Learning outcomes, after watching this video you will be able to describe single and multi-factor models, write out a two-factor model with unanticipated shocks to the risk factors and asset returns multifactor models. So far, we will assume that only one variable or factor, namely the market portfolio, affects expected returns. This may not be realistic for a couple of reasons. One, why is it that the market portfolio is the only factor that affects expected returns? It could be some other single factor like industry, and the economy, or a business cycle that affects expected returns of all risky assets. Two, why must there be only one factor that affects expected returns? It is possible that there are a number of macro economic factors that simultaneously determine expected returns. The return of any asset can be decomposed into two parts, an expected part, and an unanticipated part. The unanticipated part itself may consist of two parts. One attributable to a risk factor and another to a firm-specific shock. The return of any asset can be returned as ri equals the expected return of the asset E(ri) + Beta i X F Plus E sub i. Here, F is the unanticipated shock to the risk factor. Beta sub i is the sensitivity of asset i's returns to the risk factor. And e sub i is the unanticipated firm-specific shock. Across all risky assets, the expectation of F is and the expectation of E sub I are both equal to zero. This is because there are unanticipated shocks. For example we could write Microsoft's stock returns R sub M for the next quarter. As expected return from Microsoft, E(r sub M) + beta sub M x, the difference between next quarter's GDP growth rate and the expected GDP growth rate, + the unanticipated part of Microsoft's return next quarter, e sub M. Here we assume that the GDP growth rate is a single risk factor that affects all risky asset returns. The difference between next quarter's GDP growth rate and the expected GDP growth rate is an unanticipated shock to the risk factor. The single index model that we saw earlier is another example of a single factor model. We can extend this to a model with K factors. The return of any asset can be return as R sub I equals the expected return of the asset E of R sub I. Plus beta sub i1 times f sub 1 plus beta sub i2 times f sub 2, plus so on until beta sub ik times f sub k plus e sub i. Each f sub j represents the unanticipated shock to risk factor j, and each beta sub j is the sensitivity of the asset returns to the risk factor j. As previously, the expectation of each F sub j and the expectation of e sub i are all equal to 0. We can now extend the model from Microsoft's return next quarter, r sub m. As expected return for Microsoft, E of r sub m plus beta sub m 1 times the difference between next quarter's GDP growth rate, and the expected GDP growth rate plus beta sub m2 times the difference between next quarter's inflation and the expected inflation. Plus, then the anticipated part of Microsoft's return next quarter is a bet. In this model there are two risk factors, namely GDP growth rate and inflation. To get a better understanding of the multi-factor model, let's include some numbers. Say Microsoft's expected return is 10%, the GDP growth rate is expected to be 4% while inflation is expected to be 6%. Microsoft has a sensitivity of 1% with the respect of GDP growth rate risk factor. And the sensitivity of 0.4 with the respect to the inflation risk factor. GDP growth rate actually turns out to be 5% and inflation actually turns out to be 7%. So Microsoft's return next quarter is 14% + 1(5%- 4%) + 0.4(7%- 6%), plus the unanticipated firm-specific shock. While these factor models help us decompose returns into expected and unanticipated parts, we still need to relate factor risk premiums to expected returns, asset pricing models help us do this. Was one such model. Next time, we will look at an alternate asset pricing model