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risk free lending

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CHAPTER EIGHT
RISKFREE LENDING
AND BORROWING
DEFINING THE RISK FREE
ASSET
пЃ®
WHAT IS A RISK FREE ASSET?
• DEFINITION:
an asset whose terminal
value is certain
пЂіvariance of returns = 0,
пЂіcovariance with other assets = 0
If пЃі пЂЅ 0
i
then
пЃі ij пЂЅ пЃІ ij пЃі iпЃі
пЂЅ 0
j
DEFINING THE RISK FREE
ASSET
пЃ®
DOES A RISK FREE ASSET EXIST?
• CONDITIONS FOR EXISTENCE:
пЂіFixed-income security
пЂіNo possibility of default
пЂіNo interest-rate risk
пЂіno reinvestment risk
DEFINING THE RISK FREE
ASSET
пЃ®
DOES A RISK FREE ASSET EXIST?
• Given the conditions, what qualifies?
пЂіa U.S. Treasury security with a maturity
matching the investor’s horizon
RISK FREE LENDING
пЃ®
ALLOWING FOR RISK FREE LENDING
• investor now able to invest in either or
both,
• a risk free and a risky asset
RISK FREE LENDING
пЃ®
ALLOWING FOR RISK FREE LENDING
• the addition expands the feasible set
• changes the location of the efficient
frontier
• assume 5 hypothetical portfolios
THE EFFECT OF RISK FREE LENDING
ON THE EFFICIENT SET
пЃ®
INVESTING IN BOTH: RISKFREE AND RISKY ASSET
PORTFOLIOS
A
B
C
D
E
X1
.00
.25
.50
.75
1.00
X2
ri
di
1.0 4
0
.75 7.05 3.02
.50 10.10 6.04
.25 13.15 9.06
.00 16.20 12.08
THE EFFECT OF RISK FREE LENDING
ON THE EFFICIENT SET
пЃ®
RISKY AND RISK FREE PORTFOLIOS
E
rP
D
C
B
A
rRF = 4%
0
пЃіP
THE EFFECT OF RISK FREE LENDING
ON THE EFFICIENT SET
пЃ®
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
THE EFFECT OF RISK FREE LENDING
ON THE EFFICIENT SET
пЃ®
The Connection to the Risky Portfolio
rP
0
пЃіP
THE EFFECT OF RISK FREE LENDING
ON THE EFFICIENT SET
пЃ®
THE EFFECTS OF RISK FREE LENDING
ON THE EFFICIENT SET
• Two Boundaries Result
пЂіa line emanating from the risk free rate to the
risk portfolio B(line segment r B)
пЂіa combination of risky assets with various
weights(line segment r T)
пЂіthere will be no efficient combined portfolio
northwest of the combination of portfolios
THE EFFECT OF RISK FREE LENDING
ON THE EFFICIENT SET
TWO NEW BOUNDARIES
rP
T
B
r
0
пЃіP
THE EFFECT OF RISK FREE LENDING
ON THE EFFICIENT SET
FOR RISK AVERSE
rP
A
0
Portfolio A is
the optimal
пЃіP
THE EFFECT OF RISK FREE LENDING
ON THE EFFICIENT SET
FOR RISK LOVER
rP
B
Portfolio B
is the optimal
0
пЃіP
END OF CHAPTER 8
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