The Capital Asset Pricing Model Part 2
The point: each of the pieces had more risk when they were held separately than when they were combined in a portfolio This is a general phenomenon . When you add an assets to a portfolio, some of its risk vanishes : Part that vanishes: "Diversifiable/idiosyncratic risk" : Part that stays: "non-diversifiable/systematic risk" Need a measure of the non-diversifiable risk : Only risk that matters Assets with high non-diversifiable risk should have expected returns compared to assets with low, all else equal Assets with high diversifiable risk should have expected returns compared to assets with low, all else equal
When you add an asset to a portfolio... Question: which portfolio? Answer: in the CAPM, all investors are holding a particular portfolio of risky assets, called the "market portfolio of risky assets" . This is the portfolio, of only risky assets, whose weights are the same as if you bought all the amount outstanding of all risky assets in the world For short, we're going to refer to the market portfolio of risky assets as the "market portfolio". Don't forget what it is. List assets
Given all this
Investors hold the market portfolio : Thinking of adding an asset to it Which of the two assets will have higher expected returns? : Assets whose risk cancels out when added : Assets whose risk does not cancel out when added Just need a measure of how much risk doesn't cancel out : The beta (B)
The beta of an asset
Formula
Cov(Ri,RMkt Var(RMkt Where Ri is the return on the asset RMkt is the return on the market portfolio What is this "return on the market portfolio"?
2 things
1. It measures how much the risk of the market portfolio changes if you add a little bit of this asset to it : There's actually a formula. When adding a stock X to the market portfolio, the variance of your new portfolio is given by c+dttbeta_x, for some c, d>o 2. It measures how much the asset's returns respond to the market return on average : e.g.: when the market return goes up 20%, an asset with a beta of 2 will go up 40% on average. This does not mean that the asset's return must be 40%. It can be anything in one particular instance. How about an asset with a beta of -