Chapter Twelve Portfolio Opportunities and Choice This chapter contains 30 multiple choice questions,10 short problems,and 5 longer problems. Multiple Choice 1.A person's wealth portfolio consists of all one's and (a)retained earnings;credit (b)stocks;bonds (c)assets;liabilities (d)student loans;mortgages Answer:(c) 2.The principle of diversification usually applies to all (a)risk averse people (b)risk neutral people (c)risk tolerant people (d)b and c Answer:(a) 3.Which of the following decisions can be considered part of portfolio selection? (a)Whether to buy or rent one's house (b)What kind of life insurance to purchase (c)Whether to invest in stocks or bonds (d)All of the above Answer:(d) 12-1
12-1 Chapter Twelve Portfolio Opportunities and Choice This chapter contains 30 multiple choice questions, 10 short problems, and 5 longer problems. Multiple Choice 1. A person's wealth portfolio consists of all one’s ________ and ________. (a) retained earnings; credit (b) stocks; bonds (c) assets; liabilities (d) student loans; mortgages Answer: (c) 2. The principle of diversification usually applies to all ________. (a) risk averse people (b) risk neutral people (c) risk tolerant people (d) b and c Answer: (a) 3. Which of the following decisions can be considered part of portfolio selection? (a) Whether to buy or rent one’s house (b) What kind of life insurance to purchase (c) Whether to invest in stocks or bonds (d) All of the above Answer: (d)
4.An insurance policy that guarantees a person an income for as long as one lives is termed a (a)lump sum payment (b)life annuity (c)perpetual annuity (d)life perpetuity Answer:(b) 5.The is the length of time between decisions to revise portfolios,whereas the the total length of time for which one plans. (a)trading horizon;decision horizon (b)planning horizon;decision horizon (c)decision horizon;trading horizon (d)decision horizon;planning horizon Answer:(d) 6.In making portfolio-selection decisions,people can in general achieve a expected rate of return by exposing themselves to risk. (a)higher;no (b)higher;greater (c)higher;lower (d)lower;greater Answer:(b) 7.The the assets that make up the portfolio is found to be a very important factor when considering the ability of diversification to reduce the riskiness of an investor's portfolio. (a)expected return of (b)variance of (c)correlation among (d)skewness among Answer:(c) 12-2
12-2 4. An insurance policy that guarantees a person an income for as long as one lives is termed a ________. (a) lump sum payment (b) life annuity (c) perpetual annuity (d) life perpetuity Answer: (b) 5. The ________ is the length of time between decisions to revise portfolios, whereas the ________ is the total length of time for which one plans. (a) trading horizon; decision horizon (b) planning horizon; decision horizon (c) decision horizon; trading horizon (d) decision horizon; planning horizon Answer: (d) 6. In making portfolio-selection decisions, people can in general achieve a ________ expected rate of return by exposing themselves to ________ risk. (a) higher; no (b) higher; greater (c) higher; lower (d) lower; greater Answer: (b) 7. The ________ the assets that make up the portfolio is found to be a very important factor when considering the ability of diversification to reduce the riskiness of an investor's portfolio. (a) expected return of (b) variance of (c) correlation among (d) skewness among Answer: (c)
8.Risk tolerance can be influenced by which of the following characteristics? (a)job status (b)age (c)wealth (d)all of the above Answer:(d) 9.The is defined as a security that offers a perfectly predictable rate of return in terms of the unit of account and the length of the investor's decision horizon. (a)riskless asset (b)risky asset (c)30-day bond (d)30-day debenture Answer:(a) 10.A portfolio contains one risky asset and one riskless asset.The expected rate of return on the risky asset is 0.13 and the riskless rate is 0.05.The standard deviation of the risky asset is 0.2,and the standard deviation of the portfolio is 0.075.What is the expected rate of return on the portfolio using the trade-off line? (a0.0490 (b)0.0800 (c)0.0980 (d0.1175 Answer:(b) 11.An investor has a $100,000 investment to allocate between a risky asset and a riskless asset.The equation for the trade-off line is determined to be E(r)=0.05 +0.09w.If the investor is requiring a portfolio composition corresponding to an expected rate of return of 0.11,how much should be invested in the risky asset? (a)$18,181 (b)$33,333 (c)$66,667 (d$81,819 Answer:(c) 12-3
