Solution Manual for Macroeconomics, 2nd Edition

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SOLUTIONS MANUALWebChapter1Financial Decision MakingQuestions1.Explain the following terms:i.Compound returnsii.Principaliii. Rate of return on an investmentiv.Holding periodAnswer:i.Compound returnsare generated when short-term returns are repeatedly reinvested,thereby causing an investment to earn returns onboththe initial investmentandon pastinvestment returns.ii.An investor’sprincipalis the value of her initial investment.iii.Therate of return on investmentis calculated by (i) dividing the final value of aninvestment by the initial investment (one year earlier), and (ii) subtracting one from theratio.iv.The time delay between the initial investment and the final withdrawal is referred to as theholding period.A-head: INVESTMENT RETURNSConcept: Compound returns, principal, interest, holding period2.Suppose you choose an investment that has historically generated an average nominal return of5 percent per year. Explain how inflation and risk may affect your future real rate of return on thisinvestment.Answer:Inflation reduces the buying power of money. Any appreciation in the value of the final balance willneed to be adjusted to account for rising prices. In other words, if the prices of goods and servicesincrease during the holding period, the real rate of return on the initial investment is lower than thenominal rate of return. The real rate of return is the nominal rate of return minus the inflation rate.Risk implies that the return on the investment is not guaranteed. So the rate of return that youexperience may be greater or lower than the historical average rate of return.A-head: INVESTMENT RETURNSConcept: Inflation, risk

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2Acemoglu, Laibson, and List |Economics3.Explain the following terms:i.Securitiesii.Bondsiii. Stocksiv.Stock market indexAnswer:i.Bonds, stocks, and other financial claims that can be traded among investors are calledsecurities.ii.Bonds are long-term loans made to a borrower (debtor) by a lender (creditor).iii.Stocks, also known as shares or equity, are ownership rights in a corporation.iv.A stock market index is an average of the prices of many stocks.A-head: INVESTMENT RETURNSConcept: Securities, stock market index4.Given that shares are riskier than bonds, why do investors invest in equity?Answer:Equity investors are rewarded for taking on higher risk with an average rate of return that isgreater than the average rate of return on bonds. Although equity returns fluctuate from year to year,investors who are willing to bear the additional risk of investing in shares also benefit from a higheraverage return.A-head: INVESTMENT RETURNSConcept: Risk5.What is a patent race?Answer:A patent race refers to a winner-take-all race. Suppose two investors are racing to develop aninvention or to patent a discovery. The investor who develops the invention first or files the patentfirst will reap all the benefits. Although the other investors may have invested the same amount ofmoney in research and development as the investor who filed the patent, they will not get any returnon their investment.A-head: DIVERSIFICATIONConcept: Patent race6.What is meant by diversifying an investment portfolio? What are the advantages of diversification?Answer:Diversification means that investors spread their investment across more than one asset.Diversification allows investors to reduce risk as individual assets are hit by different economicshocks. Putting a little bit of money in all of these different investment baskets reduces exposure toany single shock.A-head: DIVERSIFICATIONConcept: Diversification

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Web Chapter 1| Financial Decision Making37.Which types of investment accounts are investors likely to choose if they are trying to minimize risk?Why?Answer:Bank accounts insured by the Federal Deposit Insurance Corporation are the safest way ofstoring and investing money. Investors trying to minimize risk will invest in FDIC-insured certificatesof deposit or money market deposit accounts.A-head: INVESTMENT ACCOUNTSConcept: Bank accounts8.What is the difference between directly holding stock in a company like Apple and investing in amutual fund that holds Apple stock?Answer:•Some investors purchase Apple shares directly and hold them in a brokerage account.•Most investors buy pre-mixed pools of assets, called mutual funds.A mutual fund is a pool ofmoney that is collected from many investors. Mutual funds typically invest in hundreds ofstocks, bonds, and/or short-term money market instruments.A-head: INVESTMENT ACCOUNTSConcept: Brokerage accounts9.The following questions are about mutual funds:i.What are index funds?ii.What is an expense ratio? How do expense ratios affect the value of an investor’s portfolio?Answer:i.An index fund is a mutual fund that is passively managed, which means that the mutual fundmanager simply tries to track the return of an index, like the Standard & Poor’s 500 stockindex.A-head: INVESTMENT ACCOUNTSConcept: Mutual fundsii.Expense ratios are annual fees charged by mutual funds in order to pay mutual fundmanagers and to pay other record-keeping and marketing costs of the fund. Expense ratiosmake a very big difference in the long-run performance of investments. Paying an annual feeof even 1 percent will reduce the annual rate of return on the investment from say,10 percent to 10 – 1 = 9 percent.A-head: INVESTMENT ACCOUNTS; CHOICE AND CONSEQUENCE: OVERLOOKING FEESConcept: Expense ratios10. What are the four core ways that households save for retirement?Answer:There are four core types of retirement savings plans:•Social Security: Social Security is a mandatory retirement savings program. Each worker pays aSocial Security payroll tax into a general government account called the Social Security trustfund. Using these funds, the Social Security trust fund pays out benefits to those workers whoare currently retired.•Defined benefit pension plans: Defined benefit pensions are contractually specifiedemployment benefits, in which the employer promises to pay the employee a fixed annuity after

