8. Portfolio expected return and risk Aa Aa A collection of financial assets and

Question

8. Portfolio expected return and risk Aa Aa A collection of financial assets and securities is referred to as a portfolio. Most individuals and institutions invest in a portfolio, making portfolio risk analysis an integral part of finance. Just like standalone assets and securities, portfolios are also exposed to risk. Portfolio risk refers to the possibility that an investment portfolio will not generate the expected rate of return Analyzing portfolio risk and return involves the understanding of expected returns from a portfolio. Consider the following case: Andre is an amateur investor who holds a small portfolio consisting of only four stocks. The stock holdings in his portfolio are shown in the following table Percentage of Expected Standard Portfolio Stock Return Deviation Artemis Inc 20% 8.00% 24.00% Babish & Co. 30% 28.00% 14.00% Cornell Industries 35% 12.00% 31.00% Danforth Motors 15% 3.00% 33.00% What is the ex pected return of Andre's stock portfolio? O 15.68% O 7.84% O 14.11% O 10.45% Suppose each stock in the preceding portfolio has a correlation coefficient of 0.4 (p 0.4) with each of the other stocks. If the weighted average of the risk (standard deviation) of the individual securities in the partially diversified portfolio of four stocks is 29%, the portfolio's standard deviation (op) most lik 29% 9. The beta coefficient Aa Aa A stock's contribution to the market risk of a well-diversified portfolio is called risk According to the Capital Asset Pricing Model (CAPM), this risk can be measured by a metric called the beta coefficient which calculates the degree to which a stock moves with the movements in the market. Based on your understanding of the beta coefficient, indicate whether each statement in the following table is true or false Statement True False A stock that is more volatile than the market will have a beta of more than 1.0 Stock A's beta is 1.0; this means that the stock moves in the same direction and magnitude as the market. Higher-beta stocks are expected to have lower required returns. There are different ways of calculating the beta coefficient for a stock. Using the information given in the following table, calculate the beta coefficient of Stock Data Stock is standard deviation 49.00% Market's standard deviation 44.80% Correlation between Stock i and the market 0.91 Beta coefficient of Stock i get the value of R2 as 0.43. Based on your To calculate the beta of another company, using regression analysis, y calculation, which of the following interpretations is true? O 57% of the variance in the company's returns can be explained by the market returns. O 43% of the variance in the company's returns can be explained by the market returns.

Explanation / Answer

Ans. a. Expected return is 10.45%

b. Systematic Risk. Market risk is also called 'Systematic Risk'.

c. Statement 1 is True. Market Beta is taken as 1 and as beta indicates the volatility of stock, beta more than 1 indicates that the stock is more volatile than makrket.

Statement 2 is true.Market Beta is taken as 1 and as beta indicates the volatility of stock, beta equal to 1 indicates the stock moves in the same magbitude as market. and ad beta is positive it indicates that the stock moves in same direction as the market.

Statement 3 is false. Beta indicates the risk. As the risk increases,so the required return should increase.

Statement 4. Beta = (Correlation Coefficient) * (Standard deviation of stock/Standard deviation of market)

= 0.91 * (49/44.80) = 0.91* 1.09375 = 0.9953125

Beta is 0.995

d. Second option. 43% of variance in company's return are due to variations in market returns

R square denotes the porportion of security return that can be accounted by variations in market returns

Stock % of Portfolio Expected Return(%) Weighted Return Artemis Inc. 0.20 8.00 1.6 Babish & Co. 0.30 14.00 4.2 Cornell Industries 0.35 12.00 4.2 Danforth Motors 0.15 3.00 0.45 Expected return 10.45 Weighted Return = Expected return* Percentage return on stock Portfolio Beta = Sum total of weighted return of all securities

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