12-3 8. Risk tolerance can be influenced by which of the following characteristics? (a) job status (b) age (c) wealth (d) all of the above Answer: (d) 9. The ________ is defined as a security that offers a perfectly predictable rate of return in terms of the unit of account and the length of the investor's decision horizon. (a) riskless asset (b) risky asset (c) 30-day bond (d) 30-day debenture Answer: (a) 10. A portfolio contains one risky asset and one riskless asset. The expected rate of return on the risky asset is 0.13 and the riskless rate is 0.05. The standard deviation of the risky asset is 0.2, and the standard deviation of the portfolio is 0.075. What is the expected rate of return on the portfolio using the trade-off line? (a) 0.0490 (b) 0.0800 (c) 0.0980 (d) 0.1175 Answer: (b) 11. An investor has a $100,000 investment to allocate between a risky asset and a riskless asset. The equation for the trade-off line is determined to be E(r) = 0.05 + 0.09w. If the investor is requiring a portfolio composition corresponding to an expected rate of return of 0.11, how much should be invested in the risky asset? (a) $18,181 (b) $33,333 (c) $66,667 (d) $81,819 Answer: (c)
12.An investor has a $100,000 investment to allocate between a risky asset and a riskless asset.The equation for the trade-off line is determined to be E(r)=0.07+0.12w.If the investor is requiring a portfolio composition corresponding to an expected rate of return of 0.17,how much should be invested in the riskless asset? (a$16,667 (b)$29,412 (c)$70,588 (d$83,333 Answer:(a) 13.An investor has a $100,000 investment to allocate between a risky asset and a riskless asset.The equation for the trade-off line is determined to be E(r)=0.07+0.12w.If the investor requires a portfolio composition corresponding to an expected rate of return of 0.17,what is the corresponding standard deviation of the portfolio?The standard deviation of risky asset is 0.3. (a)0.05 (b)0.25 (c)0.49 (d0.83 Answer:(b) 14.The expected rate of return on a risky asset is 0.13 and the riskless rate is 0.06.The standard deviation of the risky asset is 0.25.What happens to the slope of the trade-off line if the riskless rate changes to 0.05 per year and the expected return on the risky asset changes to 0.14? (a)No change (b)The slope of the line falls from 36%to 28% (c)The slope of the line rises from 28%to 36% (d)The slope of the line rises from 52%to 56% Answer:(c) 15.The formula for the trade-off line between risk and expected return is (a)E(r)=r+w[E(rs)-ri] (b)E(r)=r+[Er)- (C)E(r)=r+w[E(r)+r月 (d)all of the above Answer:(a) 12-4
12-4 12. An investor has a $100,000 investment to allocate between a risky asset and a riskless asset. The equation for the trade-off line is determined to be E(r) = 0.07 + 0.12w. If the investor is requiring a portfolio composition corresponding to an expected rate of return of 0.17, how much should be invested in the riskless asset? (a) $16,667 (b) $29,412 (c) $70,588 (d) $83,333 Answer: (a) 13. An investor has a $100,000 investment to allocate between a risky asset and a riskless asset. The equation for the trade-off line is determined to be E(r) = 0.07 + 0.12w. If the investor requires a portfolio composition corresponding to an expected rate of return of 0.17, what is the corresponding standard deviation of the portfolio? The standard deviation of risky asset is 0.3. (a) 0.05 (b) 0.25 (c) 0.49 (d) 0.83 Answer: (b) 14. The expected rate of return on a risky asset is 0.13 and the riskless rate is 0.06. The standard deviation of the risky asset is 0.25. What happens to the slope of the trade-off line if the riskless rate changes to 0.05 per year and the expected return on the risky asset changes to 0.14? (a) No change (b) The slope of the line falls from 36% to 28% (c) The slope of the line rises from 28% to 36% (d) The slope of the line rises from 52% to 56% Answer: (c) 15. The formula for the trade-off line between risk and expected return is ________. (a) E(r) = rf + w[E(rs) – rf] (b) E(r) = rf + [E(rs) – rf] (c) E(r) = rf + w[E(rs) + rf] (d) all of the above Answer: (a)
16.In the trade-off line,the risk premium depends on (a)the risk premium of the risky asset (b)the proportion of the portfolio invested in the risky asset (c)the risk premium of the riskless asset (d)both a and b Answer:(d) 17.When one of the two assets in a portfolio is riskless,the standard deviation of its rate of return and its correlation with other asset are (a)greater than zero but less than positive one (b)less than zero but greater than negative one (c)zero (d)none of the above Answer:(c) 18.The expected rate of return on a risky asset is 0.16 and the riskless rate is 0.07.The standard deviation of the risky asset is 0.2.What happens to the slope of the trade-off line if the riskless rate changes to.06 per year and the expected return on the risky asset changes to 0.15? (a)no change (b)the slope rises from 0.45 to 0.5 (c)the slope falls from 0.5 to 0.45 (d)the slope falls from 0.45 to 0.4 Answer:(a) 19.A portfolio contains a riskless asset with an expected rate of return of 0.06 and a risky asset with an expected rate of return of 0.15.The standard deviation of the risky asset is 0.25.If the expected rate of return of this portfolio is 0.10,what is its standard deviation? (a0.11 (b)0.14 (c)0.22 (d0.44 Answer:(a) 12-5
