lec01-overview-3pp

lec01-overview-3pp - Fin406 Fall 2009 Smeal College of...

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Fin406 – Fall 2009 Smeal College of Business Penn State University 1/25/2010 ©2009 JingZhi Huang 1 Lectures 5-7: Modern Portfolio Theory Fin 406 - Fall 2009 Professor Jingzhi Huang Smeal College of Business Penn State University Copyright © 2009 JZH Motivation Evaluate Performance Trade Security Selection Asset Allocation Define Objectives and Constraints Develop Market Expectations •Return •Risk •Tax •Horizon •Economy •Markets •Risk-Return Model •Benchmark Portfolios •Risk-Return tradeoff •Fixed Income •Equity •Cash •Orders •Leverage •Margin •After-tax Returns •Risk •Risk-Adj. Ret. •Benchmarks 2 Modern Portfolio Theory (MPT) provides a method for determining the optimal portfolio Illustrate the method in the following cases: Combinations of the risk-free asset and one risky asset (key concept: the capital allocation line ) Combinations of two risky assets ( Markowitz’s Theory ) Combinations of the risk-free and two risky assets (Tobin’s theory) I. One Risky Asset and the Risk-free Fix the notation T-bills S&P 500 Exp. Ret. Std. Dev. Weight r f f (= 0) 1-y E[r p ] p (> 0) y 3 Investor determines the value of y. Risky Portfolio P (e.g. S&P 500) T-Bills Investor’s Portfolio ( Complete Portfolio C ) y1 - y Q: Can finance theory tell us what the optimal combination is for a given investor? Key Formulas Given a particular complete portfolio C (represented by a particular value of y), we need to calculate its exp. ret. and std. dev. first and then its Sharpe ratio and utility To do that, we need to use the following 4 formulas: E[r C ] = y * E[r P ] + (1-y) * r f = r f + y * (E[r P ] - r f ) (1) C = y * P (2) S C = (E[r C ]- r f )/ c (3) U C (A) = E[r C ] 0.5 * A * ( C ) 2 (4) Example 1: CAL and Utility Suppose we are given the following info T-bills S&P 500 (asset P) Exp. Ret. Std. Dev. r f = 4% f = 0 E[r p ] = 12% p = 20% 5 Determine the optimal allocation between the S&P 500 and T-bills. Below we consider first a few specific portfolios and analyze their risk-return tradeoffs We compute the optimal portfolio for a given investor whose coefficient A is known We then introduce an important concept: the capital allocation line (CAL) Ex 1 (cont d): the Sharpe Ratio The number of possible combinations is infinite Consider three combinations and compute their risk, return, and Sharpe ratio (using (1) - (3)) Y=0.2 (20% in P and 80% in T-bills) Return: E[r c ] = 0.2 * 12% + 0.8 * 4% = 5.6% Risk: c = 0.2 * 20% = 4.0% 6 Sharpe ratio =(E[r c ]-r f )/ c =(5.6%-4%)/4% = 0.4 Y=0.5 (50% in P and 50% in T-bills) Return: E[r c ] = 0.5 * 12% + 0.5 * 4% = 8% Risk: c = 0.5 * 20% = 10% Sharpe ratio = (8% - 4%)/10% = 0.4 Y=1.5 (150% in P and -50% in T-bills) Return: E[r c ] = 1.5 * 12% + (-0.5) * 4% = 16% Risk: c = 1.5 * 20% = 30% Sharpe ratio = (16% - 4%)/30% = 0.4
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Fin406 – Fall 2009 Smeal College of Business Penn State University 1/25/2010 ©2009 JingZhi Huang 2 Ex 1 (cont d): Call for the Utility Observation 1: When y increases (decreases), so do E[r c ] and c .
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This note was uploaded on 04/06/2010 for the course FIN 100 taught by Professor Staff during the Fall '08 term at Penn State.

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lec01-overview-3pp - Fin406 Fall 2009 Smeal College of...

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