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4Acemoglu, Laibson, and List |Economicsretirement. The magnitude of the annuity is adjusted to reflect years of service at the employerand the level of the employee’s salary.•Defined contribution pension plans: Defined contribution pensions are individual accounts thatare owned and controlled by the employee. In most cases, the employee decides how much tocontribute to these accounts, and most employers match these contributions. These accounts arecommonly referred to as 401(k) accounts.•Individual Retirement Accounts (IRA): IRAs are retirement savings accounts that anyone canset up; they are usually not sponsored by a person’s employer. If an individual does notcontribute to her employer’s defined contribution savings plan, then she can use an IRA to savefor retirement.A-head: INVESTMENT ACCOUNTSConcept: Retirement savings plans11. How easy is it for fund managers and investment management companies to outperform or “beat” thestock market once their fees are taken into account?Answer:When a single stock is picked atrandom, there is a 50 percent chance that the stock willoutperform the total stock market in the next year. Consequently, it is possible to outperform thestock market in a single year even if the investment manager has no skill. It has been discovered thatsuccessful historical asset managers tend to performno betterin the next period than pure chancewould predict.A-head: INVESTMENT ACCOUNTSConcept: Outperforming the stock market12. How could return-chasing explain why many of Enron’s employees lost most of their retirementsavings when Enron went bankrupt?Answer:Return-chasing occurs when people invest in assets that have realized a high rate of return inthe past. Return-chasing explains why many of Enron’s employees chose to forgo the benefits ofdiversification and invested the overwhelming majority of their retirement savings in Enron stock.Enron stock had gone up by a factor of 10 in the decade before Enron went bankrupt—that’s a 1,000percent return. This led Enron employees to mistakenly believe that Enron stock was a greatinvestment for the future. Consequently, employees allocated more and more of their contributions toemployer stock, under the assumption that Enron stock prices would continue to increase in thefuture.A-head: EVIDENCE-BASED ECONOMICS: DO INVESTORS CHASE HISTORICAL RETURNS?Concept: Return chasingProblems1.Congratulations! You have just won a $1,000,000 (delayed) prize in the lottery. Your state offers youthe following alternatives: you can take $750,000 now, or 10 years from now you can receive the full$1,000,000. The delay isn’t a problem, because you weren’t planning to use any of the prize moneyfor at least 10 years.If you take the lump sum now, you figure you can invest it at an annually compounded rate of 3percent.

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Web Chapter 1| Financial Decision Making5Should you take the $750,000 now, or wait to get the full $1,000,000 in 10 years? Why or why not?Show any calculations.Answer:You should take the $750,000 now.Here are the relevant calculations:$750,000×(1 + 0.03)10= $1,007,937.So you would be $7,937 better off by taking the smaller amount now than receiving the full prize in10 years. This assumes that you will, in fact, achieve an annually compounded return of 3 percent forthe next 10 years.A-head: INVESTMENT RETURNSConcept: Comparing future valuesDifficulty: Easy/ModerateProblem-type: Calculation2.Ten years ago, you set aside $1,000. For the first 6 years, you earned a return of 6 percent per year,but for the following 4 years, that rate of return dropped to 3 percent. How much money do you nowhave at the end of the 10 years?Answer:At the end of the first 6 years, you would have $1,000×(1 + 0.06)6.After investing that money for an additional 4 years, you will have a total of[$1,000×(1.06)6]×(1.03)4= [$1,000×1.4185]×1.1255 = $1,596.56.A-head: INVESTMENT RETURNSConcept: Finding the future value at differing interest ratesDifficulty: Easy/ModerateProblem-type: Calculation3.You get your first job when you are 23. Prudently, you set aside $5,000 of your earnings to open anIRA.a.You know that stocks have returned a nominal 10 percent per year onaveragehistorically. If youkeep your money invested in a portfolio of stocks that returns 10 percent per year until you retire40 years later at age 63, how many dollars will that $5,000 have turned into?b.Assuming an inflation rate of 3 percent, how much will that $5,000 have turned into in realterms? In other words, redo the previous calculation, taking inflation into account.c.Given this investment plan, should you depend on having that much money available in the IRAaccount when you retire? Why or why not?Answer:a.()40$5,00010.10$226,296.28FinalValue=×+=b.10%3%7%riπ=−=−=()40$5,00010.07$74,872.29×+=This means that your purchasing power grew by a factor of 15 (15×$5,000 = $75,000), andyou didn’t have to do anything but postpone consumption. Of course, even if interest rateswere 0 percent, and there were no interest at all, it’s still worth putting money away becausethe only way to have money in retirement is to save.