12-5 16. In the trade-off line, the risk premium depends on ________ (a) the risk premium of the risky asset (b) the proportion of the portfolio invested in the risky asset (c) the risk premium of the riskless asset (d) both a and b Answer: (d) 17. When one of the two assets in a portfolio is riskless, the standard deviation of its rate of return and its correlation with other asset are ________. (a) greater than zero but less than positive one (b) less than zero but greater than negative one (c) zero (d) none of the above Answer: (c) 18. The expected rate of return on a risky asset is 0.16 and the riskless rate is 0.07. The standard deviation of the risky asset is 0.2. What happens to the slope of the trade-off line if the riskless rate changes to .06 per year and the expected return on the risky asset changes to 0.15? (a) no change (b) the slope rises from 0.45 to 0.5 (c) the slope falls from 0.5 to 0.45 (d) the slope falls from 0.45 to 0.4 Answer: (a) 19. A portfolio contains a riskless asset with an expected rate of return of 0.06 and a risky asset with an expected rate of return of 0.15. The standard deviation of the risky asset is 0.25. If the expected rate of return of this portfolio is 0.10, what is its standard deviation? (a) 0.11 (b) 0.14 (c) 0.22 (d) 0.44 Answer: (a)
Consider a portfolio of two risky assets with the following distribution of rates of return on risky assets for questions 20 and 21.The portfolio is 55%Risky Asset 1 and 45%Risky Asset 2,and the correlation coefficient is 0.4. Risky Asset 1 Risky Asset 2 Mean 0.16 0.09 Standard Deviation 0.25 0.18 20.What is the mean of this portfolio? (a)0.1215 (b)0.1285 (c)0.2005 (d)0.2185 Answer:(b) 21.What is the standard deviation of this portfolio? (a)0.15958 (b)0.18541 (c)0.25467 (d0.34378 Answer:(b) Consider a portfolio of two risky assets with the following distribution of rates of return on risky assets for questions 22 and 23.The portfolio is 70%Risky Asset 1 and 30%Risky Asset 2,and the correlation coefficient is 0.3. Risky Asset 1 Risky Asset 2 Mean 0.12 0.20 Standard Deviation 0.16 0.30 22.What is the mean of this portfolio? (a)0.1716 (b)0.1600 (c)0.1414 (d)0.1320 Answer:(c) 12-6
12-6 Consider a portfolio of two risky assets with the following distribution of rates of return on risky assets for questions 20 and 21. The portfolio is 55% Risky Asset 1 and 45% Risky Asset 2, and the correlation coefficient is 0.4. Risky Asset 1 Risky Asset 2 Mean Standard Deviation 0.16 0.25 0.09 0.18 20. What is the mean of this portfolio? (a) 0.1215 (b) 0.1285 (c) 0.2005 (d) 0.2185 Answer: (b) 21. What is the standard deviation of this portfolio? (a) 0.15958 (b) 0.18541 (c) 0.25467 (d) 0.34378 Answer: (b) Consider a portfolio of two risky assets with the following distribution of rates of return on risky assets for questions 22 and 23. The portfolio is 70% Risky Asset 1 and 30% Risky Asset 2, and the correlation coefficient is 0.3. Risky Asset 1 Risky Asset 2 Mean Standard Deviation 0.12 0.16 0.20 0.30 22. What is the mean of this portfolio? (a) 0.1716 (b) 0.1600 (c) 0.1414 (d) 0.1320 Answer: (c)
23.What is the standard deviation of this portfolio? (a)0.16338 (b)0.14368 (c)0.02669 (d0.02064 Answer:(a) 24.In practice,the vast majority of assets are positively correlated with each other because they are all affected by (a)common economic factors (b)firm specific factors (c)potential lawsuits (d)managerial inefficiencies Answer:(a) 25.A mutual fund company offers a safe money market fund whose current rate is 0.04.The same company also offers an equity fund with an aggressive growth objective,which historically has exhibited an expected return of 0.25 and a standard deviation of 0.30.Derive the equation for the risk- reward trade-off line. (aEr）=0.04+0.25o (b)Er)=0.04+0.7o (c)Er）=0.04+0.21o (dEr）=0.04+0.83o Answer:(b) 26.The refers to the set of portfolios of risky assets offering the highest possible expected rate of return for any given standard deviation. (a)minimum portfolio frontier (b)effective portfolio frontier (c)expected portfolio frontier (d)efficient portfolio frontier Answer:(d) 12-7
