moneyandbanking 01-09 Part2

8/14/2019 moneyandbanking 01-09 Part2

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FINANCIAL INTERMEDIARIES

Financial System: Provide efficient allocation of saving to real investment or consumption in any moderneconomy.It is through these markets that funds are offered by the lenders/savers who have excess fundsand purchased by the borrowers/spenders who need those funds.

Role of Financial System Facilitates trade in goods and services via an efficient payment system Provides for the efficient flow of funds from saving to investment via financial markets and

financial institutions Provides contracts for managing risk such as insurance, futures, and options

KEY TERMS

SURPLUS SPENDING UNIT (SSU)

Has more cash income flow than expenditure on consumption and real investments in a period oftime. The surplus then is allocated to the financial sector

Other terms for surplus unit are saver, lender, buyer of financial assets, financial investor,supplier of loanable funds, buyer of securities.

The surplus unit may buy financial assets, hold more money, pay off financial liabilities issuedearlier when in a deficit situation.

Examples: The household and foreign sectors are usually a surplus sector.

DEFICIT SPENDING UNIT (DSU)

Has more expenditures on consumption and real goods (investment) in the real sector thanincome during a period of time.

The deficit unit must participate (borrow) in the financial sector to balance cash inflows withoutflows.

Other terms for deficit spending unit are borrower, demander of loanable funds, seller of

securities. The deficit spending unit may issue financial liabilities, reduce money balances, sell financialassets acquired previously when in a surplus situation.

Examples, government and businesses are deficit spending units.

FINANCIAL CLAIMS

Contracts related to the transfer of funds from surplus to deficit budget units. Financial claims are also called financial assets and liabilities, securities, loans, financial

investments. For every financial asset, there is an offsetting financial liability.

Total receivables equal total payables in the financial system. Loans outstanding match borrowers' liabilities.

Financial markets offer opportunity for:

Financing for DSUs (primary) Financial investing for SSUs (primary and secondary) Providing liquidity via trading financial claims in secondary markets

Direct Financing DSUs and SSUs negotiate and exchange money for financial claims. DSUs issue direct financial claims; SSUs participate in direct lending. The sale of securities by an industrial firm directly to an investor (SSU or financial institution) is a


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private placement. Brokers bring DSUs and SSUs together; dealers buy the securities from DSUs and resell to the

SSUs. Investment bankers act as dealers in direct financial markets, purchasing securities from DSUs

and selling to original SSUs.

Indirect Financial Investment (INTERMEDIARIES) / Indirect Financing A financial "intermediary" writes a separate contract with the SSU (bank depositor) and DSU

(auto loan), providing each some economic value. Financial intermediaries hold direct claims on DSUs as financial assets and issue indirect

financial claims to SSUs as liabilities.

Benefits of Financial Intermediation Economies of scale from specialization. Transaction and search costs are lowered for SSUs and DSUs. Financial intermediaries may be able to gather DSU information more effectively and discreetly.

Intermediation Services

Denomination Divisibility-- Issue varying sized contracts of assets and liabilities. Currency Transformation -- buying and selling financial claims denominated in various currencies.

Maturity Flexibility-- Offer contracts with varying maturities to suit both DSUs and SSUs.

Credit Risk Diversification -- Assume credit risks of DSUs and keep the risks manageable byspreading the risk over many varied types of DSUs (loan portfolio).

Liquidity-- Provide a place to store liquidity for SSUs (deposits); a place to find (borrow) liquidityfor DSUs.

Types of Financial Intermediaries

Deposit-Type Institutions -- Offer liquid, government- insured claims to SSUs, such as demand

deposits, savings deposits, time deposits, and share accounts. Commercial Banks -- Make a variety of consumer and commercial loans (direct claim) toDSUs.

Thrift Institutions -- Make mortgage loans (direct claim) to DSUs.

Credit Unions -- Receive share-Draft account deposits and make consumer loans. Membership requires a common bond Church, business employee, or labor union.

Contractual Savings Institutions -- Issue long-term claims to SSUs in the form of insurancepolicies and pension fund obligations.

