# 1. CAPM-3-Nt - The Capital Asset Pricing Model The Risk...

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The Capital Asset Pricing Model The Risk Return Relation Formalized

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Summary As we discussed, the “market” pays investors for two services they provide: (1) surrendering their capital and forgoing current consumption and (2) sharing in the total risk of the economy. The first gets you the time value of money. The second gets you a risk premium whose size depends on the share of total risk you take on. From this we found E(R) = R f + θ We refined this to E(R) = R f + Units × Price
Summary We needed a reference for measuring risk and chose the total risk the market has to divide or the “market portfolio” as that reference. The market portfolio is defined to have one unit of risk (Var(R m ) = 1 unit of risk). Other assets are evaluated relative to this definition of one unit of risk. From E(R) = R f + Units × Price we can see that Price = {E(R m ) – R f }. (Note: Units = 1 for R m .) In other words we also defined the price per unit risk (the market risk premium).

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Summary The hard part is to show that any asset’s contribution to the total risk of the economy or Var(R m ) is determined not by Var(R i ) but rather by Cov(R i , R m ). Standardize Cov(R i , R m ) so that we measure the risk of each asset relative to our definition of one unit and we get beta: β i = Cov(R i , R m )/Var(R m ) The number of units of risk for asset i is β i . So E(R i )=R f + β i (E(R m ) – R f )=R f + Units × Price.
Risk and Return When we are concerned with only one asset its risk and return can be measured, as discussed, using expected return and variance of return. If there is more that one asset (so portfolios can be formed) risk becomes more complex. We will show there are two types of risk for individual assets: Diversifiable/nonsystematic/idiosyncratic risk Nondiversifiable/systematic/market risk Diversifiable risk can be eliminated without cost by combining assets into portfolios. (Big Wow.)

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Diversification One of the most important lessons in all of finance concerns the power of diversification. Part of the total risk of any asset can be “diversified away” (its effect on portfolio risk is eliminated) without any loss in expected return (i.e. without cost). This also means that no compensation needs to be provided to investors for exposing their portfolios to this type of risk. Why should the economy pay you to hold risk that you can get rid of for free (or which is not part of the aggregate risk that all agents must some how share). This in turn implies that the risk/return relation is actually a systematic risk/return relation.
Diversification Example Suppose a large green ogre has approached you and demanded that you enter into a bet with him. The terms are that you must wager \$10,000 and it must be decided by the flip of a coin, where heads he wins and tails you win.

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