1. 1 CHAPTER NINE RISKFREE BORROWING AND LENDING

2. 2 DEFINING THE RISK FREE ASSET WHAT IS A RISK FREE ASSET? –DEFINITION: an asset whose terminal value is certain variance of returns = 0, covariance with other assets = 0 If then

3. 3 DEFINING THE RISK FREE ASSET DOES A RISK FREE ASSET EXIST? –CONDITIONS FOR EXISTENCE: Fixed-income security No possibility of default No interest-rate risk no reinvestment risk

4. 4 DEFINING THE RISK FREE ASSET DOES A RISK FREE ASSET EXIST? –Given the conditions, what qualifies? a U.S. Treasury security with a maturity matching the investor’s horizon

5. 5 RISK FREE LENDING ALLOWING FOR RISK FREE LENDING –investor now able to invest in either or both, –a risk free and a risky asset

6. 6 RISK FREE LENDING ALLOWING FOR RISK FREE LENDING –the addition expands the feasible set –changes the location of the efficient frontier –assume 5 hypothetical portfolios

7. 7 THE EFFECT OF RISK FREE LENDING ON THE EFFICIENT SET INVESTING IN BOTH: RISKFREE AND RISKY ASSET PORTFOLIOSX 1 X 2 r i   A.001.040 B.25.757.053.02 C.50.50 10.106.04 D.75.25 13.159.06 E 1.00.00 16.20 12.08

8. 8 THE EFFECT OF RISK FREE LENDING ON THE EFFICIENT SET RISKY AND RISK FREE PORTFOLIOS A D r RF = 4% PP rPrP 0 C B E

9. 9 THE EFFECT OF RISK FREE LENDING ON THE EFFICIENT SET IN RISKY AND RISK FREE PORTFOLIOS –All portfolios lie on a straight line –Any combination of the two assets lies on a straight line connecting the risk free asset and the efficient set of the risky assets

10. 10 THE EFFECT OF RISK FREE LENDING ON THE EFFICIENT SET The Connection to the Risky Portfolio rPrP PP 0

11. 11 THE EFFECT OF RISK FREE LENDING ON THE EFFICIENT SET THE EFFECTS OF RISK FREE LENDING ON THE EFFICIENT SET –Two Boundaries Result a line emanating from the risk free rate to the risk portfolio B(line segment r B) a combination of risky assets with various weights(line segment r T) there will be no efficient combined portfolio northwest of the combination of portfolios

12. 12 THE EFFECT OF RISK FREE LENDING ON THE EFFICIENT SET TWO NEW BOUNDARIES B T r PP rPrP 0

13. 13 THE EFFECT OF RISK FREE LENDING ON THE EFFICIENT SET FOR RISK AVERSE Portfolio A is the optimal A rPrP PP 0

14. 14 THE EFFECT OF RISK FREE LENDING ON THE EFFICIENT SET FOR RISK LOVER B PP rPrP Portfolio B is the optimal 0