Life Insurance Companies -- Issue life insurance policies and purchase long-term, high-yield direct financial securities.

Casualty Insurance Companies -- Purchase long-term, liquid, direct financial securitiesfrom paid-in-advance premiums from insurance purchasers.

Pension Funds -- issue claims to SSUs (pension reserves) and invest financially in directfinancial securities (stocks and bonds).

Investment Funds -- Issue shares to investors and use these funds to purchase directfinancial claims.

Mutual Funds -- Offer indirect mutual fund shares to SSUs and purchase direct financial assets(stocks and bonds).


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Money Market Mutual Funds -- Offer (indirect) shares and purchase direct (commercialpaper) and indirect (bank CDs) money market financial assets. Most MMMFs offer check-writing privileges.

Other Types of Financial Intermediaries

Finance Companies -- Borrow (issue liabilities) directly from banks and directly fromSSUs (commercial paper) and purchase consumer and business loans.

Federal Agencies -- Sell direct claims in capital markets and lend to socially deservingDSUs (farmers, homebuyers).

Financial and Economic Development

Financial development is inextricably linked to economic growth There arent any rich countries that have very low levels of financial development.


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FINANCIAL INSTRUMENTS

A financial instrument is the written legal obligation of one party to transfer something of value usuallymoney to another party at some future date, under certain conditions, such as stocks, loans, orinsurance.

A financial instrument is a monetary claim that one party has on another. It is afinancial asset for the person who buys or holds it, and it is a financial liability forthe company or institution that issues it.---- Financial asset: any financial claim or piece of property that can be owned.Financial assets usually have no intrinsic value of their own, but they entitle thebearer to a stream of income or a share of assets from the issuer of the asset.---- Financial liability: the obligation that the issuer of an asset has to theowner/buyer of that asset. The purpose of issuing a financial instrument is to raisemoney so that you can spend it.

A SECURITY is a tradeable financial instrument, like a bond or a share ofstock.

Examples of how a financial instrument is simultaneously someone's asset andsomeone else's liability:-- Ex.: a $1,000 government bond that you own. You will receive $1,000, includinginterest, but the government (and taxpayers) must pay $1,000, including interest.-- Ex.: a share of Microsoft stock that you own. The stock gives you a share ofMicrosoft's assets and the right to receive a share of dividends (profits), if Microsoftis paying any. To Microsoft's other owners, the stock means a slightly diluted shareof the company's assets for them, and an obligation to include you in their dividend


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BONDS ("long-term," defined as maturing in >= 1 year)

-- A bond is a formal debt/IOU with a maturity length of one year or more.

--- CORPORATE BONDS;--- TREASURY BONDS, issued by the federal government to finance the national debt;

--- MUNICIPAL BONDS, issued by state and local governments to finance large, long-term

capital projects (e.g., hospitals, highways, schools).

(Bonds are also counted in another category of financial instruments, called capital-market

instruments, which also is for long-term instruments but which also includes non-interest-bearing

assets like stocks, as well as debts that are not publicly traded, like mortgage loans, consumer

loans, and business loans.)

STOCKS (same as EQUITIES) are financial instruments that make the holder a co-owner of

the company that issued them. They entitle the holder to a claim on the assets (and implicitly the

future profits) of the company. Stocks do not involve the repayment of a debt or the payment of

interest. (Some stocks pay dividends, which are shares of the company's profits, but peopletypically hold stocks not for the dividends but for the hope of reselling them later at a higher

price.)

DERIVATIVE INSTRUMENTS (which derive their value from the behavior of an

underlying financial instrument) are a different animal altogether, and their time horizons can

be very short or quite long.

-- Perhaps the oldest type of derivatives arefutures contracts, whereby one party agrees to sellanother party a certain amount of a good at a definite price at a future date. For commodities

whose prices often fluctuate (e.g., crops, oil), these contracts are important ways of reducingrisk. More recently, these kinds of contracts have been used with financial instruments. Someexamples from the world of stocks:

--Futures contracts specify that a sale of a set number of shares of a particular stock will be sold

from one party to another at a particular date. A person might purchase such a contract so as toavoid risks due to price fluctuations, ora person might purchase the contract as a way of making

a bet that the stock's price will rise (or fall) in the meantime.

