Finance 603Week 2

1
Finance 603 Week 2

• More Money

2
Notice

• My office hours (in BA 350A) will start on
  Wednesday, September 14 at the conclusion of the
  3 PM 5 PM faculty meeting

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This Weeks Agenda

• Extensions to discounting
• Periods less than one year
• Compounding
• Inflation and taxes
• Two special kinds of bank deposits
• Federal funds (deposits at the Fed)
• Eurodollars (deposits in offshore banks)
• Drop hints about foreign currencies

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Advice

• If you are lost, others are too, soASK THE
  PROFESSOR TO EXPLAIN WHAT IN THE WORLD HE IS
  TALKING ABOUT!

6
Quick Review of Bank Time Deposits and
Discounting

• Simple payment scheme from bank CDs
• Pay money in now
• Get more money out later
• The interest rate determines how much money is
  paid out later relative to the amount paid in
• To get future value multiple by (1r) to get
  present value divide by (1r), where r is the
  interest rate for the period

7
The Fundamental Relationship BetweenInterest
Rate (r) and Present Value (PV)

• Interest rates and the PV of any every financial
  instrument with constant future cash flows
  (fixed-income securities like CDs and bonds)
  always move in opposite directions
• Example The PV of 10,000 at 4 interest in 1
  year is 10,000/1.04 9,615.38
• If the interest rate goes up to 5, the PV drops
  to 10,000/1.05 9,523.81
• If the interest rate goes down to 3, the PV
  rises to 10,000/1.03 9,708.74

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More on the Fundamental Relationship

• We will examine the sensitive of various
  fixed-income securities to interest rates before
  mid-term using a measurement called duration
• While the prices of stocks and some risky bonds
  (both have very uncertain cash flows) tend to
  move in the opposite direction of interest rates,
  they sometimes move in the same direction when
  the change in interest rates indicates strength
  or weakness in the economy

9
Converting Annual Interest Rates to Periods Less
Than One Year

• Obvious method
• Multiply rate by the appropriate fraction of a
  year
• Examples
• 12 for 6 months (or ½ year) is ½ (12) 6
• 8 for 3 months (or ¼ year) is ¼ (8) 2
• Warning
• The financial world often does not conform to the
  obvious method because annual rates can be
  quoted oddly or based on a 360-day year

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FV and PV for Less Than a Year with No
Compounding

• Convert interest rate to new period length as
  demonstrated earlier
• Apply the FV and PV formulas as before
• FV C0 (1r)
• PV C1 / (1r)
• FV of 10,000 paying 4 annual rate for 6 months
  ( ½ year)
• FV 10,000 (1 0.04/2) 10,200

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Suppose We Reinvest in an Identical CD After 6
Months

• Now our outflow (initial investment) is 10,200
• The future value in six months is 10,200
  (1.02) 10,404
• Notice that this is the same as investing for an
  entire year at 4.04
• 4.04 is known as the APY (annual percentage
  yield) or EAR (effective annual rate)
• Compounding accounts for the extra 0.04,
  commonly known as 4 basis points (b.p.) or bips

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The General Formula for Future Valuewith
Compounding

• New parameters
• m Number of interest periods in a year
• m 2 means semi-annual interest
• m 4 means quarterly interest
• m 12 means monthly interest
• m 365 means daily interest
• T Future time (in years or a fraction of a year)
  when inflow of cash occurs
• Formula

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Using the Compounding Formula

• Example 10,000 at 4 annual rate for 6 months,
  compounded monthly
• Parameters
• C0 10,000
• r 4 0.04
• m 12
• T 0.5
• Plugging in FV 10,000 (1 0.04/12)0.5(12)
  10,000 (1.0033)6
  10,201.67

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APY Formula
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The Difference a Bip (or a Few Bips) Makes

• At current interest rates, EAR tends to be only a
  few bips (hundredths of a percentage point, also
  known as basis points or b.p.) higher than the
  simple interest rate
• It is important to keep interest rates straight
  because although they low small, every bip
  matters when you invest millions of dollars
• Professional bond traders and investors look at
  spreads (the interest rate relative to other
  securities) and these are measured in bips

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Three Important Points Worth Mentioning Now

• Compounding is magic because the interest on
  interest (and interest on interest on interest)
  adds up over time
• Over long periods of time (10 years or more
  depending on interest rates), small difference in
  the interest rate can make large differences in
  the future value of the investment
• Note that compounding only works if we do not
  withdraw the interest at the time that it is paid
• We will not consider the receipt of more than one
  cash flow from a financial instrument until we
  get to Treasury notes and bonds in a few weeks

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Continuous Compounding

• What happens when the compounding interval goes
  to zero (even less than a nanosecond)
• Basic calculus is required to derive the FV and
  PV formulas, but they are simple (as long as
  exponential do not bother you)

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Continuous Compounding Simplifies the Math

• Things like the Fisher equation (coming shortly)
  will not have messy (1r) terms in them
• No more keeping track of interest on interest

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The Practical Side of Continuous Compounding

• Academics and quantitative practitioners use
  continuous compounding whenever possible
• Other practitioners (especially in the retail
  market) use either APY or something else entirely
• Tradition dies hard
• The continuously compounded rate is always the
  lowest possible number (not good marketing)
• APY still allows for a reasonable direct
  comparison
• Continuous compounded is not quite natural

20
Where Does a Short-Term Interest Rate (r) Come
From?

• Glib Answer r is the price of money so it
  comes from supply and demand like any other price
• This supply-and-demand view is known as the
  loanable funds theory of interest rates.

