Fundamentals of Corporate finance Answers to review questions

Fundamentals of Corporate finance Answers to review questions

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± Answers to Concepts in Review 1. A portfolio is simply a collection of investment vehicles assembled to meet a common investment goal. An efficient portfolio is a portfolio offering the highest expected return for a given level of risk or the lowest level of risk for a given level of expected return. In trying to create an efficient portfolio, an investor should be able to put together the best portfolio possible, given his risk disposition and investment opportunities. When confronted with the choice between two equally risky investments offering different returns, the investor would be expected to choose the alternative with the higher return. Likewise, given two investment vehicles offering the same returns but differing in risk, the risk-averse investor would prefer the vehicle with the lower risk. 2. The return of a portfolio is calculated by finding the weighted average of returns of the portfolio’s component assets: = = × 1 n p jj j rw r where n = number of assets, w j = weight of individual assets, and r j = average returns. The standard deviation of a portfolio is not the weighted average of component standard deviations; the risk of the portfolio as measured by the standard deviation will be smaller. It is calculated by applying the standard deviation formula (Equation 4.10a) to the portfolio assets, rather than just the returns for one asset: = ⎛⎞ = −÷ ⎜⎟ ⎝⎠ 2 1 () ( 1 ) n pp i sr r n 3. Correlation refers to the statistical measure of the relationship, if any, between a series of numbers. The correlation between asset returns is important when evaluating the effect of a new asset on the portfolio’s overall risk. Once the correlation between asset returns is known, the investor can choose those that, when combined, reduce risk. (a) Returns on different assets moving in the same direction are positively correlated ; if they move together exactly, they are perfectly positively correlated . (b) Negatively correlated returns move in opposite directions. Series that move in exactly opposite directions are perfectly negatively correlated . (See Figure 5.1) (c) Uncorrelated returns have no relationship to each other and have a correlation coefficient of close to zero. 4. Diversification is a process of risk reduction achieved by including in the portfolio a variety of vehicles having returns that are less than perfectly positively correlated with each other. Diversification of risk in the asset selection process allows the investor to reduce overall risk by combining negatively correlated assets so that the risk of the portfolio is less than the risk of the individual assets in it. Even if assets are not negatively correlated, the lower the positive correlation between them, the lower the resulting risk.
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5. Combining assets with high positive correlation increases the range of portfolio returns; combining assets with high negative correlation reduces the range of portfolio returns. When negatively correlated assets are brought together through diversification, the variability of
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This note was uploaded on 05/10/2011 for the course STATS 202 taught by Professor Emil during the Spring '11 term at Aberystwyth University.

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Fundamentals of Corporate finance Answers to review questions

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