Suppose the aggregate stock market is made up of only two kinds of stocks, small stocks and large stocks. If you regress the excess return on a small stock, indexed by i, on the excess market return, you find the following relation:

,,=3%+1.3,,+,

Every small stock behaves in this way, but different small stocks have different , which are uncorrelated with each other. Similarly, if you regress the excess return on a large stock, indexed by j, on the excess market return, you find the following relation: ,,=1%+0.9,,+,

Every large stock behaves in this way, but different large stocks have

different , which are uncorrelated with each other.

a. What fraction of the aggregate stock market value is accounted for by large stocks, and what fraction by small stocks?

b. Show that if you can freely trade in small and large stocks, and if you have an infinite number of stocks available, then there is an arbitrage opportunity.