Risk and Return 79average returns from these portfolios to be the same due to their differential sensitivity to macroeconomic
factors. The APT tries to capture these significant factors. The trick is to incorporate multiple sources of
economic risk by having more than one beta. Each beta (called factor beta) measures the sensitivity of the
stock to the corresponding factor. The APT model does not tell us what those factors are. It assumes that the
investor knows which systematic factors affect stock returns.
The investors can construct his/her model, unlike in CAPM where the beta is thrust upon us. The APT
model can be written as:
Expected return = Risk-free rate + [(sensitivity to factor 1) × (risk premium on factor 1)] +
[(sensitivity to factor 2) × (risk premium on factor 2)] + ···E(R)= Rf + β 1 [E(RM 1 – Rf)] + β 2 [E(RM 2 – Rf)] + ···If the stock market index is the sole factor explaining security returns, we would get back to our CAPM.
Studies in America have shown that about 5–6 factors affect US stock prices. One important study by Chen,
Roll and Ross (1980) suggests that growth in industrial production, unexpected changes in the term structure
of interest rates, spreads between high and low grade bond portfolio returns and unexpected inflation deter-
mine security returns.
Assume that a portfolio’s returns are dependent on two factors—say, industrial production and inflation.
Any unexpected change in the industrial production from the current levels would change the expected
returns in the same direction, while changes in inflation from current levels would change expected returns
in the opposite direction. Assume that there are four stocks whose returns and sensitivities are as follows:^8
Expected return Prod. Inflation
Stock (percent) sensitivity sensitivity
1 13 0.2 2.0
2 27 3.0 0.2
3 16 1.0 1.0
4 20 2.0 2.0
This is not possible because one can buy the first two stocks and short sell the remaining stocks (so
investment is zero) and still generate a positive return. This cannot happen in competitive markets. To con-
struct an arbitrage portfolio the following equations must be satisfied:
- INV 1 + INV 2 + INV 3 + INV 4 = 0, i.e., no investment.
- INV 1 [Sensit (P) 1] + INV 2 [Sensit (P) 2] + INV 3 [Sensit (P) 3] + INV 4 [Sensit (P) 4] = 0, i.e., no pro-
duction risk. - INV 1 [Sensit (I) 1] + INV 2 [Sensit (I) 2] + INV 3 [Sensit (I) 3] + INV 4 [Sensit (I) 4] = 0, i.e., no Inflation
risk.
(^8) Bower et al. (1992).