Money & Banking Connect HW Ch. 1-5
If offered the choice of receiving $2,000 today or $2,000 in two year's time, which option would you choose, and why?
$2,000 today because time has value and by receiving the money today you can put it to use immediately. Core Principle 1 states that time has value, so by choosing to receive the $2,000 today you can immediately put the money to use. Perhaps you buy a new computer or put the money in the bank to earn interest. Regardless of what you do with the money, waiting a year to receive the money involves an opportunity cost.
Approximately how long would it take for an investment of $100 to reach $800 if you earned 5 percent (annual interest)? What if the interest rate were 10 percent? How long would it take an investment of $200 to reach $800 at an interest rate of 5 percent? Why is there a difference between doubling the interest rate and doubling the initial investment?
43.2 ± 1 years. 21.6 ± 1 years. 28.8 ± 1 years. The difference between doubling the interest rate and doubling the initial investment is due to compounding—the higher interest earnings having interest paid on them in subsequent years has a bigger impact than the interest being calculated from a larger initial investment. Using the rule of 72, we know that if the interest rate is 5 percent, it will take 72/5 = 14.4 years for the investment to double to $200. Repeating the exercise twice more (doubling from $200 to $400 and then from $400 to $800), we see that the investment will take 43.2 years to reach $800. If the interest rate is 10 percent, it will take 72/10 = 7.2 × 3 = 21.6 years to double—exactly half the time. (You can check that your calculations are approximately correct using the future value formula. Alternatively, you could have directly solved for nin the future value formula to find the number of years needed to get to $800.) If $200 is invested at 5 percent, it will take 72/5 = 14.4 × 2 = 28.8 years to reach $800—which is more than half the time it took for $100 to reach $800 at the same interest rate. The reason lies in the compounding—the greater interest earnings having interest paid on them in subsequent years has a bigger impact than the interest being calculated from a larger initial investment.
Which of the following investments would be most attractive to a risk-averse investor? (Picture a Chart Below) Investment : Expected Value : Standard Deviation A : 30 : 3 B : 35 : 3 C : 35 : 5 How would your answer differ if the investor were described as risk-neutral?
A risk-averse investor will prefer investment B because it has a higher expected return than investment A for the same level of risk and the same expected return as investment C for a lower level of risk. A risk-neutral investor would be indifferent between investments B and C and prefer them to investment A because they have a higher expected value.
You wish to buy an annuity that makes monthly payments for as long as you live. Describe what happen to the purchase price of the annuity if (1) your age at the time of purchase goes up, (2) the size of the monthly payment rises, and (3) your health improves.
As your age at the time of purchase goes up, the number of expected monthly payments decreases so the price of the annuity decreases. The price of the annuity rises as each monthly payment is larger. Because of your good health you are expected to live longer, therefore, the number of expected monthly payments is higher and the price of the annuity increases. (1) The number of expected monthly payments decreases so the price of the annuity decreases. (2) The price of the annuity rises as each monthly payment is larger. (3) Because of your good health you are expected to live longer, therefore, the number of expected monthly payments is higher and the price of the annuity increases.
Life insurance companies tend to invest in long-term assets such as loans to manufacturing firms to build factories or to real estate developers to build shopping malls and skyscrapers. Automobile insurers tend to invest in short-term assets such as Treasury bills. What accounts for these differences?
Automobile insurers generally need to have funds readily available when a policyholder makes a claim, and Treasury bills are highly liquid. Life insurance companies have liabilities with a much longer horizon. A life insurance policy is expected to pay off in 30 years, say, so that assets with longer horizons correspond to their longer-term liabilities.
Commercial banks, insurance companies, investment banks, and pension funds are all examples of financial intermediaries. Identify the source of their funds and how they are used. Commercial banks: Insurance companies: Investment banks: Pension funds:
Commercial banks receive deposits in checking and savings accounts and borrow from other entities. The funds they receive are used to make loans and purchase government securities. Insurance companies receive premium payments, which they invest in securities or other assets to earn income until claims are paid. Investment banks charge fees for advising clients on mergers and acquisitions and for preparing new stock and bond issues for the market. They may use funds to participate in some of the initial public offerings they distribute. Pension funds receive regular contributions from firms providing for retirement promises. These funds are invested in long-term assets that will later be used to pay benefits to firms' retirees.
As of July 2016, 19 European Union countries have adopted the euro, while the remaining member countries have retained their own currencies. What are the advantages of a common currency for someone who is traveling through Europe?
Each country has the same unit of account, making it easier for a traveler to compare prices in different countries. The traveler also saves the costs of exchanging currencies.
You receive a check drawn on another bank and deposit it into your checking account. Even though this is a "demand deposit," the funds are not immediately available for your use. Why? Would your answer change if the check is drawn on the account of another customer of your own bank?
