest rate
Why remove the one from risk adjusted interest rate?
We remove the one to isolare the excess return over the principal.
What is APT
APT offers a different approach to asset pricing, based on fewer assumptions:
Assumption 1: Multi-Factor Returns –>
Multiple macroeconomic or financial factors with each having zero expected value(shocks)
Assumption 2: No Arbitrage
APT requires no arbitrage — meaning prices must be set so there are no free lunches.
Only one smart investor needs to see this — not all must agree (unlike CAPM!)
What does APT not assume
No assumptions about:
Market portfolio
Normal distributions
Investor preferences
Homogeneous expectations
This makes APT more general and flexible.
APT Key insight
APT is about relative pricing: if two assets have the same risk exposure, they must offer the same return. If not, there’s arbitrage.
APT Implications
- Uncertainty
We don’t know which state will occur in the future, but we know the possible outcomes (states of the world).
Law of One Price
Securities with:
Positive payoffs → must have positive prices.
Same payoffs → must have the same price.
Otherwise → there’s an arbitrage opportunity
APT Portfolio (1-Factor Case)
Purpose of This Portfolio:
Total Beta = 0 → No risk exposure
Total Cost = 0 → Zero investment
Therefore: must have zero expected return, or there’s arbitrage
So this “test portfolio” proves that:
If the market prices are inconsistent with risk, someone can construct a zero-cost, zero-risk portfolio with positive return.
That violates the no-arbitrage condition.
Hence, market prices must adjust to avoid this.
Final APT Portfolio Equation
The portfolio constructed has:
No net investment
No exposure to the risk factor
No expected return
If it did return something, it would be arbitrage — which violates APT’s core assumption.
Key benefit of APT
APT is a more general and empirically robust model. It avoids many of the theoretical issues (like Roll’s critique) by not requiring a true market portfolio or specific investor behavior. It’s especially relevant in modern asset pricing, where returns are understood to be driven by multiple sources of risk (size, value, momentum, macro factors).
APT Equilibrium
The excess return per unit of factor risk (beta) must be the same across all assets.
APT to SML Equation in the factor - Derivation
APT to SML Equation in the 1-factor - Derivation
This is the Security Market Line (SML) — but derived without needing the full assumptions of CAPM, just no arbitrage and linear pricing.
Key Takeaways - APT to SML Equation in the 1-factor
APT derives the SML using arbitrage, not investor preferences.
The market portfolio doesn’t even need to be the true market.
Only works well for diversified portfolios, where idiosyncratic risk is diversified away.
Multi-Factor APT - Generalized version of APT
More realistic than CAPM because it recognizes multiple sources of risk.
Only two assets are needed to calculate these lambdas using real market data.
APT One Factor Pricing - Step by Step
Spotting Arbitrage in APT
APT Overview
CAPM Overview
