Risk Free Borrowing And Lending

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Risk Free Borrowing And Lending

  1. 1. RISKFREE BORROWING AND LENDING
  2. 2. DEFINING THE RISK FREE ASSET <ul><li>WHAT IS A RISK FREE ASSET? </li></ul><ul><ul><li>DEFINITION: an asset whose terminal value is certain </li></ul></ul><ul><ul><ul><li>variance of returns = 0, </li></ul></ul></ul><ul><ul><ul><li>covariance with other assets = 0 </li></ul></ul></ul>If then
  3. 3. DEFINING THE RISK FREE ASSET <ul><li>DOES A RISK FREE ASSET EXIST? </li></ul><ul><ul><li>CONDITIONS FOR EXISTENCE: </li></ul></ul><ul><ul><ul><li>Fixed-income security </li></ul></ul></ul><ul><ul><ul><li>No possibility of default </li></ul></ul></ul><ul><ul><ul><li>No interest-rate risk </li></ul></ul></ul><ul><ul><ul><li>no reinvestment risk </li></ul></ul></ul>
  4. 4. DEFINING THE RISK FREE ASSET <ul><li>DOES A RISK FREE ASSET EXIST? </li></ul><ul><ul><li>Given the conditions, what qualifies? </li></ul></ul><ul><ul><ul><li>a U.S. Treasury security with a maturity matching the investor’s horizon </li></ul></ul></ul>
  5. 5. RISK FREE LENDING <ul><li>ALLOWING FOR RISK FREE LENDING </li></ul><ul><ul><li>investor now able to invest in either or both, </li></ul></ul><ul><ul><li>a risk free and a risky asset </li></ul></ul>
  6. 6. RISK FREE LENDING <ul><li>ALLOWING FOR RISK FREE LENDING </li></ul><ul><ul><li>the addition expands the feasible set </li></ul></ul><ul><ul><li>changes the location of the efficient frontier </li></ul></ul><ul><ul><li>assume 5 hypothetical portfolios </li></ul></ul>
  7. 7. THE EFFECT OF RISK FREE LENDING ON THE EFFICIENT SET <ul><li>INVESTING IN BOTH: RISKFREE AND RISKY ASSET </li></ul><ul><li>PORTFOLIOS X 1 X 2 r i   </li></ul><ul><li> </li></ul><ul><li> A  .00 1.0 4 0 </li></ul><ul><li>B .25 .75 7.05 3.02  </li></ul><ul><li>C .50 .50 10.10 6.04 </li></ul><ul><li>D .75 .25 13.15 9.06 </li></ul><ul><li>E 1.00 .00 16.20 12.08 </li></ul>
  8. 8. THE EFFECT OF RISK FREE LENDING ON THE EFFICIENT SET <ul><li>RISKY AND RISK FREE PORTFOLIOS </li></ul>A D r RF = 4%  P r P 0 C B E
  9. 9. THE EFFECT OF RISK FREE LENDING ON THE EFFICIENT SET <ul><li>IN RISKY AND RISK FREE PORTFOLIOS </li></ul><ul><ul><li>All portfolios lie on a straight line </li></ul></ul><ul><ul><li>Any combination of the two assets lies on a straight line connecting the risk free asset and the efficient set of the risky assets </li></ul></ul>
  10. 10. THE EFFECT OF RISK FREE LENDING ON THE EFFICIENT SET <ul><li>The Connection to the Risky Portfolio </li></ul>r P  P  0
  11. 11. THE EFFECT OF RISK FREE LENDING ON THE EFFICIENT SET <ul><li>THE EFFECTS OF RISK FREE LENDING ON THE EFFICIENT SET </li></ul><ul><ul><li>Two Boundaries Result </li></ul></ul><ul><ul><ul><li>a line emanating from the risk free rate to the risk portfolio B(line segment r B) </li></ul></ul></ul><ul><ul><ul><li>a combination of risky assets with various weights(line segment r T) </li></ul></ul></ul><ul><ul><ul><li>there will be no efficient combined portfolio northwest of the combination of portfolios </li></ul></ul></ul>
  12. 12. THE EFFECT OF RISK FREE LENDING ON THE EFFICIENT SET <ul><li>TWO NEW BOUNDARIES </li></ul>B T r  P r P 0
  13. 13. THE EFFECT OF RISK FREE LENDING ON THE EFFICIENT SET <ul><li>FOR RISK AVERSE </li></ul>Portfolio A is the optimal A r P  P 0
  14. 14. THE EFFECT OF RISK FREE LENDING ON THE EFFICIENT SET <ul><li>FOR RISK LOVER </li></ul>B  P r P Portfolio B is the optimal 0

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