Funds drawn on another bank are not immediately available until the funds are transferred through the check-clearing process. Yes. The funds will be internally transferred, so the funds may be available almost immediately.
What risks might financial institutions face by funding long-run loans such as mortgages to borrowers (often at fixed interest rates) with short-term deposits from savers?
If savers decide to withdraw in large numbers from the financial institution, the institution may not have sufficient funds readily available for them if the funds have been lent out as 30-year mortgages. If savers decide to withdraw in large numbers from the financial institution, the institution may not have sufficient funds readily available for them if the funds have been lent out as 30-year mortgages. For example. (Assume mortgages are held on the balance sheet of the institution in question.) Moreover, long-term mortgage loans are often made at fixed interest rates while rates on short-term deposits fluctuate with the market. The financial institution faces the risk that interest rates will rise, requiring higher interest rates to be paid to continue to attract deposits while the payments received from the mortgage loans stay the same.
Under what circumstances might you be willing to pay more than $1,000 for a coupon bond that matures in three years, has a coupon rate of 10 percent, and a face value of $1,000?
If the interest rate in the market were less than 10%, the present value of the payment flows associated with the bond would be higher than $1,000. You can use the present value formula to verify this. For example, suppose the interest rate were 8%. The present value of the payment flows associated with the bond would be 100/1.08 + 100/(1.08)^2 + 100/(1.08)^3 + 1,000/(1.08)^3 = $1,051.54.
Under what circumstances might you expect barter to reemerge in an economy that has fiat money as a means of payment?
If there are periods of high inflation and the public loses confidence or trust in fiat money, barter may reemerge. You might expect an economy to revert to barter when the public loses confidence in the fiat money issued by the government, perhaps because of over-use of the printing presses. For example, this as happened during episodes of extremely high inflation, such as that experienced in Zimbabwe during much of the 2000's.
Under what circumstances might money in the form of currency be the best option as a store of value?
If there were deflation in the economy, then paper currency would increase in value. When deflation occurs, overall prices in the economy are falling and so the currency you hold has more purchasing power. During periods of falling prices of goods and services, prices of assets often fall too and so currency might be an attractive option as a store of value.
Consider an investment that pays off $700 or $1,400 per $1,000 invested with equal probability. Suppose you have $1,000 but are willing to borrow to increase your expected return. What would happen to the expected value and standard deviation of the investment if you borrowed an additional $1,000 and invested a total of $2,000? What if you borrowed $2,000 to invest a total of $3,000?
If you just invest your own $1,000, the expected value = 0.5($700) + 0.5($1400) = $1,050, or 5 percent, and the standard deviation is 350. If you borrow an additional $1,000, the expected value is $1,100, or 10 percent. The expected return has doubled. The standard deviation is 700 and so has doubled. If you borrowed $2,000 to invest a total of $3,000, the expected value is $1,150, or 15 percent. The expected return has tripled compared with the unleveraged investment. The standard deviation is 1,050 and so has tripled compared with the unleveraged investment.
Consider two scenarios. In the first, the nominal interest rate is 6 percent and the expected rate of inflation is 4 percent. In the second, the nominal interest rate is 5 percent and the expected rate of inflation is 2 percent. In which situation would you rather be a lender? In which would you rather be a borrower?
In the first scenario you would rather be a borrower. In the second scenario, you would rather be a lender. In the first scenario the real interest rate is 2 percent (the difference between the nominal interest rate and the expected inflation rate) and in the second the real interest rate is 3 percent. As a lender you want a high real return and so would rather lend with the real interest rate at 3 percent (when the nominal rate is 5 percent). As a borrower, you want a low real interest rate and so would rather borrow when the real rate is 2 percent (even though the nominal interest rate is 6 percent).
Recently, some lucky person won the lottery. The lottery winnings were reported to be $85.5 million. In reality, the winner got a choice of $2.85 million per year for 30 years or $46 million today. a. Explain briefly why winning $2.85 million per year for 30 years is not equivalent to winning $85.5 million. b. The evening news interviewed a group of people the day after the winner was announced. When asked, most of them responded that, if they were the lucky winner, they would take the $46 million up-front payment. Suppose (just for a moment) that you were that lucky winner. How would you decide between the annual installments or the up-front payment?
It is not equivalent to winning because of the time value of money. With the annual payments over 30 years, you don't receive most of the money until sometime in the future, so the value is less because of foregone interest. The equivalent today of the annual payments over 30 years is the sum of the present value of the sequence of payments. I would compare the present value of the installments over 30 years using an appropriate interest rate from the market with $46 million to see which option represented the highest present value. a. They are not equivalent because of the time value of money. If you received all the money today, you could invest it and earn interest on it. Given that you don't receive most of the money until sometime in the future, the value is less because of the foregone interest. The equivalent today is the sum of the present values of the sequence of payments. b. I would calculate which payment option gave me the highest present value. I would look at the market to determine the appropriate interest rate to use and calculate the PV of the installments over 30 years. I would compare this with $46 million to see which option is highest. Another factor to consider would be whether the tax treatment was the same for both options.
