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CHAPTER NINE

CHAPTER NINE. RISKFREE BORROWING AND LENDING. 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. DEFINING THE RISK FREE ASSET. DOES A RISK FREE ASSET EXIST?

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CHAPTER NINE

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  1. CHAPTER NINE 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 = 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 ridi 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 rP E D C B A sP rRF = 4% 0

  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 rP sP 0

  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 rP TWO NEW BOUNDARIES B T r sP 0

  13. THE EFFECT OF RISK FREE LENDING ON THE EFFICIENT SET FOR RISK AVERSE rP A Portfolio A is the optimal sP 0

  14. THE EFFECT OF RISK FREE LENDING ON THE EFFICIENT SET FOR RISK LOVER rP B Portfolio B is the optimal sP 0

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