1

RISKFREE BORROWING AND LENDING

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 = 00i

jiijij 0

If

then

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 ri

A.00 1.0 4 0B .25 .75 7.05 3.02C .50 .50 10.10 6.04D .75 .25 13.15 9.06E 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

rRF = 4% P

rP

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 PortfoliorP

P0

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

THE EFFECT OF RISK FREE LENDING ON THE EFFICIENT SET

TWO NEW BOUNDARIES

BT

r

P

rP

0

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THE EFFECT OF RISK FREE LENDING ON THE EFFICIENT SET

FOR RISK AVERSE

Portfolio A isthe optimal

A

rP

P0

14

THE EFFECT OF RISK FREE LENDING ON THE EFFICIENT SET

FOR RISK LOVER

B

P

rP

Portfolio Bis the optimal

0