Has the distinction between direct and indirect forms of finance become more or less important in recent times? Why?
Less important. The increasing sophistication of the financial system has led to greater institutionalization, so that even direct finance transactions usually involve a financial institution to some extent. The distinction has become less important. The increasing sophistication of the financial system has led to greater institutionalization, so that even direct finance transactions usually involve a financial institution to some extent.
Joe and Mike purchase identical houses for $200,000. Joe makes a down payment of $40,000 while Mike only puts down $10,000. For each individual, the down payment is the total of his net worth. Assuming everything else equal, who is more highly leveraged? If house prices in the neighborhood immediately fall by 10 percent (before any mortgage payments are made), what would happen to Joe's and Mike's net worth? (Assume Joe and Mike have no other assets or liabilities.)
Mike Joe's net worth would fall but remain positive ($20,000) while Mike's net worth would become negative (-$10,000). Mike is more highly leveraged because he has financed a larger part of his asset with borrowing (95 percent compared to Joe's 80 percent). Assuming they have no other assets or liabilities, if house prices fall by 10 percent, Joe's net worth would be $20,000 but Mike's net worth would be negative. He would owe $190,000 on his mortgage for a house worth $180,000.
Is the challenge of making "time consistent" policy unique to fiat-based paper money?
No. Even if the value of money is linked to a commodity such as gold, the government could abolish the current commitment at a point in the future. No. Even if the value of money is linked to a commodity such as gold, the government could abolish this current commitment at a point in the future such as in a time of crisis. For example, the United States exited the Gold Standard in 1933, allowing the price of gold to vary in dollar terms for the first time in a century.
Assuming the chances of being paid back are the same, would a nominal interest rate of 10 percent always be more attractive to a lender than a nominal rate of 5 percent?
Not always. Lenders are concerned with the real return they receive. Lenders are concerned with the real return they receive. If the higher nominal interest rate represents a higher real interest rate, then the lender will find it more attractive. If, on the other hand, the higher nominal interest rate merely reflects higher expected inflation, this may not be to the benefit of the lender. For example, a nominal interest rate of 10 percent, reflecting expected inflation of 8 percent and a real interest rate of 2 percent, would not be preferred by lenders over a nominal interest rate of 5 percent, reflecting expected inflation of 1 percent and a real interest rate of 4 percent. It is the real, not the nominal, interest rate that matters.
Assuming that the current interest rate is 3 percent, compute the present value of a five-year, 5 percent coupon bond with a face value of $1,000. What happens when the interest rate goes to 4 percent? What happens when the interest rate goes to 2 percent?
PV at an interest rate of 3 percent (i = 3%) = ($1,000 × 0.05)/(1.03) + ($1,000 × 0.05)/(1.03)^2 + ($1,000 × 0.05)/(1.03)^3 + ($1,000 × 0.05)/(1.03)^4 + ($1,000+1,000 × 0.05)/(1.03)^5 = $1,091.59 PV for a five-year, 5 percent coupon bond with face value of $1,000 at an interest rate of 4 percent (i = 4%) = ($1,000 × 0.05)/(1.04) + ($1,000 × 0.05)/(1.04)^2 + ($1,000 × 0.05)/(1.04)^3 + ($1,000 × 0.05)/(1.04)^4 + ($1,000 + 1,000 × 0.05)/(1.04)^5 = $1,044.52. The present value falls when the interest rate rises to 4 percent. PV for five-year, 5 percent coupon bond with face value of $1,000 at an interest rate of 2 percent (i = 2%) = ($1,000 × 0.05)/(1.02) + ($1,000 × 0.05)/(1.02)^2 + ($1,000 × 0.05)/(1.02)^3 + ($1,000 × 0.05)/(1.02)^4 + ($1,000 + 1,000 × 0.05)/(1.02)^5 = $1,141.40. The present value rises when the interest rate falls to 2 percent.
The design and function of financial instruments, markets, and institutions are tied to the importance of information. Describe the role played by information in each of these three pieces of the financial system. Financial instruments: Financial markets: Financial institutions:
Summarize essential information about the borrower. Aggregate information from many sources and communicate it widely. Produce information to screen and monitor borrowers. The design and function of financial instruments, markets, and institutions are tied to the importance of information. Financial instruments summarize essential information about the borrower. Financial markets aggregate information from many sources and communicate it widely. Financial institutions produce information to screen and monitor borrowers.
Suppose a significant fall in the price of certain stocks caused the market makers in those stocks to experience difficulties with their funding liquidity. Under what circumstances might that development lead to liquidity problems in markets for other assets?
