CHAPTER 8 POWERPOINT PRESENTATION

(1)

CHAPTER EIGHT

RISKFREE LENDING

AND BORROWING

(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



_i

 0

j i ij

ij

  

 

(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)

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)

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)

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)

THE EFFECT OF RISK FREE LENDING ON THE EFFICIENT SET

 INVESTING IN BOTH: RISKFREE AND RISKY ASSET

PORTFOLIOS X₁ X₂ r_i _



A.00 1.0 4 0

B .25 .75 7.05 3.02

C .50 .50 10.10 6.04 D .75 .25 13.15 9.06

E 1.00 .00 16.20 12.08

(8)

THE EFFECT OF RISK FREE LENDING ON THE EFFICIENT SET

 RISKY AND RISK FREE PORTFOLIOS

A

D

r_RF= 4%



_P

r

_P

0

C B

E

(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)

THE EFFECT OF RISK FREE LENDING ON THE EFFICIENT SET

 The Connection to the Risky Portfolio

r

_P



(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

(12)

THE EFFECT OF RISK FREE LENDING ON THE EFFICIENT SET

TWO NEW BOUNDARIES

T B

r



_P

r

_P

0

(13)

THE EFFECT OF RISK FREE LENDING ON THE EFFICIENT SET

FOR RISK AVERSE

Portfolio A is the optimal A

r

_P



(14)

THE EFFECT OF RISK FREE LENDING ON THE EFFICIENT SET

FOR RISK LOVER

B



_P

r

_P

Portfolio B

is the optimal

0

(15)

END OF CHAPTER 8