LN3_RiskAndReturn

# LN3_RiskAndReturn - Investments and Security Markets...

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FIN 320, Lecture Notes, Korniotis Page 1 Investments and Security Markets (Lecture Notes) George Korniotis 514J Jenkins Building University of Miami Coral Gables, FL 33124 Email : gkorniotis@miami.edu Phone: (305) 284-5728. Fall 2011

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FIN 320, Lecture Notes, Korniotis Page 2 Lecture Notes 3 Risk and Return Lecture notes 2 and 3 cover Chapters 5 and 6 (BKM). From Chapter 5 focus on sections: 5.1 – 5.5 Main Topics: Part A: From Chapter 5 1. Computing returns over multiple periods 2. Difference between real and nominal returns 3. Sharpe ratio Part B: From Chapter 6 4. Risk-Return Characteristics of a Portfolio with Two Assets. 5. Asset Allocation Example: 1 Risky and 1 Riskless Asset. 6. Capital Allocation Line (CAL) and the Capital Market Line (CML). Part C: 7. Risk Tolerance Suggested Problems from Chapter 6 : 4, 5, 13, 14, 15, 16, 18, and 27
FIN 320, Lecture Notes, Korniotis Page 3 Part A Main Steps to build a portfolio 1. Choose assets to include in a portfolio 2. Uncover the range of values for the asset’s returns and the probability distribution of these returns Range of returns and probability distribution depends on the holding horizon We need to be able to compute returns at long horizons We also have to account for inflation, if our holding horizon is long 3. Simplify the probability distribution 4. Determine the portfolio weights 5. Determine the portfolio payoffs 6. Compare portfolios using summary statistics 7. Conditional on investor risk tolerance, choose a portfolio Return Calculations for Long Horizons 1 2 3 T r 1 r 2 r 3 . . . . . . . . . . . . . . . . . . . r T Suppose there are T time periods. Arithmetic return (Total) , r A = r 1 + r 2 + . . . . + r T . Geometric return (Total) , r G = [(1 + r 1 ) (1+ r 2 ) . . . . (1 + r T )] – 1 (compounding) Note: Returns are not in percent terms.

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FIN 320, Lecture Notes, Korniotis Page 4 If returns are fixed, the above formulas are simpler Annualized return: How much could I have earned in a year? APR = (Per period return) (# of periods in a year). ( r ) ( n ) Effective Annual Rate (compounding) EAR = (1 + r) n – 1. Ex: r = 2% per month, n = 12. A P R = 2 12 = 24% EAR = (1 + 0.02) 12 – 1 = 0.2682 = 26.82% Accounting for Inflation Our purchasing power changes because prices change. For long-term investment, we need to account for inflation. Nominal versus Real Rate of Return. Nominal return: the return you actually earn ( R ). Real return: the return you earn after adjusting for inflation ( r ). L e t i % be the inflation rate. r = R – i APPROXIMATE RELATION More accurately, (1 + r) = (1 + R) (1 + i) r = 1 + R 1 or, r = R – i EXACT 1 + i 1 + i REACTION Ex: R = 8%, i = 5% Approximation = 8 – 5 = 3 % Exact = ( 0.08 – 0.05 ) / ( 1 + 0.05) = 2.9 %
FIN 320, Lecture Notes, Korniotis Page 5 Main Steps to build a portfolio 1. Choose assets to include in a portfolio 2. Uncover the range of values for the asset’s returns and the probability distribution of these returns 3. Simplify the probability distribution 4. Determine the portfolio weights 5. Determine the portfolio payoffs 6. Compare portfolios using summary statistics a. We compute the expected return of the portfolio (reward for taking on risk) b. We measure the level of risk we are exposed to with the standard deviation c. Is there a way to see if we are taking on too much risk given the expected return?

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## This note was uploaded on 09/18/2011 for the course FIN 320 taught by Professor Barrett during the Spring '08 term at University of Miami.

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LN3_RiskAndReturn - Investments and Security Markets...

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