Chapter 5 Portfolio Choices - Chapter 5 Portfolio Choices...

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Chapter 5 Portfolio Choices In Chapter 3, we studied the theory of asset demand. This theory outlines criteria that are important when deciding which assets are worth buying. The theory of asset demand plays a pivotal role in the study of money, banking, and financial market. For example, we have used the theory to examine the behavior of interest rates. In this chapter, which is closely linked to the theory of asset demand, will further give us an idea why it is good to diversify by buying several types of assets and not to put all our eggs, i.e. wealth, in one basket. A. Calculate the expected return and standard deviation Below we briefly explain how to calculate the expected return and standard deviation of a portfolio if (a) there is only one risky asset in the portfolio, and (b) there is more than one risky asset in the portfolio a. 0nly one risky asset in the portfolio Illustration The stock of Business Adventures sells for $40 a share. Its likely dividend payout and end-of-year depend on the state of the economy by the end of the year as follows: Scenario Probability Dividend Stock Price Boom 0.3 $2.00 $50 Normal Economy 0.5 1.00 43 Recession 0.2 0.50 34 Calculate the expected return and standard deviation of the stock. Expected return = = n i i i k k P k 1 ) ( n : The number of possible outcomes on the investment i k : The value of the i th possible rate of return k : The expected rate of return 5-1
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) ( i k P : The chance or probability that the i the outcome or return will occur Standard deviation = - = n i i i k P k k 1 2 ) ( ) ( σ b . More than one risky asset in the portfolio i. Two risky assets We now form a risky portfolio which consists of two risky assets: stock fund and bond fund. Furthermore, we assume that there are S w proportion of capital invested in a stock fund and B w proportion of capital invested in a bond fund. Efficient and inefficient frontiers in the two-risky-assets case 5-2
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Illustration Calculate the expected return and standard deviation of the following risky portfolio which consists of a stock fund and a bond fund. Scenario ( i ) Probability Rate of return Stock Fund ( S i k , ) Bond Fund ( B i k , ) Boom 1/3 -7% 17% Normal Economy 1/3 12% 7% Recession 1/3 28% -3% Case 1: In the portfolio, the amount invested in the stock fund is $700,000 and the amount to be invested in the bond fund is $300,000. Case 2: In the portfolio, the amount invested in the stock fund is $400,000 and the amount to be invested in the bond fund is $600,000. Expected return The rate of return on a portfolio is a weighted average of the rates of return of each asset comprising the portfolio, with the portfolio proportions as weights. b B S S P k w k w k + = S w = Proportion of funds in the stock fund B w = Proportion of funds in the bond fund = = n i S i S i S k k P k 1 , , ) ( = Expected return on the stock fund = = n i B i B i B k k P k 1 , , ) ( = Expected return on the bond fund Standard deviation When two risky assets with variances 2 S σ and 2 B , respectively, are combined into a portfolio with portfolio weights S w B w , respectively, the portfolio variance is given by ) ( 2 2 2 2 2 2 B S S S
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This note was uploaded on 06/21/2009 for the course ECONOMY 101 taught by Professor Ken during the Spring '08 term at Abraham Baldwin Agricultural College.

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Chapter 5 Portfolio Choices - Chapter 5 Portfolio Choices...

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