Arbitrage pricing Theory or apt Apt was developed by Stephen Ross in the 1970s as an alternative to cap M. Like cap M apt is focused on systemic risk to estimated expected returns. However, it differs from cap M and that it recognizes several different broad risk sources the most significant difference between apt and cap m is the way systematic risk is defined cap M Advocates a single market-wide risk factor while apt considers several factors in an environment of a single factor market the APT leads to cap M apt allows for different risk factors, but unlike capm the APT does not indicate the Identity or even the number of risk factors.

The APT is similar in nature to cap M. However, while capm uses specifically defined assumptions apt does not except however for Arbitrage remember that cap M takes the risk-free rate such as a US Treasury and adds the market risk premium multiplied by the Stock's beta to estimate the expected return the Arbitrage pricing theory-based model aims to do away with the limitations of the one factor model that different stocks will have different sensitivities to different Market factors, which may be totally different from any other stock under observation in layman terms one can say that not all stocks can be assumed to react to the single insane parameter always and hence the need to take the multi-factor approach along with their sensitivities note that the measure of an investment sensitivity to any macroeconomic Factor takes the form of a beta called a factor beta both models only price assets based on systematic risk and do not consider firm or specific.

The factor risk premium represents the expected reward for bearing the risk of a portfolio with a sensitivity to a specific Factor. This is also known as the factor value or factor price and it equals the expected return on the pure Factor portfolio IE a portfolio that is only sensitive to that factor minus the risk-free rate Factor sensitivity also known as Factor betas measures the sensitivity of the return to a specific Factor.

To calculate the return on a particular portfolio. We start by taking the risk-free rate and then add risk premiums for the portfolio's exposure to different Factor risks. Each factor risk has its own risk premium. However, the portfolio may have a different sensitivity to individual Factor risk measured by the portfolios Factor beta the factor beta multiplied by the factor risk premium gives the expected return for the portfolio's exposure to that particular Factor risk.

The risk factor one has a risk premium of 2.59 percent. The portfolio has a higher sensitivity to risk factor one. So it's Factor beta of 1.27 is above one. Therefore the portfolio is expected return for exposure to the factor 1 is 1.27 times 2.59 percent higher than the factor risk premium.

Factor is 2 has a risk premium of 0.66 percent. The portfolio has a lower sensitivity to risk factor 2 so it's Factor beta of 0.56 is below one factor, 3 has a risk premium of 4.32 percent but a factor sensitivity of 0.37 again also less than 1 therefore the overall expected return for the security would be 7.26% The sum of the risk-free rate plus the other factors adjusted for their Factor sensitivities.

The APT model does not guide us in the choice of the relevant factors.

Selecting an appropriate set of macroeconomic factors involves almost as much art as it does science and by now it is a highly developed art. The practitioner requires factors that are both easy to interpret and robust over time one approach is to use economic theory to come up with the most relevant factors. However, these factors do not always do well empirically and explaining variations in security prices. Another approach is to use statistical methods to extract those factors, which explain most of the variation in security Returns. The problem with this approach is that the extracted factors often do not have meaningful economic interpretation these factors include the ones Bianca face earlier in the course when she was trying to assess the best way to invest your cash commonly cited factors as price predictors include the market index unexpected changes in the default spread unexpected changes in the spread between Triple A rated b double a rated corporate bond returns interest rates the changes in expected.

Unexpected inflation or the changes in expected inflation proxied by the changes in the t-bill rate the unexpected changes in the term spread as measured by the difference between long and short-term government bonds exchange rates commodity prices GDP and GNP and unexpected growth in industrial production. Also defined as unexpected changes in the business cycle given efficient markets. The unexpected changes in these factors are often taken as the relevant risk factor.