Suppose a significant fall in the price of certain stocks caused the market makers in those stocks to experience difficulties with their funding liquidity. Under what circumstances might that development lead to liquidity problems in markets for other assets?
In December 2015, the Federal Reserve increased its policy interest rate target. This was the first increase since cutting the target to close to zero in December 2008 to combat the economic weakness associated with the financial crisis. If central banks use interest rates to moderate business cycle swings in the economy, what might you infer from this decision about the Fed's view of the economy?
The Federal Reserve's decision to begin raising the target for the policy interest rate from its historic low level reflected its view at that time that the economic recovery was on solid footing.
For each pair of instruments below, use the criteria for valuing a financial instrument to choose the one with the highest value: a. A U.S. Treasury bill that pays $1,000 in six months or a U.S. Treasury bill that pays $1,000 in three months. b. A U.S. government Treasury bill that pays $1,000 in three months or commercial paper issued by a private corporation that pays $1,000 in three months. c. An insurance policy that pays out in the event of serious illness or one that pays out when you are healthy, assuming you are equally likely to be ill or healthy.
The Treasury bill that pays in three months because a payment that is received sooner in the future is more valuable. The U.S. Treasury bill is more valuable because the payment is more likely to be made. The insurance policy that pays out when you are seriously ill because this is when the payment is needed the most.
Suppose medical research confirms earlier speculation that red wine is bad for you. Why would banks be willing to lend to vineyards that produce red wine at a higher interest rate than before?
The future prospects for vineyards have worsened. The risks associated with lending to vineyards have risen and so banks require more compensation than before.
Your firm has the opportunity to buy a perpetual motion machine to use in your business. The machine costs $1,000,000 and will increase your profits by $75,000 per year. What is the internal rate of return?
The internal rate of return is 7.5 percent. Using the result in the appendix equation (A5) as n becomes arbitrarily large, we have PV = C / i. The price of the machine is $1,000,000 and the constant stream of profits is $75,000 per year, so the internal rate of return is i = C / P = .075, or 7.5 percent.
You are considering buying a new house, and have found that a $250,000, 30-year fixed-rate mortgage is available with an interest rate of 8 percent. This mortgage requires 360 monthly payments of approximately $1,786 each. If the interest rate rises to 9 percent, what will happen to your monthly payment?
The monthly payment will be $1,949 ± 1. The change in the monthly payment will be 9.1 ± 0.10 percent while the change in the interest rate will be 12.5 ± 0.10 percent. If the annual interest rate is 9 percent, then the monthly rate is (1.09)1/12 - 1 = 0.007207. Using the equation from Appendix 4A: C = ($250,000 × 0.007207)/[1 - (1/(1.007207)360)] = $1,949. Monthly payments have risen by ($1,949 - $1,786)/$1,786 = 9.1% and the interest rate has risen by (9% - 8%) / 8% = 12.5%.
Splitland is a developing economy with two distinct regions. The northern region has great investment opportunities, but the people who live there need to consume all of their income to survive. Those living in the south are better off than their northern counterparts and save a significant portion of their income. The southern region, however, has few profitable investment opportunities and so most of the savings remain in shoeboxes and under mattresses. How could the development of the financial sector benefit both regions and promote economic growth in Splitland?
The presence of a financial intermediary would reduce the information costs that may have prevented the southerners from lending directly to the northerners in the past. This would promote economic growth. In the absence of financial markets, resources are not being allocated to the best investment opportunities available—in this case, to the northern region. The introduction of a financial intermediary, for example, could channel the available savings from the southerners to the most productive investment opportunities that are available in the northern region. The presence of the intermediary would reduce the information costs that may have prevented the southerners from lending directly to the northerners in the past. The southerners would benefit by earning a return on their savings while the northern region would benefit from increased investment. Splitland would benefit from higher economic growth as the available resources are allocated more efficiently.
Consider an economy that only produces and consumes two goods— food and apparel. Suppose the inflation rate based on the consumer price index is higher during the year than that based on the GDP deflator. Assuming underlying tastes and preferences in the economy are the same, what can you say about food and apparel price movements during the year?
The prices of food and apparel must have changed at different rates, causing consumers to substitute one of the goods for the other. Since the GDP deflator is calculated based on what is actually purchased, it takes that substitution in to account. Since the two price indices yield different inflation rates with preferences remaining constant, the relative prices of the two goods must have changed. In other words, the price of one of the goods must have gone up by a greater percentage than the other. For example, suppose the price of food went up by 10% while the price of apparel went up by 20%. This would induce consumers to substitute away from apparel to food. As a fixed-weight index, the CPI would not take this substitution into account while the GDP deflator would, since it is calculated on the basis of what is actually purchased. Therefore, the CPI inflation rate would be higher than the rate calculated from the GDP deflator.
