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# Risk And Returns

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### Risk And Returns

1. 1. Risk and Rates of Return Return Risk
2. 2. <ul><li>Since Treasury’s are essentially free of default risk, the rate of return on a Treasury security is considered the “risk-free” rate of return. </li></ul>For a Treasury security, what is the required rate of return? Required rate of return = Risk-free rate of return
3. 3. <ul><li>How large of a risk premium should we require to buy a corporate security? </li></ul>Required rate of return = Risk-free rate of return + Risk Premium For a corporate stock or bond , what is the required rate of return?
4. 4. <ul><li>Expected Return - the return that an investor expects to earn on an asset, given its price, growth potential, etc. </li></ul><ul><li>Required Return - the return that an investor requires on an asset given its risk . </li></ul>Returns
5. 5. <ul><li>State of Probability Return </li></ul><ul><li>Economy (P) Orl. Utility Orl. Tech </li></ul><ul><li>Recession .20 4% -10% </li></ul><ul><li>Normal .50 10% 14% </li></ul><ul><li>Boom .30 14% 30% </li></ul><ul><li>For each firm, the expected return on the stock is just a weighted average : </li></ul>Expected Return
6. 6. <ul><li>State of Probability Return </li></ul><ul><li>Economy (P) Orl. Utility Orl. Tech </li></ul><ul><li>Recession .20 4% -10% </li></ul><ul><li>Normal .50 10% 14% </li></ul><ul><li>Boom .30 14% 30% </li></ul><ul><li>For each firm, the expected return on the stock is just a weighted average : </li></ul><ul><li>k = P(k 1 )*k 1 + P(k 2 )*k 2 + ...+ P(k n )*kn </li></ul>Expected Return
7. 7. <ul><li>State of Probability Return </li></ul><ul><li>Economy (P) Orl. Utility Orl. Tech </li></ul><ul><li>Recession .20 4% -10% </li></ul><ul><li>Normal .50 10% 14% </li></ul><ul><li>Boom .30 14% 30% </li></ul><ul><ul><ul><ul><li>k = P(k 1 )*k 1 + P(k 2 )*k 2 + ...+ P(k n )*kn </li></ul></ul></ul></ul><ul><ul><ul><ul><li>k (OU) = .2 (4%) + .5 (10%) + .3 (14%) = 10% </li></ul></ul></ul></ul>Expected Return
8. 8. <ul><li>State of Probability Return </li></ul><ul><li>Economy (P) Orl. Utility Orl. Tech </li></ul><ul><li>Recession .20 4% -10% </li></ul><ul><li>Normal .50 10% 14% </li></ul><ul><li>Boom .30 14% 30% </li></ul><ul><li>k = P(k 1 )*k 1 + P(k 2 )*k 2 + ...+ P(k n )*kn </li></ul><ul><li>k (OI) = .2 (-10%)+ .5 (14%) + .3 (30%) = 14% </li></ul>Expected Return
9. 9. <ul><li>The possibility that an actual return will differ from our expected return. </li></ul><ul><li>Uncertainty in the distribution of possible outcomes. </li></ul>What is Risk?
10. 10. What is Risk? <ul><li>Uncertainty in the distribution of possible outcomes. </li></ul>Company B return Company A return
11. 11. <ul><li>A more scientific approach is to examine the stock’s STANDARD DEVIATION of returns. </li></ul><ul><li>Standard deviation is a measure of the dispersion of possible outcomes. </li></ul><ul><li>The greater the standard deviation, the greater the uncertainty, and therefore , the greater the RISK. </li></ul>How do we Measure Risk?
12. 12. <ul><li>= (k i - k) P(k i ) </li></ul>n i =1 2   Standard Deviation
13. 13. <ul><li>Orlando Utility, Inc. </li></ul><ul><li>( 4% - 10%) 2 (.2) = 7.2 </li></ul><ul><li>(10% - 10%) 2 (.5) = 0 </li></ul><ul><li>(14% - 10%) 2 (.3) = 4.8 </li></ul><ul><li>Variance = 12 </li></ul><ul><li>Stand. dev. = 12 = 3.46% </li></ul>n i =1 = (k i - k) P(k i ) 2  
14. 14. <ul><li>Orlando Technology, Inc. </li></ul><ul><li>(-10% - 14%) 2 (.2) = 115.2 </li></ul><ul><li>(14% - 14%) 2 (.5) = 0 </li></ul><ul><li>(30% - 14%) 2 (.3) = 76.8 </li></ul><ul><li>Variance = 192 </li></ul><ul><li>Stand. dev. = 192 = 13.86% </li></ul>= (k i - k) P(k i ) 2   n i =1
15. 15. <ul><li>Orlando Orlando </li></ul><ul><li> Utility Technology </li></ul><ul><li>Expected Return 10% 14% </li></ul><ul><li>Standard Deviation 3.46% 13.86% </li></ul>Summary