-- Options contracts (call options to buy a set number of shares at a set price at a set date,put

options to sell...) are also common, and less risky to purchase, because you have the option of

notmaking that future trade if the prices have not moved in your favor.

Q : Give an example of a financial asset that is both a store of value and ameans of transfering risk (in particular, one of the risks listed above).

A: Whole life insurance, which is a life insurance policy that makes a big payout toyour beneficiary if you die early (insures against the risk of early death) and makesa smaller but still sizeable "maturity" payment to you if you live to a ripe old age(store of value -- your premiums accrue over time into a larger sum of money).


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FINANCIAL MARKETS:

Financial Markets are the places where financial instruments are bought and sold

Financial markets are like the "central nervous system" of the economy, says Cecchetti's textbook. Stock,bond, and other financial markets respond to a host of factors that others in the economy might easilyoverlook. And their reactions are easily readable in the form of price movements -- e.g., of individualstocks and the stock-market averages, interest rates on Treasury and corporate bonds, mortgage rates.

Financial markets are also vitally important to an economy's development, because of the role they playin allocating resources to their most profitable and productive uses. In a well-developed financial market,

financial instruments become streamlined and standardized in their characteristics, making it a lot easierfor potential buyers to know what they're getting. When this happens, more people will want to purchasefinancial assets, and firms can finance their investment more easily. This is good for household portfoliosand for the economy's long-term growth.

Financial instruments are bought and sold in both PRIMARY and SECONDARY MARKETS.

-- PRIMARY FINANCIAL MARKET: where newly issuedfinancial assets are bought and sold (e.g.,companies sell new stock or bonds to finance investment in new physical capital, i.e., plant andequipment)

-- SECONDARY FINANCIAL MARKET: wherepreviously issuedfinancial assets are bought andsold. The stock market is by and large a secondary financial market, with new issues accounting for lessthan 1% of total shares outstanding. (Although not directly connected with new investment, having asecondary financial market surely raises the level of investment, and hence raises the stock of physicalcapital, because it makes stocks and bonds a lot more liquid, since you can resell them any time youwant.)

Markets may be differentiated by when a security is sold.

The initial financing of the DSU is the primary market; subsequent resale of the financialclaims of the DSU are traded in the secondary markets.

Primary markets are important from a real saving/investment perspective; Secondary markets provide liquidity and portfolio rebalancing capacity for the investor.

Markets may be differentiated by how or where they are traded. Organized exchanges provide a physical meeting place and communication facilities.

Securities may trade off the exchange in the over-the-counter (OTC) market. OTC marketshave no central location.

Markets may be differentiated by maturity.

High quality short-term (less than one-year) debt securities are issued and traded in themoney market.

Long-term (greater than one-year) securities are issued and traded in the capital market.


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Spot and futures markets--variation in timing of delivery and payment.

Items traded in the market for immediate delivery and payment are traded in the spot market. When delivery at a specific price(payment) is not "spot," a "futures or forward market

transaction has occurred. Futures contracts are traded on organized exchanges. Forward contracts are traded over the counter.

Option markets trade contracts specifying price and conditional delivery of a quantity of assetfor a specific period of time.

A call option is an option to buy; a put is an option to sell.

Options are traded on major security and commodity exchanges as well as in various over-the-counter markets.

Foreign exchange markets.

Foreign exchange, the value of one currency relative to another, is traded in the foreignexchange market.

Foreign exchange is traded in the spot, forward, futures, and option markets.

CAPITAL MARKETS

Market for long-term claims

Government Bonds

Corporate Bonds

Common Stock

Mortgages

Market finances real investment

Secondary market important for investors


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OVERVIEW OF MONEY MARKET

Short-term debt market -- most under 120 days

A few high quality borrowers

Many diverse investors

Informal market centered in New York City

Standardized securities -- one security is a close substitute for another

Good marketability -- secondary market Large, wholesale open-market transactions

Many brokers and dealers are competitively involved in the money market.

