Money & Banking Mid-Term Prep
Deficit Units
"Borrowers" participants who spend more money than they receive, such as borrowers
Firms such as Moody's and Standard & Poor's study corporations that issue bonds. Then then publish "ratings" for the bonds - i.e., valuations of the likelihood of default. Define "default." Suppose that all ratings companies were shut down. What impact would this have on the bond market? What effects would this have on banks?
"Default" refers to the failure to make contracted payments; in this case, it refers to failure to make promised interest and principal payments. It differs from insolvency (which refers to having negative net worth) or bankruptcy (which refers to going to court to strike a deal with creditors so that they get some fraction of the promised payments). If they are accurate, published bond ratings help reduce the problem of asymmetric information in financial markets where surplus units (Ball's "savers") and deficit units (his "investors") have a direct relationship through markets (rather than an via financial intermediaries). Reducing the problem of asymmetric information between surplus and deficit units leads to more effective channeling of funds to profitable uses by reducing the role of adverse selection (AS). If the rating companies went out of business, cutting asymmetric information problems would be more costly for surplus units and reduce the volume of funds they put into financial markets. They would insist on getting higher returns to pay for the higher risk they'd be taking in those markets. Some safe bond issuers (deficit units) would leave this market because the interest rate has risen, justifying the surplus units' fear of bond-buying and the high interest rates; this is AS. Banks would benefit because surplus units would put funds into them instead (since banks will continue to screen potential borrowers for riskiness, providing much of the same service that bond-rating companies provide). Financial intermediaries are an alternative way to overcome asymmetric information (and can replace bond ratings).
Surplus Units
"savers" participants who receive more money than they spend, such as investors.
Future Value (FV) function
$1 today = $(1+i)^n
Inflation Rate Formula
(Price index in year 2 - price index in year 1)/(Price index in year 1) x 100
indirect finance
A flow of funds from savers to borrowers through financial intermediaries such as banks. Intermediaries raise funds from savers to lend to firms (and other borrowers).
Suppose you win the lottery. You have a choice between (a) receiving $100,000 a year for 19 years (after an immediate payment of $100,000) or (b) an immediate payment of $1,300,000. Which choice should you take if the interest rate is 3%? If it is 6%?
ANSWER: For both interest rates you need to figure out the present value of the 20 annual payments of $100,000. Assuming that each future annual payment is received at the end of the year (so that the seconc payment is received after one year, etc.), the equation for the discounted present value of the 20 annual payments reads: PV = the sum of all Xt/(1 + i)t for all points in time 0 to 19 = $100,000 + $100,000/(1 + i) + $100,000/(1 + i)2 + $100,000/(1 + i)3 + ... + $100,000/(1 + i)19 For the 3% interest rate (i = 0.03), the present value is: PV = $1,532,379.91. For the 6% interest rate (i = 0.06), the present value is: PV = $1,215,811.65. Note: the present value of fixed future cash flows always falls as the discounting interest rate rises. With a discounting interest rate of 3%, you should take the 20 annual payments of $100,000 because its PV exceeds $1,300,000. With a discounting interest rate of 6%, you are better off to take an immediate payment of $1,300,000, since that exceeds $1,215,811.65 (the PV of the stream of income). The table below shows how future payments are discounted more and more as they're received more and more in the future. It also shows how the add up to the present value.
Suppose the yield to maturity (interest rate) on a 1-year bond is 6%. Everyone expects inflation over the year to be 3%, but it turns out to be 5%. What is the nominal interest rate on the bond, the ex-ante real rate, and the ex-post real rate?
ANSWER: In this case, i = 6%, representing the nominal interest rate. The real interest rate is (approximately) calculated by deducting the inflation rate. Where πexpected is the inflation rate expected to prevail over the year, the ex-ante (before the fact, expected) real rate is approximately equal to: Expected or prospective real interest rate = rex ante ≈ i − πexpected = 6% − 3% = 3% Where πactual is the actual inflation rate that prevails over the year, the ex post or realized real interest rate (the real rate actually earned, once the year is done) is Actual, after-the-fact, or realized real interest rate = rex post ≈ i − πactual = 6% − 5% = 1%
For what range of interest rates does the price exceed the face value? Can you explain the answer?
ANSWER: Note that the $5 coupon payments on a bond with face value of $100 translate into a 5% interest rate when the bond is priced at its face value. Thus, for any interest rate above 5%, the present value of future payments will fall below 100. This happens when the coupon rate (C/F) = i. Note: if i equals 5%, then PB = $5/(1 + 0.05) + $5/(1 + 0.05)2 + $105/(1 + 0.05)3 = $100 = the face value (and i = the coupon rate).