12-7 23. What is the standard deviation of this portfolio? (a) 0.16338 (b) 0.14368 (c) 0.02669 (d) 0.02064 Answer: (a) 24. In practice, the vast majority of assets are positively correlated with each other because they are all affected by ________. (a) common economic factors (b) firm specific factors (c) potential lawsuits (d) managerial inefficiencies Answer: (a) 25. A mutual fund company offers a safe money market fund whose current rate is 0.04. The same company also offers an equity fund with an aggressive growth objective, which historically has exhibited an expected return of 0.25 and a standard deviation of 0.30. Derive the equation for the riskreward trade-off line. (a) E(r) = 0.04 + 0.25σ (b) E(r) = 0.04 + 0.7σ (c) E(r) = 0.04 + 0.21σ (d) E(r) = 0.04 + 0.83σ Answer: (b) 26. The ________ refers to the set of portfolios of risky assets offering the highest possible expected rate of return for any given standard deviation. (a) minimum portfolio frontier (b) effective portfolio frontier (c) expected portfolio frontier (d) efficient portfolio frontier Answer: (d)
27.The optimal combination of risky assets is found as between a straight line representing the riskless asset and the efficient frontier of risky assets. (a)the point of bisection (b)the point of intersection (c)the point of tangency (d)the point of highest return Answer:(c) 28.The power of diversification to reduce the riskiness of an investor's portfolio depends on the among the assets that make up the portfolio. (a)expected returns (b)variances (c)correlations (d)none of the above Answer:(c) 29.In the context of the optimal combination of risky assets,in order to decide on the menu of asset choices to offer its customers a financial intermediary should consider: (a)investor preferences (b)the expected returns and standard deviations of the risky assets (c)both a and b (d)neither a nor b Answer:(b) 30.An investor has $100,000 invested in a portfolio that is composed of a tangency portfolio and a riskless asset,such that 35%is in the tangency portfolio and 65%is in the riskless asset.If the tangency portfolio is composed of 43.75%Risky Asset A and 56.25%Risky Asset B,which of the following accurately displays the amount of money invested in each component of the portfolio? (a)$35,000 in Riskless Asset;$43,750 in Risky Asset A;$56,250 in Risky Asset B (b)$65,000 in Riskless Asset;$43,750 in Risky Asset A;$56,250 in Risky Asset B (c)$35,000 in Riskless Asset;$28,437.50 in Risky Asset A;$36,562.50 in Risky Asset B (d)$65,000 in Riskless Asset:$15,312.50 in Risky Asset A:$19,687.50 in Risky Asset B Answer:(d) 12-8
12-8 27. The optimal combination of risky assets is found as ________ between a straight line representing the riskless asset and the efficient frontier of risky assets. (a) the point of bisection (b) the point of intersection (c) the point of tangency (d) the point of highest return Answer: (c) 28. The power of diversification to reduce the riskiness of an investor’s portfolio depends on the ________ among the assets that make up the portfolio. (a) expected returns (b) variances (c) correlations (d) none of the above Answer: (c) 29. In the context of the optimal combination of risky assets, in order to decide on the menu of asset choices to offer its customers a financial intermediary should consider: (a) investor preferences (b) the expected returns and standard deviations of the risky assets (c) both a and b (d) neither a nor b Answer: (b) 30. An investor has $100,000 invested in a portfolio that is composed of a tangency portfolio and a riskless asset, such that 35% is in the tangency portfolio and 65% is in the riskless asset. If the tangency portfolio is composed of 43.75% Risky Asset A and 56.25% Risky Asset B, which of the following accurately displays the amount of money invested in each component of the portfolio? (a) $35,000 in Riskless Asset; $43,750 in Risky Asset A; $56,250 in Risky Asset B (b) $65,000 in Riskless Asset; $43,750 in Risky Asset A; $56,250 in Risky Asset B (c) $35,000 in Riskless Asset; $28,437.50 in Risky Asset A; $36,562.50 in Risky Asset B (d) $65,000 in Riskless Asset; $15,312.50 in Risky Asset A; $19,687.50 in Risky Asset B Answer: (d)
Short Problems 1.Discuss the time horizons as they relate to portfolio planning. Answer: In formulating a plan for portfolio selection you begin by determining our goals and time horizons.The planning horizon is the total length of time for which one plans.The longest time horizon would typically correspond to the retirement goal and would be the balance of one's lifetime.There are also shorter planning horizons that correspond to specific financial goals,such as paying for a child's education.The decision horizon is the length of time between decisions to revise the portfolio.The length of the decision horizon is controlled by the individual,within certain limits.The shortest possible decision horizon is the trading horizon,defined as the minimum time interval over which investors can revise their portfolios. 2.What is the riskless asset if the unit of account is the Japanese Yen and the length of the decision horizon is a month? Answer: The Japanese Yen one-month zero-coupon bond. 3.Describe the steps involved in the portfolio optimization process. Answer: ) Find the optimal combination ofrisky assets. 2) Mix this optimal risk-asset portfolio with the riskless asset. 12-9
