What about points on the CAL to the right of portfolio P? If investors can borrow at the (risk-free) rate of rf 7%, they can construct portfolios that may be plotted on the CAL to the right of P.

Suppose the investment budget is $300,000 and our investor borrows an additional $120,000, investing the total available funds in the risky asset. This is a leveraged position in the risky asset; it is financed in part by borrowing. In that case   420,000 300,000 1.4   and 1 y 1 1.4 .4, reflecting a short position in the risk-free asset, which is a bor- rowing position. Rather than lending at a 7% interest rate, the investor borrows at 7%. The distribution of the portfolio rate of return still exhibits the same reward-to-variability ratio:

E(rC) 7% (1.4 8%) 18.2%

C 1.4 22% 30.8%

E(rC) rf S C 18.2 7 30.8   .36

As one might expect, the leveraged portfolio has a higher standard deviation than does an unleveraged position in the risky asset.

Of course, nongovernment investors cannot borrow at the risk-free rate. The risk of a borrowers default causes lenders to demand higher interest rates on loans. Therefore, the nongovernment investors borrowing cost will exceed the lending rate of rf 7%. Suppose the borrowing rate is r B 9%. Then in the borrowing range, the reward-to- variability ratio, the slope of the CAL, will be [E(rP) rfB]/ P 6/22 .27. The CAL will therefore be "kinked" at point P, as shown in Figure 7.3. To the left of P the investor

II. Portfolio Theory 7. Capital Allocation between the Risky Asset and the Risk−Free Asset

The McGraw−Hill Companies, 2001

190 PART II Portfolio Theory

Figure 7.3 The opportunity set with differential borrowing and lending rates.