265 stock (price per share multiplied by the number of shares outstanding) divided by the total market value of all stocks.

2. Not only will the market portfolio be on the efficient frontier, but it also will be the tangency portfolio to the optimal capital allocation line (CAL) derived by each and every investor. As a result, the capital market line (CML), the line from the risk- free rate through the market portfolio, M, is also the best attainable capital allocation line. All investors hold M as their optimal risky portfolio, differing only in the amount invested in it versus in the risk-free asset.

3. The risk premium on the market portfolio will be proportional to its risk and the degree of risk aversion of the representative investor. Mathematically,

-
E(rM ) rf A 2 .01
-

where 2 is the variance of the market portfolio and A is the average degree of risk aversion across investors.4 Note that because M is the optimal portfolio, which is efficiently diversified across all stocks, 2 is the systematic risk of this universe.

4. The risk premium on individual assets will be proportional to the risk premium on the market portfolio, M, and the beta coefficient of the security relative to the market portfolio. Beta measures the extent to which returns on the stock and the market move together. Formally, beta is defined as   Cov(ri,rM) i 2 M   and the risk premium on individual securities is

Cov(ri,rM) E(ri) rf 2 M [E(rM) rf] i[E(rM) rf]   We will elaborate on these results and their implications shortly.

Why Do All Investors Hold the Market Portfolio?

What is the market portfolio? When we sum over, or aggregate, the portfolios of all indi- vidual investors, lending and borrowing will cancel out (since each lender has a corre- sponding borrower), and the value of the aggregate risky portfolio will equal the entire wealth of the economy. This is the market portfolio, M. The proportion of each stock in this portfolio equals the market value of the stock (price per share times number of shares out- standing) divided by the sum of the market values of all stocks.5 The CAPM implies that as individuals attempt to optimize their personal portfolios, they each arrive at the