12-9 Short Problems 1. Discuss the time horizons as they relate to portfolio planning. Answer: In formulating a plan for portfolio selection you begin by determining our goals and time horizons. The planning horizon is the total length of time for which one plans. The longest time horizon would typically correspond to the retirement goal and would be the balance of one’s lifetime. There are also shorter planning horizons that correspond to specific financial goals, such as paying for a child’s education. The decision horizon is the length of time between decisions to revise the portfolio. The length of the decision horizon is controlled by the individual, within certain limits. The shortest possible decision horizon is the trading horizon, defined as the minimum time interval over which investors can revise their portfolios. 2. What is the riskless asset if the unit of account is the Japanese Yen and the length of the decision horizon is a month? Answer: The Japanese Yen one-month zero-coupon bond. 3. Describe the steps involved in the portfolio optimization process. Answer: (1) Find the optimal combination of risky assets. (2) Mix this optimal risk-asset portfolio with the riskless asset
4.Who would you expect to be more risk tolerant,a young investor or an elderly one?An investor or moderate means or a wealthy one? Answer: A young person with a secure job can look forward to a long period of earning a salary that will probably increase with the rate of inflation.For her,investment in stocks would not be as risky as for an older person who needs to ensure a steady source of income for the rest of his life.A wealthier individual may be willing to take more risks (than a poorer person)because his capacity to take bigger gambles and lose is higher.That is,he may still be quite wealthy after his losses. 5.An investor has a $100,000 investment to allocate between a risky asset and a riskless asset.The equation for the trade-off line is determined to be E(r)=0.05+0.07w.If the investor requires a portfolio composition corresponding to an expected rate of return of 0.10,how much should be invested in the risky asset?In the riskless asset? Answer: E(r) =0.05+0.07w 0.10 =0.05+0.07w 0.05 =0.07w 0.71429=w The investor should invest $71,429 in the risky asset and $28.571 in the riskless asset. 6.An investor has $75,000 to allocate between a risky asset and a riskless asset.The equation for the trade-off line is determined to be E(r)=0.06 +0.1w.If the investor requires a portfolio composition with an expected rate of return of 0.12,how much should be invested in each asset? Answer: Er)=0.06+0.1w 0.12=0.06+0.1w 0.06=0.1w 0.6=w 0.6(S75,000)=S45,000 should be invested in the risky asset 0.4(S75,000 S30,000 should be invested in the riskless asset There would have to be 16 million uncorrelated drugs in the portfolio. 12-10
12-10 4. Who would you expect to be more risk tolerant, a young investor or an elderly one? An investor or moderate means or a wealthy one? Answer: A young person with a secure job can look forward to a long period of earning a salary that will probably increase with the rate of inflation. For her, investment in stocks would not be as risky as for an older person who needs to ensure a steady source of income for the rest of his life. A wealthier individual may be willing to take more risks (than a poorer person) because his capacity to take bigger gambles and lose is higher. That is, he may still be quite wealthy after his losses. 5. An investor has a $100,000 investment to allocate between a risky asset and a riskless asset. The equation for the trade-off line is determined to be E(r) = 0.05 + 0.07w. If the investor requires a portfolio composition corresponding to an expected rate of return of 0.10, how much should be invested in the risky asset? In the riskless asset? Answer: E(r) = 0.05 + 0.07w 0.10 = 0.05 + 0.07w 0.05 = 0.07w 0.71429= w The investor should invest $71,429 in the risky asset and $28,571 in the riskless asset. 6. An investor has $75,000 to allocate between a risky asset and a riskless asset. The equation for the trade-off line is determined to be E(r) = 0.06 + 0.1w. If the investor requires a portfolio composition with an expected rate of return of 0.12, how much should be invested in each asset? Answer: E(r) = 0.06 + 0.1w 0.12 = 0.06 + 0.1w 0.06 = 0.1w 0.6 = w 0.6($75,000) = $45,000 should be invested in the risky asset 0.4($75,000 = $30,000 should be invested in the riskless asset There would have to be 16 million uncorrelated drugs in the portfolio