Payment in Federal Funds -- immediately available funds.

Physical possession of securities seldom made -- centralized safekeeping.

ECONOMIC ROLE OF MONEY MARKET

The money market is a market for l iquidity

Liquidity is stored in MM by investing in MM securities.

Liquidity is bought in MM by issuing securities (borrowing).

There are few high-quality borrowers and many diverse MM investors. Some issuers, such asGE, are in the money market on a continuous basis.

High quality borrowers; low default risk

Short-term maturity

High marketability providing excellent liquidity

Low interest rate risk

FINANCIAL MARKET EFFICIENCY

Allocational Efficiency

Funds will be allocated to highest valued use

Informational Efficiency

Securities prices are the best indicators of relative value in an informationally efficientmarket

market prices reflect all relevant information

Operational Efficiency The costs of conducting transactions are as low as possible


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FINANCIAL INSTITUTIONS

FINANCIAL INSTITUTION -- a business whose primary activity is buying,selling, or holding financial assets.-- Financial institutions are sometimes called FINANCIAL INTERMEDIARIES(businesses that connect savers with borrowers), since they serve as middlemen, or

mediate, between individuals, firms, and financial markets.

---- FINANCIAL INTERMEDIATION or INDIRECT FINANCE is the process ofobtaining funds or investing funds through third-party institutions likebanks and mutual funds. As a source of funds for American businesses, indirectfinance is far more common than direct finance. For every dollar that firms raise byborrowing directly from households or selling stocks directly to households, theyraise about $20 through indirect finance -- bank loans, selling bonds and stocks tomutual funds, pension funds, insurance companies, etc. In future units we'llexamine the reasons why in detail. For now, the short answer is that lending yourmoney to a business firm is generally cheaper and safer with a financial institution

serving as middleman than if you do it on your own.

Types of financial institutions:

1. Depository institutions

(BANKS, CREDIT UNIONS, SAVINGS & LOAN ASSOCIATIONS)-- Their main liabilities (sources of funds) are deposits, and their main assetsare loans.

2. Insurance companies-- They collect premiums (regular payments) from policy-holders, and pay compensation to policy-holdersif certain events occur (e.g., fire, theft, sickness).-- They invest the premiums in securities and real estate, and these are their main assets.

3. Pension funds-- They collect contributions from current workers and make payments to retired workers.-- Like insurance companies, they invest the contributions in securities and real estate, and these are theirmain assets.

4. Securities firms (provide firms and individuals with access to financial markets)

-- This category covers a wide array of financial institutions:-- INVESTMENT BANKS: sell new securities for companies. Unlike regular banks, they don't holddeposits, or make loans. (They hold zero assets/liabilities.) Closely related are underwriters, which notonly sell the new securities but pledge to purchase some or all of any unsold shares.-- BROKERS: buy/sell old securities on behalf of individuals.-- MUTUAL-FUND COMPANIES: pool the money of small savers (individuals), who buy shares in thefund, and invest that money in stocks, bonds, and/or other assets. These are popular because they allowsmall savers relatively easy and cheap access and also enable them to reduce risk by holding adiversified portfolio.


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-- Hedge funds: pool the money of a small number of wealthy individuals and institutions and invest invarious financial instruments, notably derivatives.

5. Finance companies-- Like banks, they use people's savings to make loans to businesses and households, but instead ofholding deposits, they raise the cash to make these loans by selling bonds and commercial paper.-- They tend to specialize in certain types of loans, e.g., automobile (GMAC) or mortgage loans.

1. Government-sponsored enterprises (federal credit agencies)-- Some of these provide loans directly, such as to farmers and home buyers.-- Some, such as the Federal National Mortgage Association (FNMA, "Fannie Mae"), guarantee orbuy up private loans, notably mortgage and student loans.-- Some, such as the Social Security Administration, administer social insurance programs

ROLE OF FINANCIAL INSTITUTIONS

Reduce transactions cost by specializing in the issuance of standardized securities Reduce information costs of screening and monitoring borrowers. Issue short term liabilities and purchase long-term loans.