Suppose that people expect a company's earnings to grow in the future at the same rate they have grown in the past. Does this behavior satisfy the assumption of rational expectations?
ANSWER: Rational expectations rely on the best possible forecast at the time that the expectations are formed given all of the available information. Expectations of a constant earnings rate are only rational if the company's circumstances and the economic situation do not change. Any major changes, for example, the onset of a recession or release of a new product — should lead to revisions of expected earnings growth when people form rational expectations (the best possible forecast). Mere extrapolation from the past into the future is not "rational" unless all available information indicates that the future is going to be the same as the past (or a lack of information means that extrapolation is the best you can do). Note that J.M. Keynes would say that because of the role of (fundamental) uncertainty, "what other people think is going to happen" (the conventional wisdom) is one thing that people use to calculate their best possible forecasts. That, of course, means that expectations may be far from what actually happens, while bubbles and crashes may occur.
A bond has a maturity of 3 years, annual coupon payments (C) of $5, and a face value (F) of $100. In general, PB = Bond price = C/(1 + i) + C/(1 + i)2 + (F + C)/(1 + i)3 a. If i = 4%, is the price of the bond higher or lower than the face value? What if the interest rate is 6%?
ANSWER: where PB is the price of the bond, PB equals the present value of the future payments. PB = $5/(1 + 0.04) + $5/(1 + 0.04)2 + $105/(1 + 0.04)3 = $4.81 + $4.62 + $93.34 = 102. 78 So, with an interest rate of 4%, the bond price is higher than the face value. PB = $5/(1 + 0.06) + $5/(1 + 0.06)2 + $105/(1 + 0.06)3 = $4.72 + $4.45 + $88.16 = 97.33 So, with an interest rate of 6%, the bond price is lower than the face value.
Explain how each of these events affects the amount of M2 that people [want to] hold. ATMs are invented. Credit cards are invented. Debit cards are invented Stored-value cards are invented Interest rates on bonds rise.
ATMs are invented. The ATM now gives you 24-hour access to your checking account balances, whereas before you had to go to a live person in a bank branch during regular business hours to make a withdrawal. Their introduction probably reduced the amount of cash you carry in your wallet or purse - since there is no need for large cash balances if you can always get to an ATM machine to get more cash. However, since both cash and checking deposits are part of M1, the total amount of M1 should not be affected when ATMs give you access to your checking account. If the ATM also gives you access to your savings account (as most of them do now), you may start to keep more in the savings account (to earn a bit more interest) because you could make regular ATM withdrawals from your savings deposits if necessary. This will reduce the amount of M1 that people want to hold because lower balances are held in checking deposits and higher balances are held in savings deposits. But note that M2 will not be affected by this decision, since it includes M1: the "non-M1" part of M2 will grow in step with the growth of M1.) b. Credit cards are invented. Using a credit card to make a purchase means that you borrow until you pay off the credit card bill. You have to use checking deposits to pay your credit card company to pay your bill to them. Instead of accessing your checking account each time you make a purchase, you know that you need your checking deposit only one time each month when you pay your credit card bill. If you keep most of your money in a savings account until you have to pay your credit card bill, only transferring the necessary funds into checking deposits when necessary, your average monthly balance in checking deposits will be lower compared to a situation where you do not have a credit card. (This reduces the amount of M1 you want to hold. However, this event has no effect on the amount of M2 that people want to hold.) c. Debit cards are invented. The use of debit cards for payment means that your checking deposit is reduced each time you make a purchase, just as when you pay by check. Contrary to using a credit card, however, you are not able to put off reducing your checking account deposits to make monthly payments. Thus, the introduction of debit cards should not change the desire to hold M1. d. Stored-value cards are invented. A stored-value card (like a OneCard) can be thought of as a prepaid debit card, holding a certain amount of money that you can use up over time. In that sense, the stored-value card becomes an alternative to holding checking deposits. Like checking deposits, the stored-value card gives you access to liquid assets that are available as a medium of exchange. However, because stored-value card balances are not counted as part of M1 (or M2), the amount of M1 people want to hold is reduced by their introduction. (Economic theory suggests that the balances on stored-value cards might be counted as part of M1 - but they aren't.) e. Interest rates on bonds rise. If interest rates on bonds rise, it becomes more costly to hold both cash and checking deposits, neither of which pay significant amounts of interest. With a higher interest rate, people have an incentive to manage their liquid, non-interest-bearing assets (or low-interest-bearing assets with unchanging interest rates) more closely so that more assets can be held as bonds. Thus, a higher interest rate should reduce average cash and checking deposit balances and thus reduce the amount of M1 that people want to hold.