Why might one doubt that current forms of digital money, such as Bitcoin, will replace more traditional fiat currencies? The private digital currencies currently do not fulfill the following key functions of money as well as government-issued fiat money:
The private digital currencies currently do not fulfill any of the key functions of money— store of value, means of payment, and unit of account.
If higher leverage is associated with greater risk, explain why the process of deleveraging (reducing leverage) can be destabilizing.
The problem arises if too many institutions try to reduce their leverage at the same time. A large number of institutions selling assets will push down asset prices. With asset values falling relative to liabilities, net worth falls, increasing leverage and prompting further asset sales, potentially destabilizing those markets. If higher leverage is associated with greater risk, the process of deleveraging (reducing leverage) can be destabilizing. The problem arises if too many institutions try to reduce their leverage at the same time. A large number of institutions selling assets will push down asset prices. With asset values falling relative to liabilities, net worth falls, increasing leverage and prompting further asset sales, potentially destabilizing those markets.
Given a choice of two investments, would you choose one that pays a total return of 15 percent over 5 years or one that pays 0.3 percent per month for 5 years? What annual rate of return does each give you?
The return of 15 percent over 5 years provides an annual return of 2.83 ± 0.10 percent. The return of 0.3 percent per month for 5 years provides an annual return of 3.66 ± 0.10 percent. The investment that pays 0.3 percent per month over 5 years is preferable. To compare these investments, you need to measure their returns in the same units. In this case, convert both these returns to annual rates. Option 1: The return of 15 percent over 5 years provides an annual return of: ({1.15:0.00}})(1/5)) − 1 = 0.0283, or 2.83 percent. Option 2: The return of 0.3 percent per month for 5 years provides an annual return of: ([1.003)(12) − 1 = 0.0366, or 3.66 percent. Therefore, you should chose the investment that pays 0.3 percent per month for 5 years.
What would you expect to happen to investment and growth in the economy if the U.S. government decided to abolish the Securities and Exchange Commission?
The role of the Securities and Exchange Commission (SEC) is to protect investors by working to insure that all investors have access to certain knowledge about companies. If the SEC were abolished, it would be more difficult for investors to make good, well-informed decisions. Capital markets would likely function less efficiently to the detriment of investment and growth.
Suppose you need to take out a personal loan with a bank. The problems in the interbank lending market such as those seen during the 2007-2009 financial crisis would have affected your ability to take out a personal loan with a bank. Explain how.
The strains in the interbank market pushed up interbank lending rates, which increased the cost of funds to banks and would likely have lead to an increase in the rate on your personal loan. If your bank is having trouble obtaining short-term funding in the interbank market, it may decide to hold more cash and reduce lending, affecting your ability to secure a loan. The problems in the interbank lending market such as those seen during the 2007-2009 financial crisis would have affected your ability to take out a personal loan with a bank. The strains in the interbank market pushed up interbank lending rates, which increased the cost of funds to banks and would likely have led to an increase in the rate on your personal loan. If your bank is having trouble obtaining short-term funding in the interbank market, it may decide to hold more cash and reduce lending, impacting your ability to secure a loan.
Using the information from the table below, in dollar terms what is the value at risk associated with a $1,000 investment? (Picture a Chart Below) State of the Economy : Probability : Return High Growth : 0.2 : + 30% Normal Growth : 0.7 : + 12% Recession: 0.1 : - 15%
The value at risk: $ 150 ± 1.0 Since the worst outcome is a loss of 15 percent, the value at risk is $150 (= $1,000 × 0.15).
The Chicago Mercantile Exchange has announced the introduction of a financial instrument that is based on rainfall in the state of Illinois. The standard agreement states that for each inch of rain over and above the average rainfall for a particular month, the seller will pay the buyer $1,000. Who could benefit from buying such a contract? Who could benefit from selling it?
This instrument could be sold by someone who benefits from above average rainfall, and someone who is harmed by above average rainfall should buy the contract. Someone who benefits from above average rainfall could sell the contract, and someone who is harmed by above average rainfall should buy the contract. Crops can benefit from additional rainfall during certain times of the year, but may be harmed by too much rain at other times; so, depending on the season, farmers could be buying or selling derivatives. Hydroelectric companies could also sell the contracts, while people who benefit from dry weather - like golf course operators - would buy them.
Assuming no interest is paid on checking accounts, what would you expect to see happen to the relative growth rates of M1 and M2 if interest rates rose significantly?
When interest rates rise, you would expect that people would shift funds from checking accounts into savings accounts, as the opportunity cost of holding funds in a noninterest-bearing account has risen. Checking accounts are a component of M1 while both checking and some savings accounts are included in M2. Therefore, any shift from checking to savings accounts would depress growth in M1 to a greater degree than growth in M2, leading to a relative increase in the M2 growth rate.
Consider two possible investments whose payoffs are completely independent of one another. Both investments have the same expected value and standard deviation. If you have $1,000 to invest, could you benefit from dividing your funds between these investments? Explain your answer.
