Hello everyone and welcome back to our discussion of the Capital Asset Pricing Model. In the last lecture we learned that the market portfolio is the optimal risky portfolio, right. And that all investors will choose to hold the market portfolio in some combination with the risk free asset, with the safe asset, based on their degree of risk aversion. Now the question remains, right, is what is the equilibrium market risk premium, right, provided by this optimalistic portfolio, right. What should be the risk compensation that investors will require to expose themselves to the risk, to the market risk of their market portfolio. Okay, so saw last time in the last lecture, that in a CAPM world, right, the efficient frontier is represented by the capital market line, right? Which goes through. So these are individual risky assets, right? Here is the mean base official frontier. So the official frontier is presented by the capital market line, which goes through, all right. The market portfolio. All right, there is the market portfolio, and it, it's represents all combinations of the safe asset and the market portfolio. All right, so we can think of an investor who holds 100% of the market portfolio as representing the average investor, all right. Think of averaging across all investors' positions, all right? The risk free positions will cancel out, right? Because some people will be borrowing, some people will be landing. And basically the average investor will be holding the market portfolio. This allows us to write down an expression, for the market risk premium. All right, if you recall back to the solution to the optimal weight in the risky asset, right. Which was the risk premium on the risky asset, divided by the risk aversion coefficient, and the variance of the risky asset, okay. Well for the average investor. Right, this way, this equal to 1. Right, and let's call the average investor risk or version coefficient gamma 1. So basically now I can write that as, the market risk premium, the excess return on the market portfolio, right? The excess return provided by the market portfolio divided by gamma bar times the variance of the market portfolio. Well, if I rewrite this slightly differently, right? Move things a little bit. What does this mean? Well, this means that the market risk premium, right, is given by the average risk aversion coefficient in the economy times the variance of the market portfolio. Or the market risk. All right, so this is basically your second insight, right? Look what this is saying. This is saying that the market risk in the economy. All right, the initial compensation investors are rewarded for holding to the market portfolio, all right? Is determined by the average risk aversion in the economy, or the risk aversion of the average investor. Whichever way you want to think about it. And the market portfolio risk. But remember, the market portfolio is the portfolio, right? In other words, it has already the least volatility among all other portfolios with the same average return. All right, it actually has no idiosyncratic risk, right, it has all the idiosyncratic risk is already diversified away, right. So it is intuitive that democratic premium, right, is depending on the average risk conversion in the economy. And the amount of market risk, right, that has diversified away all the, after diversifying away all the risk, right. Now this is for the average investor right. This position is for the average investor right. Since investors will differ from the average investor right in their risk aversion. How much they want to be exposed to the market risk, will depend on their own risk preferences, of course. But the aggregate market risk premium provided by the market portfolio, right. Is going to depend on average risk aversion in the economy, and the amount of market risk. Okay? So that's the second insight. So in this lecture we added one more result to our insights from the capital asset pricing model. Namely that the market is premium is determined by the average risk aversion in the economy. And the amount of market risk that can not be diversified away.