Financial (Paper) Claims
Bonds, Treasury bills, promises to pay back plus gained interest.
M2 money supply
Includes all of M1 money supply plus most savings accounts, money market accounts, and certificates of deposit.
Suppose that you were required to put all of your retirement savings in the securities of a single company. What company would you choose - and why? Would you choose the company you work for?
It's best to put your money in securities which are very diversified because its earnings will not be hurt if only one or a few of its lines of business suffer from low demand or similar problems. It's really a bad idea to put your money into securities issued by your employer, since if the company gets into trouble, you could lose both your pension and your job. (This is what happened with Enron at the end of 2001: that company pushed employees hard to get them to buy its stock.)
National credit bureaus collect information about individuals' credit histories. They are likely to know whether you have ever defaulted on a loan. Suppose that a new privacy law makes it illegal for credit bureaus too collect this information? What impact would this have on the banking sector?
Just as ratings companies help to reduce asymmetric information in financial markets, credit bureaus that provide individual credit scores help to reduce asymmetric information between banks (lenders) and borrowers, assuming that the ratings are accurate. (Credit ratings give banks more information about borrowers' credit worthiness, but not to borrowers, who already know that.) If banks were no longer able to collect information on credit scores, the problem of asymmetric information and thus AS would worsen. Banks and other intermediaries would lend less and use more resources screening borrowers. These make loans more expensive, reducing the amount of funds available at any given interest rate. Some profitable projects may not be funded at all (even though borrowers are willing to pay the interest rate and live up to other loan conditions) because banks would have a harder time distinguishing good risks from bad risks. (Credit rationing.)
Benefits of finance
Matches surplus with deficit units, provides liquidity, allows risk sharing.
Suppose that the "Cash 4 Less" Company raises funds by issuing commercial paper. It uses the funds to make loans to individuals. This firm is a finance company. Is a finance company a bank? (Here and in all of this class, use the economist's definition.)
No, a finance company is not a type of bank. Banks are defined as financial institutions that both take deposits and make loans. (Deposits are a bit like loans to banks, but the funds can be withdrawn (or "called") very quickly and often at unpredictable times.) Finance companies raise funds not from deposits but instead by issuing commercial paper (i.e., short-term bonds which mature quickly and have to paid off on a regular schedule). Like banks, finance companies make loans. But because their source of funds is different, they are not banks. Both banks and finance companies engage in maturity transformation: they receive short-term funds by selling short-term bonds - or, in the case of a bank, by taking deposits- and then lend the funds out for longer-term loans. Thus, economists sometimes refer to finance companies as one type of "shadow bank." But they aren't really banks as economists define them. Those who buy the bonds that finance companies sell cannot cash them instantly (and without brokerage costs) so these funds are less liquid (to their owners) than bank deposits. Note that these bonds (unlike deposits) are not insured while finance companies are subject to significantly fewer government regulations than banks are.
For a citizen of the United States, how liquid is each of the following assets? Explain. Bonds issued by the U.S. government. Bonds issued by corporations. Postimpressionist1 paintings. British pounds.
Note: selling any of these assets involves a brokerage fee (a transactions cost), no matter how well the market is organized. This fee makes them less liquid than cash or checking account balances. a. Bonds issued by the U.S. government. You can find daily information on government bonds on many web-sites and in the financial pages of all newspapers. U.S. government bonds are traded in large volumes on a daily basis (in well-organized markets). This makes these bonds very liquid [easy to convert into money and thus into goods and services] but not as liquid as money itself. It is easy to convert those types of bonds into US$ cash or checkable deposits, which is the most liquid assets available. Note: to confuse everyone, the market for T-bills and similar short-term assets are often called "money markets." But that uses the bankers' definition of "money" as opposed to the economist's definition. b. Bonds issued by corporations. Bonds issued by corporations can also be traded in a daily market, but the quality of those types of bonds varies depending on which corporation has issued them, and the volume traded is not as large (for bonds issued by a single corporation) as for government bonds. The weaker market organization for corporate bonds makes them less liquid than U.S. government bonds. c. Postimpressionist1 paintings. There is a market for Postimpressionist paintings, but this market is harder to access and understand than the well-organized bond markets. Also, it's usually people with a lot of wealth (a small minority of the population) which can afford to get into this market. So, only a small number of buyers are available at most times and it may take some time to sell such a painting. Thus, it is harder to convert the painting into cash than any kind of bond. Because they are idiosyncratic, paintings are a less liquid form of holding an asset than bonds. They are very illiquid. d. British pounds. Like the U.S. dollar, the British pound sterling is a major international currency, easily exchanged for other major currencies. Given the current political situation and with access to a major financial institution, the British pound can easily be converted into U.S. dollar cash or checkable deposits as a U.S. government bond. But they are less liquid than US dollars, since you have to pay a fee to turn them into US$. Moving down from a to b to c, we see decreasing liquidity (increased illiquidity). British pounds are approximately as liquid as T-Bills.