RISK OF FINANCIAL INSTITUTIONS

Credit or default riskis the risk that a direct DSU issuer will not pay as agreed, thus affectingthe rate of return on a loan or security.

Interest rate riskis the risk of fluctuations in a security's price or reinvestment income caused bychanges in market interest rates.

Liquidity riskis the risk that the financial institution will be unable to generate sufficient cashflow to meet required cash outflows.

Foreign exchange riskis the risk that foreign exchange rates will vary in the future affecting theprofit of the financial institution.

Political riskis the cost or variation in returns caused by actions of sovereign governments orregulators.


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THE VALUE OF MONEY

I. FUTURE VALUE

Q: I have $100 in my pocket right now. If I save it for the next five years, how much will I have in fiveyears?A: Need more information. Am I investing this money? At interest? If so, what interest rate will I begetting?-- Suppose I invest the money in a bank CD at 5% interest.

---- At the end of one year I'll have my original $100 (theprincipal) plus 5%, or $5, interest = $105---- At the end of two years I'll have that $105 plus 5% interest on it (.05 * $105 = $5.25) => total of$110.25------ (Note that the interest is larger in the second year than in the first, because I'm earning interest not

just on the $100 principal but also on my interest from the first year. This is called compounding ofinterest-- earning interest on your interest and in larger and larger amounts each year.)---- At the end of three years I'll have $110.25 + (.05 * $110.25) = $110.25 + $5.5125 = $115.7625.-- By now a pattern may be apparent:After 1 year the CD is worth $105, or $100 * 1.05. (In other words, the CD's value is now 105% of what itwas initially.)After 2 years the CD is worth $100 * 1.05 * 1.05. (Its value went up 105% the first year, and the secondyear, too.)After 3 years the CD is worth $100 * 1.05 * 1.05 * 1.05 (or $100 * 1.05^3).After 4 years the CD is worth $100 * 1.05 * 1.05 * 1.05 * 1.05 (or $100 * 1.05^4)After 5 years the CD is worth $100 * 1.05 * 1.05 * 1.05 * 1.05 * 1.05 (or $100 * 1.05^5)-- Note that 1.05 is (1 + the interest rate). The exponent is the same as the number of years, becausethat's how many times the interest accumulates.

--> A current sum of money, invested at an interest rate ofiovern years will have a FUTUREVALUE (FV) of

FV = (current sum of money) * (1 + i)^n


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Ex.: Suppose that you are 20 years old. Your generous grandparent gives you $10,000, to be investedand not touched for 50 years, until you are 70 and retired. How much will that investment be worth in 50years, if it's earning 10% per year?A: Apply the FV formula, with n = 50 and i = .10 (i.e., 10% in decimal form. Note that the phenomenonof compounding applies to more than just interest. As long as the yearly returns stay in the investmentand are not withdrawn or spent, compounding occurs. So you could invest the $10,000 in a stock mutualfund, for example.) Do the math:

FV = $10,000 * (1+.10)^50 = $10,000 * (1.10)^50 = $10,000 * 117.390853 = $1,173,908.53

Not bad -- you retire a millionaire.

Q: With compounded returns, small differences in annual returns become very large over time. Going backto the previous example, imagine that the 50-year, $10,000 investment is in a mutual fund. Mutual fundcompanies charge fees, which lower your returns a bit, but some charge higher fees than others. Comparetwo different stock mutual funds. The first has fees of 1.4% per year (the industry average), which give youan annual return of 8.6%. The second, with fees of 0.5%, has an annual return of 9.5%.--> Exactly how much more would you have with the second fund at the end of 50 years?

A: Apply the future value formula, plugging in .086 for i in the first case and .095 in the second case:

First fund: FV = $10,000*((1.086)^50) = $618,716Second fund: FV = $10,000*((1.095)^50) = $934,733--> The second fund will be worth $316,056 more (or 51% more) at the end of 50 years.