Yes. By dividing your funds, you are adding combinations of possible payoffs that lie between the worst- and best-case scenarios and so the probability-weighted spread of the possible payoffs is smaller. Yes, even though the investments have the same standard deviation, by spreading your $1,000 across both of them, you reduce your risk. Intuitively, you are adding combinations of possible payoffs that lie between the worst- and best-case scenarios and so the probability-weighted spread of the possible payoffs is smaller. Mathematically, the variance of the payoffs is halved.
Consider two possible investments whose payoffs are completely independent of one another. Both investments have the same expected value and standard deviation. You have $1,000 to invest between these investments. Now suppose that there were 12 independent investments available rather than just two. Would it matter if you spread your $1,000 across these 12 investments rather than two?
Yes. The gains from spreading your investments would be larger if you spread the $1,000 across 12 investments. Yes. The gains from spreading your investments would be larger if you spread the $1,000 across 12 investments. The risk, as measured by the variance of the payoffs, is inversely related to the number of independent investments, n.
If the U.S. Securities and Exchange Commission eliminated its requirement for public companies to disclose information about their finances, what would you expect to happen to the stock prices of these companies?
You should expect the stock prices to fall. Gathering sufficient information upon which to make an informed decision would become much more costly for investors, reducing the demand for the stock at a given price.
You have the option to invest in either Country A or Country B but not both. You carry out some research and conclude that the two countries are similar in every way except that the returns on assets of different classes tend to move together much more in Country A—that is, they are more highly correlated in Country A than in Country B. Which country would you choose to invest in and why?
You should invest in Country B as the benefits from diversification are greater. You should invest in Country B as the benefits from diversification are greater than in Country A. If everything else is equal, spreading your risk across different asset classes brings greater benefit when the correlation among the returns is lower.
You are considering three investments, each with the same expected value and each with two possible payoffs. The investments are sold only in increments of $500. You have $1,000 to invest so you have the option of either splitting your money equally between two of the investments or placing all $1,000 in one of the investments. If the payoffs from Investment A are independent of the payoffs from Investments B and C and the payoffs from B and C are perfectly negatively correlated with each other (meaning when B pays off, C doesn't and vice versa), which investment strategy will minimize your risk?
You should put $500 into each of Investments B and C. Because one pays off when the other doesn't, you eliminate your risk by hedging. You should put $500 into each of Investments B and C. Because one pays off when the other doesn't, you eliminate your risk by hedging. Spreading your investment across A and either B or C would reduce your risk compared with investing all $1,000 in one investment but would not eliminate it.
If the current interest rate increases, what would you expect to happen to bond prices?
You would expect bond prices to fall because bond prices are the sum of the present values of the future payments associated with the bond. The higher the interest rate, the lower the present value of these payments. Interest rates and bond prices are inversely related so bond prices will fall when interest rates increase. Bond prices are the sum of the present values of the future payments associated with the bond. The higher the interest rate, the lower the present value of these payments.
If the coupon rate decreases, what would you expect to happen to bond prices?
You would expect bond prices to fall since bond prices are the sum of the present values of the future payments associated with the bond. The lower the interest rate, the lower the present value of these payments.
Consider a game in which a coin will be flipped three times. For each heads you will be paid $100. Assume that the coin comes up heads with probability 2/3. a. Construct a table of the possibilities and probabilities in this game. b. Compute the expected value of the game. c. How much would you be willing to pay to play this game? d. Consider the effect of a change in the game so that if tails comes up two times in a row, you get nothing. How would your answers to the first three parts of this question change?
a. (Picture a Chart Below) Probabilities : Probability ; Outcome 1: 1/27 ; 0 H, 3 T 2: 4/27 ; 1 H, 2 T 3: 4/27 ; 2 H, 1 T 4: 4/27 ; 3 H, 0 T 5: 2/27 ; 1 H, 2 T 6: 2/27 ; 1 H, 2 T 7: 2/27 ; 1 H, 2 T 8: 8/27 ; 1 H, 2 T b. The expected value = 1/27($0) + 3(2/27)($100) + 3(4/27)($200) + 8/27($300) = $200 c. A person who is risk averse will want to pay less than $ =200; a person who is risk-neutral will be willing to pay $200. d. (Picture a Chart Below) Probabilities : Probability : Outcome : Payoff 1: 1/27 : 0 H, 3 T : $0 2: 4/27 : 1 H, 2 T : $100 3: 4/27 : 2 H, 1 T : $0 4: 4/27 : 3 H, 0 T : $0 5: 2/27 : 1 H, 2 T : $200 6: 2/27 : 1 H, 2 T : $200 7: 2/27 : 1 H, 2 T : $200 8: 8/27 : 1 H, 2 T : $300 Expected value = $185 A person who is risk-averse will want to pay less than $ 185 ; a person who is risk- neutral will be willing to pay $185 .