Costs of finance
Possibility of fraud, restriction (non-price rationing) of loans, speculative bubbles and crashes, extremely complicated financial agreements
Define the difference between the average interest rate and the average inflation rate.
The interest rate is the reward a surplus unit (e.g., a bond-buyer or depositor) gets for giving a deficit unit credit. (This may occur indirectly, via banks.) On the other hand, the inflation rate refers to the average percentage rate of increase of a measure of the average price of real goods and services, i.e., the percentage decrease in the ability of money to purchase goods and services.
Suppose Otis, an owner of a corporation, needs $1 million to finance a new (tangible) investment project. If his total net worth is $1.2 million, would it be better to use his own funds for the investment or to issue stock (equity) in the corporation. How does your answer change if his net worth is $1 billion?
The principle of diversification suggests that Otis is more likely to finance the new investment by issuing stock when his wealth is lower. Having only the $1.2 million and using only his own funds, he would have to put "all of his eggs in one basket." If he sells new stock, it's like bringing on new partners to share the risk. On the other hand, if Otis has cool $1 billion, he can finance a number of projects with his own funds, getting the benefits of diversification without issuing any stock. Put another way, if he loses the funds he invests in this project, the impact on his net worth is small.
The U.S. population is approximately 300 million. Calculate the average amount of U.S. currency (cash) per citizen. Do most Americans hold that much cash? If not, where is it?
The total amount of currency in March 2008 was $882,000 million (see table 2-1 of the book). For a U.S. population of 300 million, this is an average currency holding of $882,000/3000 = $2,940 per person. Clearly most of us usually do not carry that much cash regularly. A lot of currency is held outside of the United States where the U.S. dollar is judged to be a better store of value than the local currency. Much of the large currency holdings by a small number of people within the United States can also be attributed to illegal activities: $100 bills and larger, for example, are used in a lot of illegal transactions.
When a bank makes a loan, it sometimes requires that borrowers maintain a checking account at the bank until the loan is paid off. What is the purpose of this requirement?
This requirement helps to reduce moral hazard (MH) problems. In this case, MH is the risk that a bank loan will be used in a way that makes default on the loan more likely, which of course harms the bank. One way that this problem is addressed is that checking balances serve as collateral for the bank. Requiring that a borrower maintain a checking account with the bank also provides a means of monitoring some of the borrower's ongoing financial transactions: changes in the checking account balances serve as an early warning system to the bank, helping the bank to monitor the borrower's financial decisions after the loan has been given.
"I just bought my first house. Economists are predicting low inflation in the future, but I sure hope they're wrong!" Why might it make sense for someone to say this?
This statement makes sense if you bought your house by borrowing funds at a fixed nominal interest rate (as with a classic 25 or 30-year fixed-rate mortgage). If you have to pay a fixed nominal interest rate, then any increase in the inflation rate will reduce the (ex post, after the fact) real rate you pay to your bank. In other words, you get to repay your loan with money that has a lower purchasing power. With higher inflation you give up less real purchasing power (measured in the amount of goods, say hamburgers, you can buy) with each loan payment. Further, inflation is likely to increase the market price of your house, so that the real value or purchasing power price of your house doesn't fall even though that of your debts falls. Of course, the prediction could be wrong in a different way: if it turns out that the inflation rate < 0 (deflation), then the money you'd pay in the future would have more purchasing power than today's money, so you'd end up paying a higher real interest rate ex post.
Suppose that you are planning ahead for retirement and you desire a steady income during your "golden years." Name one advantage that social security (OASI) has over 401k or 403b accounts. Name one disadvantage that OASI has over these accounts. Name one disadvantage that OASI has over these accounts.
Unlike 403b or 401k accounts (which are based on fixed contributions to a fund), OASI (Old Age and Survivor's Insurance) pays a fixed amount of benefits every year. Unlike the returns on 403b or 401k accounts, OASI benefits are protected from most inflation. Both types could become insolvent: for the first, the stock market and dividends could fall drastically; for the second, or Congress and the President could decide not to fund OASI benefits. (Contrary to popular belief, the financial fate of OASI depends on political decisions.) The main disadvantage is that OASI often does not provide enough income during retirement years to allow people to attain the standard of living that they're used to. It must be complemented by income from 401k or 403b accounts or individual savings. Another disadvantage of OASI is that it's inflexible: neither your contributions to the system nor the distribution can be changed. Only your retirement age can change. (The OASI benefit/contribution formula replaces much bureaucracy, making social security one of the most efficient programs the government has to offer.)