A relatively simple application of future value is the Rule of 72 (or 70), which tells you how quickly anasset will double in value. But first, let us see how Future Value leads us to two related concepts:Present-Day Value, and Internal Rate of Return.

II. PRESENT-DAY VALUE (PDV)

Present-day value, present value, and present discounted value all mean the same thing: what somefuture payment or set of future payments is worth to you today, i.e., right here, right now. The essence ofthis very important concept is that a dollar in the future is worth less than a dollar today, because if you

had that dollar today, you could invest it and earn interest on it and end up in the future have more thanjust a dollar. (This concept is sometimes called the time value of money.)

Breaking it down, word for word:PRESENT DISCOUNTED VALUE| | |

right now "discounting" for what it's worththe way that interestreduces the value offuture payments relativeto current payments

Or, in a nutshell: PRESENT-DAY VALUE = what it's worth now

The present-day value (PDV) of any future payment will depend on three things:*The size of the payment positively affects its PDV -- a million dollars tomorrow is still better than $100today.* The higher the current interest rate, the lower the PDV of any future payment. The higher theinterest rate, the greater the value of $1 today relative to $1 in the future. If the interest rate is very high,you would forgo a lot of interest if you said, "Sure, I'll give you $100 today, and when you give me $100four years from me now, that'll be just as good." (It would be if the interest rate were zero, there were noinflation, and you were very patient, but even if there's no inflation and you have infinite patience, as long


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as i> 0%, then the PDV of $1 in the future is less than $1.)* The longer you wait for the payment, the lower its PDV (the more it has to be "discounted"). As longas you have to wait at all for the payment, it's not worth as much as having the same amount of moneyright now. (The character named Wimpy in the Popeye cartoons who says "I'd gladly pay you Tuesdayfor a hamburger today" is a man who understands the concept of PDV.)

The basic present-value formula should look very familiar to you, because it's just the Future Value (FV)formula rearranged. Let FV be the amount of a future payment (i.e., its Future Value), and recall that iisthe market interest rate and n is the number of years between now and the date of the payment, and theformula is

PDV = FV/(1+i)n

Ex.: Back again to the generous-grandparent problem. Using the Rule of 70 we estimated that an initialinvestment of $7,800 today will, with a 10% compounded annual return, grow to be $1 million in 50 years.What's the exactamount that the initial investment would have to be?A: By definition, the PDV of a future payment is the amount you'd have to set aside today to be able tomake that payment. So we can apply the PDV formula, with FV = $1,000,000, i= .10, and n = 50:

PDV = $1,000,000/((1.10)^50) = $1,000,000 / 117.390853 = $8,518.55.

The PDV of a stream of several future payments, to be made at different times, is equal to the sum of theseparate PDV's of each of the payments. That is, to compute the PDV of several future payments, you'llneed to apply this formula for every single payment and then add all those PDV's up.-- Is there ever a shortcut? Yes, if the future payment amounts are all the same and are made at regularintervals. (Coming up in the chapter 6 notes.)

III. INTEREST RATES AND LONG-TERM RATES OF RETURN

The INTEREST RATE on a debt is calculated as the net annual payment on the debt, as apercentage of the total amount of the debt.-- Ex.: Simple loan: You borrow $1000, and must pay back $1100 a year from now.

==> Net interest payment = $1100 - $1000 = $100Interest rate = $100/$1000 = 1/10 = 10%

Usually calculating the interest rate is not quite that simple, as the length of the loan or the asset's lifetimeis not exactly one year. But it's simple enough, as we can rearrange the basic Future Value equation tocalculate the interest rate, as long as we know the values of Future Value (FV) and Present-Day Value(PDV).

-- The FV equation: FV = PDV * [(1+i)^n]

---- (English translation: A current sum of money, $PDV, earning interest at rate i, aftern years will beworth $FV.)

Rearranging that equation to solve fori, [refer to your class notes to see all the steps], we end up with

i = { (FV/PDV)^(1/n) -1 } (*100%)

-- (The "*100%" is there because interest rates are normally expressed in percentage form. For example,the numbers .08 and 8% are mathematically equivalent, but we would say the interest rate is 8%, not .08,when reporting it.)