In June 2016, the United Kingdom (U.K.) held a referendum on whether the country should remain a member of the European Union (EU). A decision to leave the EU was commonly referred to as Brexit and many expert commentators predicted that a vote for Brexit would diminish U.K. economic growth. Suppose you were a international investor around this time. Assume that the downside risk for the U.K. economy from a Brexit vote would be much greater than for the rest of the global economy. Some countries could even benefit from a Brexit vote. a. Why might you demand a relatively higher return on U.K. investments ahead of the vote? A higher return on demanded on U.K. investments could reflect: b. What strategy might you employ to reduce the risk associated with your U.K. investments?
a. A higher risk premium required in the face of increased perceived risk. Core Principle 2 tells us that risk requires compensation. A higher return demanded on U.K. investments could reflect a higher risk premium required in the face of additional perceived risk surrounding the vote. b. An international investor would face idiosyncratic risk , therefore both hedging and spreading risk would be the best strategy. From a global perspective, the Brexit vote could be viewed as more of an idiosyncratic risk. Suppose, for example, that another country stood to gain from a Brexit vote as it became a relatively more attractive location for firms. An investor could then hedge U.K. investments that were likely to lose out with a Brexit vote placing investments in the other country. Spreading risks across investments in different countries that were not highly correlated (even if they were not negatively correlated) also could help reduce risks.
For each of the following events, identify whether it represents systematic risk or idiosyncratic risk. a. Your favorite restaurant is closed by the county health department. b. Real estate values have dropped by 20 percent in your local area. c. Freezing weather in Florida destroys the orange crop. d. An outbreak of scarlet fever sickens many people in your city.
a. Idiosyncratic risk b. Idiosyncratic risk c. Idiosyncratic risk d. Idiosyncratic risk
In June 2016, the United Kingdom (U.K.) held a referendum on whether the country should remain a member of the European Union (EU). A decision to leave the EU was commonly referred to as Brexit, and many expert commentators predicted that a vote for Brexit would diminish U.K. economic growth. Suppose you were a small business owner in the United Kingdom around this time. a. Ahead of the vote, what kind of risk would you classify the possibility of a vote for Brexit? b. Do you think a strategy to reduce the risk through hedging or spreading risk would be successful?
a. The prospect that the U.K. would vote to leave the European Union and suffer a loss of economic growth as a consequence is an example of systematic risk, a risk that is economy-wide, rather than being specific to one firm or a small group of firms. The potential for harm to economic growth would affect firms across the entire economy. b. Neither hedging nor spreading risk would be the best strategy. Hedging and spreading risk are strategies that can be employed to manage idiosyncratic risks but not systematic risks. Given the economy-wide nature of the Brexit risk, it is unlikely that you find a way to hedge by assuming an opposing risk. For this reason, the benefits of spreading risk within the U.K. economy would likely be limited.
You visit a tropical island that has only four goods in its economy—oranges, pineapples, coconuts, and bananas. There is no money in this economy. a. How many price pairs are possible in this economy? (You should check your answer using the n(n − 1)/2 formula where n is the number of goods.) b. An islander suggests designating oranges as the means of payment and unit of account for the economy. How many prices would there be if her suggestion were followed?
a. There would be six prices in total.The combinations are: Bananas / Oranges, Bananas / Pineapples, Bananas / Coconuts Coconuts / Oranges, Coconuts / Pineapples Pineapples / Oranges b. There would be three prices—pineapples/oranges, coconuts/oranges and banana/oranges.
Some friends of yours have just had a child. Thinking ahead, and realizing the power of compound interest, they are considering investing for their child's college education, which will begin in 18 years. Assume that the cost of a college education today is $125,000. Also assume there is no inflation and no tax on interest income used to pay college tuition and expenses. a. If the interest rate is 7 percent, how much money will your friends need to put into their savings account today to have $125,000 in 18 years? b. What if the interest rate were 10 percent? c. The chance that the price of a college education will be the same 18 years from now as it is today seems remote. Assuming that the price will rise 3 percent per year, and that today's interest rate is 8 percent, what will your friends' investment need to be? d. Return to the case with a 7 percent interest rate and no inflation (part a). Assume that your friends don't have enough financial resources to make the entire investment at the beginning. Instead, they think they will be able to split their investment into two equal parts, one invested immediately and the second invested in five years. What is the amount of each part?