Moral Hazard
When the act of insuring an event increases the likelihood that the event will happen
direct finance
a flow of funds from savers to firms through financial markets, such as the New York Stock Exchange
Consider two bonds. Each has a face value of $100 and matures in 10 years. One (bond A) has no coupon payments (so it's a zero coupon bond), and the other (bond B) pays $10 per year. Calculate the price of each if the interest rate is 3% and if the discounting interest rate is 6%. When the interest rate rises from 3% to 6%, which bond price falls by a larger percentage? Explain why.
a. Calculate the price of each if the interest rate is 3% and if the discounting interest rate is 6%. ANSWER: bond A: if i = 3% PB = $100/(1 + 0.03)10 = 74.63. If i = 6% PB = $100/(1 + 0.06)10 = 55.87. Bond B: if i = 3% PB = $10/(1 + 0.03) + $10/(1 + 0.03)2 + ... + $110/(1 + 0.03)10 = 159.71 (see above). If i = 6% = $10/(1 + 0.06) + $10/(1 + 0.06)2 + ... + $110/(1 + 0.06)10 = 129.44 (see above). b. When the interest rate rises from 3% to 6%, which bond price falls by a larger percentage? Explain why. ANSWER: Percentage change (bond A) = (55.87 − 74.63)/74.63 = −0.25 = −25% Percentage change (bond B) = (129.43 − 159.70)/159.70 = −0.19 = −19% The drop in the no-coupon bond A is larger in percentage terms. On average, the coupon bond does not get discounted as heavily as the no-coupon bond when interest rates increase, because most of the payments are made earlier than the 10 year mark and are therefore discounted less.
Consider two stocks (equity shares): for each, the expected dividend next year (D1) is $100 and the expected growth rate of dividends (g) is 3%. The risk premium is 3% for one stock (the blue-chip stock or BC) and 8% for the other (the big risk-taker, RT). The economy's safe interest rate is 5%. What does the difference in risk premia tell us about the dividends of each stock? Use the Gordon growth model to compute the price of each stock. Why is one price higher than the other? Suppose that g rises to 0.05 for both stocks. Compute the new price for each. Which stock's price increases by a larger percentage? Explain.
a. What does the difference in risk premia tell us about the dividends of each stock? ANSWER: the BC is likely to have a more stable and predictable expected flow of dividends than the RT. They may be the same on average, but we have to pay attention to the variation. b. Use the Gordon growth model to compute the price of each stock. Why is one price higher than the other? ANSWER: first, BC's discounting interest rate (i) is the safe rate plus its risk premium, i.e., 0.05 + 0.03 = 0.08, while RT's discounting interest rates is the safe rate plus its risk premium, i.e., 0.05 + 0.08 = 0.13. Then, the Gordon growth model tells us that the price of the equity should be PE = D1/(i - g), so that for the BC, PE = $100/(0.08 - 0.03) = $100/0.05 = 2,000. for the RT, PE = $100/(0.13 - 0.03) = $100/0.1 = 1,000. The BC price is higher because its lower risk premium means that its expected future dividends are discounted less. Put another way, you wouldn't buy the riskier stock unless its price were lower. c. Suppose that g rises to 0.05 for both stocks. Compute the new price for each. Which stock's price increases by a larger percentage? Explain. ANSWER: it's just a matter of restating the formulas with a different value of g: for the BC, PE = $100/(0.08 - 0.05) = $100/0.03 = 3,333.33 an increase of (3333.33-2000)/2000 = 66.7%. for the RT, PE = $100/(0.13 - 0.05) = $100/0.08 = 1,250 an increase of (1250-1000)/1000 = 25%. The BC's price rose more (as a percentage) because the smaller risk premium meant less discounting of future earnings.
Money
class of assets serves as an economy's medium of exchange.
M1 money supply
includes all currency plus checking accounts and traveler's checks
potential output, or potential GDP
the level of aggregate output that can be sustained in the long run without inflation
Adverse Selection
the problem of incomplete information - of choosing alternatives without fully knowing the details of available options
Real GDP
the production of goods and services valued at constant prices (Y)
Nominal GDP
the production of goods and services valued at current year prices (Y*P)
