22.13. Ford is considering building a factory to produce its new Taurus. The factory will cost $100 million and will produce 10,000 automobiles one year from now, but its cost and production can be scaled up or down. As an analyst at Ford, you run a regression of the historical sales margin of 10,000 cars against the return of Ford’s stock. You find that the regression coefficient is –$130 million, that the sales margin of a Taurus one year from now has a standard deviation of $1,000, and that the volatility of Ford’s stock is 0.5. The risk-free rate over the coming year will be 10 percent. You can assume that the return on the factory is the total sales margin from all cars produced by the factory divided by the cost of the factory, less one.

Your task is the following:

a. To identify the minimum variance portfolio combination of Ford stock and the factory, and to interpret the results.

b. To identify the tangency portfolio mix of factory and stock if the expected selling margin of the Taurus is $22,000 and the expected return of Ford stock is 30 percent over the next year.