The Constants of the APT Equation

The Constants of the APT Equation

The existence of the risk free asset yields a risk free rate of return that is a constant. The asset does not have sensitivity to the factor for example, the industrial production.

In other words, λ0 is equal to the risk free rate of return. If the single factor portfolio’s sensitivity is equal to one i.e. b1 = 1 then

This can be rewritten as

Thus λ1 is the expected excess return over the risk free rate of return for a portfolio with unit sensitivity to the factor. The excess return is known as risk premium.

Factors Affecting the Return

The specification of the factors is carried out by many financial analysts. Chen, Roll and Ross have taken four macro economic variables and tested them. According to them the factors are inflation, the term structure of interest rates, risk premium and industrial production. Inflation affects the discount rate or the required rate of return and the size of the future cash flows. The short term inflation is measured by monthly percentage changes in the consumer price index. The interest rates on long term bonds and short term bonds differ. This difference affects the value of payments in future relative to short term payments. The difference between the return on the high grade bonds and low grade (more risky) bonds indicates the market’s reaction to risk. The industrial production represents the business cycle. Changes in the industrial production have an impact on the expectations and opportunities of the investor. The real value of the cash flow is also affected by it. Burmeister and McElroy have estimated the sensitivities with some other factors. They are given below

Default risk

Time premium

Deflation

Change in expected sales

The market returns not due to the first four variables.

The default risk is measured by the difference between the return on long term government bonds and the return on long terms bonds issued by corporate plus one-half of one per cent. Lime premium is measured by the return on long term government bonds minus one month Treasury bill rate one month ahead.

Deflation is measured by expected inflation at the beginning of the month minus actual inflation during the month. According to then, the first four factors accounted 25% of the variation in the Standard and 1or Composite Index and all the four co-efficient were significant.

Salomon Brothers identified five factors in their fundamental factor model. Inflation is the only common factor identified by others. The other factors are given below

Growth rate in gross national product

Rate of interest

Rate of change in oil prices

Rate of change in defence spending

All the three sets of factors have some common characteristics. They all affect the macro economic activities. Inflation and interest rate are identified as common factors. Thus, the stock price is related to aggregate economic activity and the discount rate of future cash flow

APT and CAPM

The simplest form of APT model is consistent with the simple form of the CAPM model. When only one factor is taken into consideration, the APT can be stated as:

R_i = λ₀ + b_i λ_i

It is similar to the capital market line equation

R = R_f + ß (R_{m            f})

Which is similar to the CAPM model?

APT is more general and less restrictive than CAPM. In APT, the investor has no need to bold the market portfolio because it does not make use of the market portfolio concept. The portfolios are constructed on the basis of the factors to eliminate arbitrage profits. APT is based on the law of one price to hold for all possible portfolio combinations.

The APT model takes into account of the impact of numerous factors on the security. The macro economic factors are taken into consideration and it is closer to reality than CAPM.

The market portfolio is well defined conceptually. In APT model, factors are not well specified. Hence the investor finds it difficult to establish equilibrium relationship. The well defined market portfolio is a significant advantage of the CAPM leading to the wide usage of the model in the stock market.

The factors that have impact on one group of securities may not affect another group of securities. There is a lack of consistency in the measurements of the APT model.

Further, the influences of the factors are not independent of each other. It may be difficult to identify the influence that corresponds exactly to each factor. Apart from this, not all variables that exert influence on a factor are measurable.