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Note: The term 1+i, which appears in the FV and PDV formulas, is called the gross interest rate. Theidea here is that the 1 includes the repayment of principal. Interest compounds over time because theamount on which interest is paid becomes larger each year -- each year the amount gets multiplied by1+i.

IV. THE RULE OF 72:

An asset with a compounded annual return of X% will double in value in approximately 72/X years.

This rule is very handy because the number 72 is evenly divisible by a lot of numbers (1, 2, 3, 4, 6, 8, 9,12, 18). As long as you remember your times tables from grade school, you can produce decentestimates of the rate of doubling without having to use a calculator.

The Rule of 70 is a common alternative and actually gives a closer approximation than 72/X does forsmall values of X (1, 2, 3, 4, 5). But since simplicity is really the goal with these rules, I suggest you use70 for numbers that divide evenly into 70 (2, 5, 7, 10, 14) and 72 otherwise..

Note well that this rule is only an approximation, and it doesn't work for particularly large values of X(those larger than, say, 25). For values of X larger than, say, 25, the time to double will be more than72/X years. (For example, an asset earning 100% per year will double in value in exactly 1 year, not in72/100 years.) But, most financial assets have long-term annual returns well under 25% anyway.

Exs.:* Savings account, which pays 3% interest--> value of your account will double in ~72/3 = 24 years (or, a little more precisely, about 69/3 = 23years)* A CD that pays an annual return of 7% a year--> value of that CD will double in ~70/7 = 10 years* Stocks in the late 1990s; annual return was about 24% a year--> value of a stock portfolio doubled in ~72/24 = 3 years

Ex.: Back to the generous-grandparent problem. Now suppose your grandfather wants to set up aninvestment account for you earning 10% per year and having a value of $1 million fifty years from now,when you're 70. About how much does he need to put in the account now?A: We'll apply the Rule of 70, since 10 divides evenly into 70 --> that account will double in value every 7years (= 70/10). So over the next 50 years, your initial investment will double in value 7 times (since 7*7=49, very close to 50). Working backwards, we just need to divide $1,000,000 in half 7 times (with somerounding, since the point of the exercise is to keep the arithmetic fairly simple): 1) $500,000. 2)$250,000. 3) $125,000. 4) $62,000. 5) $31,000. 6) $15,500. 7) $7,800.-- So investing about $7,800 today makes you a millionaire 50 years later. (We'll solve for the exactamount when we move on to present discounted value.)

V. COMPOUND ANNUAL INTEREST RATES AND ANNUAL PERCENTAGE YIELDS

Compounded interest has been called the most powerful force in the world. That might be exaggerated,but the magic of compounded interest is something you should acquaint yourself with. The main way that"the rich get richer" is through compounded interest or compounded dividends. It's also a way that manymiddle-class people become rich.-- Real-life ex.: A former psychology professor at SUNY-Oswego put all his pension fund contributions(TIAA-CREF) into stocks, with all dividends reinvested (works much like compounded interest), andretired a millionaire.


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At many banks, where interest rates on CD's and other accounts are listed, there are often two rateslisted for each one: the regular, or nominal, interest rate (i) and the annual percentage yield (APY), whichthe textbook calls the compound annual interest rate. In a better, simpler world, these two rates wouldalways be the same, but because of the way interest is calculated, they often are not. The annualpercentage yield (APY) is the total value of the interest payments on a financial asset as apercentage of its original purchase price. The APY would be the exact same thing as the interest rateif the bank paid out the interest only at the end of the year; instead, in most cases interest iscompounded (paid out) at several times during the year, e.g. monthly. Some banks have continuouscompoundingof interest, whereby your account balance earns some tiny amount of interest every secondof every day. If a bank compounds interest m times per year, then, instead of paying out i% interest at theend of the year, it pays out (i/m)% interest m times per year.-- Ex.: If the interest rate on your credit-card balance is 24% and that interest is compounded everymonth, then, instead of being charged 24% interest on your unpaid balance at the end of the year, you'llbe charged 2% (= 24%/12) interest at the end of every month, and your total interest charges will bemuch higher.-- Ex.: If the interest rate on savings account is 5% and the bank compounds interest fourtimes per year,then the bank pays out 1.25% interest on those accounts at the end of every third month.-- The greater the frequency of interest payments or compounding, the larger the total interest paymentsover the year. For an account holder orcreditor(someone to whom money is owed), the more frequentthe compounding, the better, and continuous compounding is the best. For a debtor(someone who owes

money), the less frequent the compounding, the better, and continuous compounding is the worst.