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6Acemoglu, Laibson, and List |Economicsc.As discussed in the section entitled Risky Returns, investing in stocks is inherently risky.Whether you end up with a great deal of money or very little depends on whether yourparticular holding period happens to be period with high or low returns.A-head: INVESTMENT RETURNS; RISKY RETURNSConcept: Compound returns; Risky returnsDifficulty: EasyProblem-type: Hypothetical real-world scenario4.Ernest calculates that he will need $220,000 to provide for his 8-year-old daughter’s college tuitionand expenses. Due to a recent inheritance, he will have some money to put aside now but will not beable to add to it over time. He is confident that he can realize a return of 5 percent, compoundedannually, on the money he puts aside. Assume his daughter will start college at the age of 18.Calculate how much money Ernest needs to invest now in order to fund his daughter’s collegeeducation.Answer:We can start with the formula given in the chapter:(Initial Investment)×(1 +r)T= $220,000.wherer= 0.05 is the rate of return, andT= 18 – 8 =10 is the number of years the money is invested(in other words,Tis the holding period).So, all we really need to do is to solve the above equation for the Initial Investment:Initial Investment = $220,000(1 +r)T=$220,000(1+0.05)10=$135,060.92So Ernest needs to invest $135,060.92 of his inheritance at 5 percent in order to realize a final valueof $220,000 after a 10-year holding period.A-head: INVESTMENT RETURNSConcept: Finding the present value given the future valueDifficulty: HardProblem-type: Hypothetical real-world scenario; calculation5.The following table shows the nominal return on the 10-year Treasury bond as well as the 3-monthTreasury bill from year-end 1999 to year-end 2016.Year3-MonthT-BillRate(Annualized)10-Year TreasuryBond Total Return20005.76%16.66%20013.67%5.57%20021.66%15.12%20031.03%0.38%20041.23%4.49%20053.01%2.87%20064.68%1.96%

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Web Chapter 1| Financial Decision Making720074.64%10.21%20081.59%20.10%20090.14%-11.12%20100.13%8.46%20110.03%16.04%20120.05%2.97%20130.07%-9.10%20140.05%10.75%20150.21%1.28%20160.51%0.69%Source: NYU Stern Historical Return data compiled by Aswath Damodaran. 10-Year Treasury total returnincludes coupon payments and price appreciationa.Use the data points to plot a graph for both the data series.b.Which security has given a higher rate of return over this period? Why do you think this is thecase?Answer:a.The following graph plots the returns on Treasury bonds and bills listed in the table.b.The return on the 10-year Treasury bond is usually higher than the return on the 3-monthTreasury bill. This is because long-term loans are riskier than short-term loans. Bondinvestors are rewarded for bearing this risk with a rate of return that usually exceeds the rateof return on money market accounts, or short-term loans.A-head: RISKY RETURNSConcept: Treasury bills, bondsDifficulty: Moderate/HardProblem-type: Data-based problem

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8Acemoglu, Laibson, and List |Economics6.The following table shows data on the nominal return in the Standard & Poor’s 500 stock marketindex (including dividends and price appreciation) and the return on the 3-month Treasury bill. Thetable reports returns from year-end 1999 to year-end 2016.Year3-MonthT-Bill Rate(Annualized)Return on S&PIndex (IncludingDividends)20005.76%-9.03%20013.67%-11.85%20021.66%-21.97%20031.03%28.36%20041.23%10.74%20053.01%4.83%20064.68%15.61%20074.64%5.48%20081.59%-36.55%20090.14%25.94%20100.13%14.82%20110.03%2.10%20120.05%15.89%20130.07%32.15%20140.05%13.52%20150.21%1.38%20160.51%11.74%Source: NYU Stern Historical Return data, compiled by Aswath Damodaran. Returns on S&P 500 are equal-weighted and include dividendsa.Use the data points to plot a graph for both the data series.b.What does Standard & Poor’s 500 represent? Would it have been riskier to invest in the S&P 500or the 3-month Treasury bill during this period? Why?

