where R is the actual total return the expected part of the return and U stands

# Where r is the actual total return the expected part

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, where R is the actual total return, the expected part of the return, and U stands for the unexpected part of the return. 8
Factor models: announcements, surprises, and expected returns Any announcement can be broken into two parts: the anticipated or expected part and the surprise or innovation. Announcement = expected part + surprise The expected part of any announcement is part of the information the market uses to form the expected return. The surprise is the news that influences U. 9
Systematic risk and unsystematic risk: a revisit A systematic risk is any risk that affects a large number of assets (market risk). An unsystematic risk is a risk that specifically affects a single asset or a small group of assets (idiosyncratic risk). Uncertainty about general economic conditions, such as GNP, interest rates, or inflation, is an example of systematic risk. In contrast, the unexpected retirement of the company’s president is an unsystematic risk. It is unlikely to have an effect on the whole market. 10
Systematic risk and unsystematic risk We can break the total risk into two components: , where m is the systematic risk, which influences all assets in the market to some extent. ε is the unsystematic risk , because ε A is specific risk of company A, and is unrelated to the specific risk of company B, ε B . 11
Factor models The influence of a systematic risk (like inflation) on a stock is captured by the beta coefficient. The beta coefficient, β, tells us the response of the stock’s return to a systematic risk. For example, if a company’s stock is positively related to the risk of inflation, the stock has a positive inflation beta. If it is negatively related to inflation, its inflation beta is negative, and if it is uncorrelated with inflation, its inflation beta is zero. Suppose we have identified three systematic risks on which we want to focus: inflation, GNP, and interest rate. Thus, every stock will have a beta associated with each of these systematic risks: an inflation beta, a GNP beta, and an interest rate beta. F stands for a surprise, where it can be inflation, GNP, or interest rates. This model is called a factor model (3-factor model). A factor is a variable that affects the returns of risky assets in a systematic fashion. 12
Factor models In general, a K-factor model In practice, researchers frequently use a one factor model for returns and the factor is the returns on market index. This model is called a market model. It can be written as 13 F R R R R R M M ) (
The single-index model This model relates returns on each security to the returns on a broad market index of common stock returns. 12/4/18 14
The single-index model In this model, the covariance depends only on market risk. Therefore, the covariance between any two securities can be written as The total risk of a security, as measured by its variance, consists of two components: market risk and unique risk.

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