**Steps in Calculating Expected Return under Arbitrage Pricing Theory**

The following three steps are involved in estimating the expected return on an asset under Arbitrage pricing theory,

- Searching for the factors that affect the assets return
- Estimating of risk premium for each factor
- Estimating of factor beta

**Factors **

What factors are important in explaining the expected return? How are they identified? Arbitrage pricing theory does not indicate the factors that explain assets returns. The factors are empirically derived from the available data. Different assets will be affected differently by the factors.

The following factors were found important in a research study in the USA,

- Industrial production
- Changes in default premium
- Changes in the structure of interest rates
- Inflation rate
- Changes in the real rate of return

Is this an exhaustive list of macro economic factors? All do not agree. In another study, it has been found that price to book value rations and sizes are correlated with the actual returns. These measures have been found as good proxy of the risk.

**Risk premium**

What is the risk premium for each factor? Conceptually it is the compensation, over and above the risk free rate of return that investors require for the risk contributed by the factor. One could use past data on the forecast ed and actual values to determine the premium.

**Factors beta**

The beta of the factor is the sensitivity of the assets return to the changes in the factor. We can use regression approach to calculate the factor beta. For example a firm’s returns could be regressed to inflation relate to determine the inflation beta.

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