B2 Study Pack.pdf - F370 B2 Study Pack Solutions Page 1 ©...

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F370 B2 Study Pack Solutions -- Page 1 © 2015 Dan Greiner 1 Solutions to B2 Problems 1. Return and Wealth Confidence Intervals. You have built a portfolio of stocks and believe that its expected (required) return is r = 0.09 and its total risk is r = 0.25 for the coming year. a) What is your belief as to the 95% confidence interval for the return that you can earn on your portfolio across the next year? b) You have all of your investment wealth ($500,000) invested in this portfolio. What then is your belief as to the 95% confidence interval for the amount of wealth you’ll have at the end of the year? Upper Limit to 95% Confidence Interval on Wealth = $500,000 (1+ 95 upper return) = 500,000 (1.59) = $795,000 Lower Limit to 95% Confidence Interval on Wealth = $500,000 (1+95 lower return) = 500,000 (0.59) = $295,000 Note: the mean projected wealth would be $500,000 (1 + .09) = $545,000 Comment : When you take a look at these dollar levels, this level of total risk ( r = 0.25) will seem like too much risk for a person to take with their total wealth. Would you be willing to see your life savings drop $205,000 or more in one year? A 9% return seems like too little return for this level of total risk. One would guess that this investor hasn’t diversified away much firm-focused risk and is following a poor or inferior investment strategy.
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F370 B2 Study Pack Solutions -- Page 2 © 2015 Dan Greiner 2 Now suppose that this investor spread their wealth across more stocks (and thus reduce firm-focused risk and sigma. They also adds stocks with higher betas to increase their return level. Let’s say that they end up with a portfolio that they believe has a mean return r =0.12 and total risk of r = 0.15. c) What is your belief as to the 95% confidence interval for the return that you can earn on your portfolio across the next year? 95 upper return = 0.12 + 2(0.15) = 0.42 95 lower return = 0.12 - 2(0.15) = -0.18 d) You have all of your investment wealth ($500,000) invested in this portfolio. What then is your belief as to the 95% confidence interval for the am ount of wealth you’ll have at the end of the year? The answers to parts a) and b) above are given in small italic red font right after the answers found for this section. Upper Limit to 95% Confidence Interval on Wealth = $500,000 (1+ 95 upper return) = 500,000 (1.42) = $710,000 (795,000) Lower Limit to 95% Confidence Interval on Wealth = $500,000 (1+95 lower return) = 500,000 (0.82) = $410,000 (295,000) Note: the mean projected wealth would be $500,000 (1 + .12) = $560,000 (545,000) Can you see how diversification opens up some superior investment strategies for our investor?
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F370 B2 Study Pack Solutions -- Page 3 © 2015 Dan Greiner 3 2. Statistically Superior and Inferior Securities. Consider the following table with estimates of mean return ( r ) and volatility of return ( r ) for various stocks and portfolios. Asset r r A 0.12 0.25 B 0.20 0.30 C 0.16 0.25 D 0.12 0.30 E 0.16 0.20 F 0.08 0.18 G 0.10 0.16 H 0.10 0.13 Which subset of these eight assets are NOT statistically dominated by any other assets in the group? You can use the graph below to help you answer this question.
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