a. They would need to put $36,983 ± 1 into their savings account today. PV = $125,000 /(1.07)^18 = $ 36,983 b. They would need to put $22,482 ± 1 into their savings account today. PV = $125,000 /(1.10)^18 = $22,482 c. The amount of the investment would be $53,254 ± 1. If the price rises 3 percent per year, the cost of a college education in 18 years will be: PV = [$125,000 × (1.03)18]/(1.08)^18 = $53,254 d. The required size of the two investments would be $21,590 ± 1. If x is the size of each investment: $125,000 = x(1.07)^18 + x(1.07)^13
For each of the following actions, identify whether the method of risk assessment motivating the action is due to the value at risk or the standard deviation of an underlying probability distribution. a. You buy life insurance. b. A car buyer chooses comprehensive insurance coverage when she purchases a new vehicle. c. In your role as a central banker, you provide emergency loans to illiquid intermediaries. d. A software developer expands by purchasing a robotics manufacturer.
a. Value at risk b. Value at risk c. Value at risk d. Standard deviation
You decide to start a business selling covers for smart phones in a mall kiosk. To buy inventory, you need to borrow some funds. Why are you more likely to take out a bank loan than to issue bonds?
A person starting up a small business would be more likely to take out a bank loan, because issuing bonds is a form of direct finance and would require finding a buyer who would be willing to bear the information and monitoring costs associated with the loan. For a small, unknown business these costs would usually be prohibitive. In the case of a bank loan, the lending organization acts as the counterparty to the transaction. These organizations overcome problems associated with asymmetric information by using their expertise to screen loan applicants and use standardized loan contracts to decrease transaction costs. Issuing bonds is a form of direct finance and would require finding a buyer who would be willing to bear the information and monitoring costs associated with the loan. For a small, unknown business these costs would usually be prohibitive. In the case of a bank loan, the lending institution becomes the counterparty to the transaction. These financial institutions overcome problems associated with asymmetric information by using their expertise to screen loan applicants and use standardized loan contracts to reduce transaction costs.
Compute the future value of $800 at an 8 percent interest rate 5, 10, and 15 years into the future. What would the future value be over these time horizons if the interest rate were 5 percent?
Future value in 5 years at 8 percent = $800 × (1.08)^5 = $1,175.46 Future value in 10 years at 8 percent = $800 × (1.08)^10 = $1,727.14 Future value in 15 years at 8 percent = $800 × (1.08)^15 = $2,537.74 Future value in 5 years at 5 percent = $800 × (1.05)^5 = $1,021.03 Future value in 10 years at 5 percent = $800 × (1.05)^10 = $1,303.12 Future value in 15 years at 5 percent = $800 × (1.05)^15 = $1,663.14
How might broader access to finance benefit a country where access was previously very limited? Greater access to finance can boost economic growth by:
Greater access to finance can boost economic growth by lowering transaction costs, facilitating the channeling of savings to the most productive uses, and enabling greater specialization.
You visit a tropical island that has only four goods in its economy—oranges, pineapples, coconuts, and bananas. There is no money in this economy. Under what circumstances would you recommend the issue of a paper currency by the government of the island? What advantages might this strategy have over the use of oranges as money?
If islanders have enough confidence in their government to accept paper currency notes that have no intrinsic value and are backed only by a government decree. The money supply would be controlled by the government and not subject to random variation based on islanders' decisions to grow oranges. The money supply would be more durable than oranges, easier to carry, and more divisible. The islanders must have enough confidence in their government to accept notes backed only by a government decree that have no intrinsic value themselves. They have to believe that these notes will be widely accepted by other islanders as final payment for goods and services and in settlement of debts. They must trust that the government will not print too much money and undermine its value.
If money growth is related to inflation, what would you expect to happen to the inflation rates of countries that join a monetary union and adopt a common currency such as the euro?
Once countries join a monetary union, they effectively share a common money supply. Given the link between money growth and inflation, you would expect the inflation rates of these countries to converge.
As the manager of a financial institution, what steps could you take to reduce the risks that your institution might face by funding long-term loans such as mortgages to borrowers (often at fixed interest rates) with short-term deposits from savers?
Pool mortgages into mortgage-backed securities and sell them. Some strategies include pooling mortgages into mortgage-backed securities and selling them or using derivative instruments to transfer the risk associated with interest rate increases. This could be done, for example, by purchasing a derivatives instrument that paid off when interest rates rose.
Compute the present value of a $1,000 investment made 4 months, 7 years, and 15 years from now at 10 percent interest.
Present value of investment made in 4 months at 10 percent = 1,000/(1.10)^0.33 = $968.73 Present value of investment made in 7 years at 10 percent = 1,000/(1.10)^7 = $513.16 Present value of investment made in 15 years at 10 percent = 1,000/(1.10)^15 = $239.39 Remember, you are calculating the present value of an investment to be made in the future. Notice that the exponent for the 4-months calculation is 0.33, representing one-third of one year into the future.
A financial institution offers you a one-year certificate of deposit with an interest rate of 5 percent. You expect the inflation rate to be 5 percent. What is the real return on your deposit?
The real return on your investment is 0 percent. The real interest rate equals the nominal rate less the expected rate of inflation; therefore 5% - 5% = 0%