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Web Chapter 1| Financial Decision Making9Answer:a.The following graph shows the annual return in the S&P 500 and the 3-month Treasury bill.b.The Standard and Poor’s 500 is a stock market index that summarizes the value of 500 of thelargest U.S. companies, representing about 75 percent of the value of all companies tradedon U.S. stock exchanges. The variability of the returns of the S&P 500 stock index is higherthan the variability of the annual returns of holding 3-month Treasury bills. Stocks are, ingeneral, riskier than corporate bonds as companies make payments to shareholders only aftermaking payments to bondholders. This means that shareholders are the ones who primarilysuffer when a company earns less income. Moreover, lending to the government is less riskythan lending to a corporation. Putting these observations together, 3-month Treasury billreturns are less risky than short-term corporate bonds, which are less risky than corporateshares. Because shares are therefore riskier than 3-month Treasury bills, shares offer higherreturns in order to compensate for the higher level of risk. Although equity investors receivea higher return onaverage, the return on equity also fluctuates a lot, even going negativefrom time to time.Link to graph: http://www.research.stlouisfed.org/fred2/graph/?g=t1wA-head: RISKY RETURNSConcept: Stock market index, Treasury bonds, riskDifficulty: Moderate/HardProblem-type: Data-based problem7.The following table shows the income distribution for American households in terms of percentiles inthe United States in 2015.PercentileIncome1013,2592022,8004043,5115056,5166072,001

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10Acemoglu, Laibson, and List |Economics80117,00290162,18095214,462a.What was the median income in 2015? What does this number mean?b.Suppose you are told that, in 2015, 60 percent of the population earned an average income of$72,001. Refer to the table and explain whether you would agree with this statement or not.Answer:a.The median in a distribution is the 50th percentile. The median household income in 2015was $56,516. This number divides the distribution into half, which means that 50 percent ofthe U.S. households earned less than $56,516, while the remaining 50 percent earned morethan $56,516.b.No, the statement is incorrect. The 60th percentile is a cutoff that divides the data so that 60percent of the population is below the cutoff. This means that, of the total number ofhouseholds in the country, 60 percent of the households earned less than $72,001, while therest of the 40 percent of the households earned more than this amount.Data credit: United States Census BureauA-head: RISKY RETURNSConcept: PercentilesDifficulty: Moderate/HardProblem-type: Calculation problem8.Alexander Graham Bell was credited with inventing the telephone in 1876. What many do not knowis that Bell filed for the telephone patent hours before Elisha Gray, who also had a prototype for thetelephone.a.Since Bell filed the patent first, his company went on to earn millions of dollars in profits fromthe sales of the telephone. Because Elisha Gray’s patent came second, he did not earn profits fromhis invention. What is this situation called?b.Suppose you are an investor who was willing to invest in either Bell’s or Gray’s telephonecompanies. You expect that the value of the company that files the patent first will double invalue. Assume that each inventor had an equal chance of filing the telephone patent. If you didnot know who would file the patent first, what investment strategy would minimize your risk?Answer:a.This is an example of a patent race, where the winner takes all. Only the inventor who filesthe patent first reaps all the profits from the invention. Other companies or inventors do notgain, although they may have spent the same or more time and money on a similarinvention.b.Given that either company has an equal chance of filing the patent and doubling its value,you should invest an equal amount of money in both companies. By diversifying yourinvestment across both companies, you reduce the risk that you face if you invest in onlyone company and happen to pick the company that loses.A-head: DIVERSIFICATIONConcept: Patent race; diversificationDifficulty: Easy/ModerateProblem-type: Real world scenario