For an asset with an interest rate of i and payments that are compounded m times per year, the annualpercentage yield (APY), oreffective interest rate orcompounded interest rate, is calculated as follows:

APY= [ (1 + i/m)m - 1 ] (* 100%)

Ex.: Suppose a CD at HSBC Bank has an interest rate of 12%. Let us see how its APY varies with theamount of compounding.

i Frequency of compounding APY

12% (= .12) yearly (m=1) (1+.12/1)1 - 1 = 1.12 - 1 = 12%

12% monthly (m=12) (1+.12/12)12 - 1 = 1.0112 - 1 = 12.683%

12% daily (m=365) (1+.12/365)365 - 1 = 1.000328767365 = 12.747%

Q: If your boss offered to cut your salary to a penny a day but to double it every day (to 2 cents tomorrow,4 cents the next day, etc.), would you come out ahead by accepting the offer?

A: Absolutely! That's a 100% daily interest rate. Your daily salary would increase by leaps and bounds, to$0.64 after the first week, $81.92 after the second week, over $10,000 after the third week, over $1 millionby the end of the fourth week, and over $1 billion after 38 days. Well before the end of the second month,your salary would be larger than all of world GDP.-- In this example, your salary reaches such huge heights so fast because iis very large (100%) and thecompounding is very frequent (daily, orm=365). The APY in this case is so large as to be beyond thelimits of most calculators.

If the compounding is continuous (i.e., m = infinity), then the APY is even larger. To calculate it precisely,we would use the exponential function e (e is the inverse of the natural logarithm; it's on most scientificcalculators. The APY in this case isAPY = e i- 1. Alternatively, you could just use the regular APYformula and plug in a very large value form, like 100,000. That will give you a very, very closeapproximation of the correct answer.

VI. REAL VS. NOMINAL INTEREST RATES


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The nominal interest rate idoes not account for the impact of inflation. The REAL INTEREST RATE isthe inflation-adjusted interest rate, and it is the one that matters.

NOTATION:i = nominal interest rate (the posted interest rate)ir= real interest rate

p = inflation ratepe = expected inflation rate

ex ante (or expected) real interest rate = ire= i- pe-- this is the real interest rate that drives investment by firms in new plant and equipment

ex post(after-the-fact) real interest rate = ir= i- p-- ir indicates the real (inflation-adjusted) cost of borrowing and lending

Q: What is the real interest rate (ex ante) on a 1-year bond today that pays 6% interest, if the expectedinflation rate over the next year is 2%?A: ire = 6% - 2% = 4%

Q: What is the ex postreal interest rate on that bond if inflation turns out to be 5% over the next year?A: ir = 6% - 5% = 1%

If inflation rises,* borrowers (debtors) benefit (their debts become a lot easier to pay off, and less burdensome)* lenders (creditors, savers) lose (the real value of their savings shrinks, and the real interest rates theyreceive are reduced and could even become negative)-- "Inflation is when people who have saved for a rainy day get soaked"

Looking only at nominal interest rates can be misleading. In the late 1970s, for example, nominal interestrates were very high, yet real interest rates were actually negative, because inflation was high andaccelerating.

Two recent financial innovations, designed to protect lenders from the ravages of inflation, are (1)variable-interest-rate mortgages, on which the interest rate, rather than being fixed (as on a regularmortgage), is adjusted periodically as the inflation rate or other interest rates change; and (2) inflation-indexed Treasury bonds, which guarantee the bondholder a certain positive real interest rate.

moneyandbanking 01-09 Part2

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