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Web Chapter 1| Financial Decision Making119.You have $100 to invest, and you are considering two stocks. In the next year, each stock will eitherhave a return of +30 percent or –10 percent. Assume as well that the performance of one stock isunrelated to the performance of the other (in other words, the stock returns are uncorrelated). Thetable shows the resulting four possibilities, depending on whether each of the two stocks gains orloses value. (To read the table, note that the first outcome listed in each cell is for Stock 1, and thesecond outcome in each cell is for Stock 2.)Stock 1Stock 2GainLoseGainStock 1 GainStock 2 GainStock 1 GainStock 2 LoseLoseStock 1 LoseStock 2 GainStock 1 LoseStock 2 LoseAssume that the probability of Stock 1 gaining is 50 percent. Assume that the probability of Stock 2gaining is 50 percent. Assume that each of the four possibilities listed in the table above is 25percent.a.If you put all of your money into Stock 1 or Stock 2, what is the average return that you willreceive? (Hint: average the returns of +30 percent and –10 percent.)b.If you split your money equally between the two stocks ($50 in Stock 1 and $50 in Stock 2), whatwould be your total return at the end of the year in each of the boxes above? Fill out the followingtable to indicate the total return you would have in each of the four possible situations. (Hint:average the returns of the two investments in each box.)Stock 1Stock 2GainLoseGainLosec.If you split your money between the two stocks, what is the average return that you will receive?(Hint: take the total return for each box in part (b) and calculate the average across the four boxesgiving each box equal weight.)d.Is there any benefit in splitting your money between the two stocks? How does this relate to theconcept of diversification?Answer:a.There is a one-half chance that you will gain 30 percent, and a one-half chance that you willlose 10 percent, so the average return is()0.530%0.510%10%.×+× −=b.Because half of your portfolio is in each stock, we multiply the returns for that stock by theirportfolio weight (0.5) in each situation.

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12Acemoglu, Laibson, and List |EconomicsStock 1Stock 2GainLoseGain0.530%0.530%30%×+×=0.530% 0.5( 10%)10%×+× −=Lose()0.510%0.51.210%× −+×=()()0.510%0.510%10%× −+× −=−c.There is a 25 percent chance you will end up in each of the four possibilities, so the expectedvalue is()0.2530%0.2510%0.2510%0.2510%10%×+×+×+× −=d.We saw in parts a and c that the expected value of your investment is the same whether youinvest in a single stock or split your money between the two stocks. However, there is lessvolatility in your payout if you diversify by investing half your money in both stocks ratherthan investing all of your money in a single stock. In other words, if you invest all of yourmoney in a single stock, you will either win big or lose big. However, if you split yourmoney between the two stocks, there is a third possibility that one stock will gain and theother one will lose, and the two effects will cancel each other out. This leads to a lessvolatile return. When you are planning for retirement, it is very important, when budgeting,to know approximately how much money you will have. Finding out that all of your stockshave lost value at the same time can be quite a blow. Therefore, people are advised todiversify so that they do not have “all of their eggs in one basket.”A-head: RISKY RETURNS; DIVERSIFICATIONConcept: Risky returns; DiversificationDifficulty: Moderate/HardProblem-type: Calculation10. Suppose that a mutual fund, Washington Peak Strategic Bond Fund, believes it has hit upon awinning investment strategy. The fund uses an active management strategy to try to outperform thebond market. According to Washington Peak’s prospectus, investors need to pay fees of 2 percentannually. Based on the historical success of their active investment strategy, the strategy is projectedto generate annual returns (once fees are paid) of 8 percent. A friend of yours is considering investingin Washington Peak and asks you for investment advice. What would you suggest?Answer:One of the problems with Washington Peak’s investment strategy is the lack ofdiversification. By investing most of the fund’s money in one investment strategy, Peak will not beable to diversify its returns. It should therefore not be alargefraction of your friend’s totalinvestment portfolio. Second, Peak’s traders base their strategy on historical data. It is not necessarilythe case that historical trends will continue to play out in the future. This fact introduces someadditional risk. The third factor that your friend will need to consider is the expense ratio thatWashington Peak is charging. An expense ratio of 2 percent is generally considered to be very highfor a mutual fund. High expense ratios lower the net annual return that your friend receives on hisinvestment.A-head: RISKY RETURNS; DIVERSIFICATION; INVESTMENT ACCOUNTSConcept: Diversification, expense ratiosDifficulty: Easy/ModerateProblem-type: Fictional ‘real-world’ scenario11. Tom, a government employee, has a defined benefit pension. He has worked for his employer for 35years before retiring at age 65. His final salary was $85,000. Calculate how much of his finalpreretirement income a standard defined benefit pension plan would replace.

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