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Supply and Demand of Loanable Funds
Demand
Supply
Interest Rate
r
Quantity of Loanable Funds Supplied and Demanded
22
What Affects Demand for Loanable Funds?

• Economic Growth
• More growth means more borrowing to create more
  goods
• Productivity
• The more productive that capital goods are, the
  more that companies will substitute them for
  labor and borrow to purchase them
• Government Deficits
• Inflation We are willing to borrow at higher
  rates when we can pay back in dollars with less
  value

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Federal Open Market Committee (FOMC)

• The part of the Fed that conducts U.S. monetary
  policy at its eight annual meetings and
  occasionally between meetings
• Main Issue Too much money leads to inflation and
  too little money leads to recession (negative
  growth)
• Primary tool is open market operations, the
  purchase and sale of Treasury securities
• Purchasing these securities expands the Feds
  balance sheet and injects liquidity into the
  economy
• Selling these securities contracts the Feds
  balance sheet and drains liquidity from the
  economy

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Whoa!! Explain That Slide Again

• Suppose the Fed purchases Treasury securities
• Their added demand drives up prices
• Prices up means interest rates down
• The Fed pays with money that banks can use as
  reserves that further adds to demand
• Suppose the Fed sells Treasury securities
• Their added supply drives down prices
• Prices down means interest rates up
• The Fed receive money from banks that reduce
  reserves and further reduces demand

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Alan Greenspan

• Chairman of the Fed and the FOMC
• Generally considered the most powerful person in
  the world
• Scheduled to retire in early 2006
• Approves the wording of the statement issued
  after every FOMC meeting

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What is the FOMCs Target?

• In the 1970s, the FOMC directly targeted the
  money supply, though not very successfully
• Notice that there are many different measure of
  the money supply, with M1, M2, and M3 being the
  most popular
• Beginning in the 1980s, it targeted the federal
  funds rate (always referred to as the fed funds
  rate) and began making formal pronouncements of
  the target in 1995

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Federal Funds (more commonly known as Fed
Funds)

• A loan, usually overnight, of balances at the Fed
  from one bank to another bank
• The typical rate (on an annual basis) that these
  carry is the fed funds rate referred to on the
  previous slide
• These loans typically occur so that banks can
  meet the Feds reserve requirement each day

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Fed Funds Target Rate

• The 30-day target rate is set by the FOMC
• The actual fed funds rate is usually within a few
  bips of this rate

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Why is This Target Rate So Important?

• It helps determine inflation and economic growth
• It is built into all other short-term interest
  rates, including the two rates that most
  influence the financial system
• LIBOR
• U.S. Treasury bills (generally the 3-month rate)
• It indirectly influences longer-term rates
• 10-year Treasury note
• 30-year Treasury bond

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What Has the FOMC Been Doing Lately and What
Might It Do in the Future?
31
Interest Rates from the September 7, 2005Wall
Street Journal
32
The Regularly Scheduled Events That Tend to Move
Financial Markets

• FOMC meeting announcements
• Preliminary quarterly GDP growth numbers
• Monthly nonfarm employment (payroll) and
  unemployment numbers
• Monthly CPI (consumer price index) numbers
• Monthly PPI (producer price index) numbers

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Some Comments

• What matters to markets is not the numbers
  themselves, but how the numbers compare with the
  markets expectations for them
• None of these numbers is real, they are
  targets or estimates (subject to seasonal and
  other statistical adjustments) and they are
  reported with a significant lag

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And Some More Comments

• Academic studies show that these events do matter
  (in a big way)
• Practitioners (including smart individual
  traders) know they do
• These events affect fixed-income markets the
  most, but these effects spill over into the stock
  market and other markets

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FOMC Announcements

• Announcements at 215PM on the last day of every
  scheduled meeting
• There are normally 8 meetings at year at roughly
  6-week intervals (sometimes longer during holiday
  periods)
• The FOMC holds special, unscheduled meetings at
  another timesin recent years usually only to
  deal with emergencies

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U.S. Economic Growth GDP Quarterly Growth

• Announced by the Bureau of Economic Analysis
  (BEA) at the U.S. Department of Commerce
• GDP (Gross Domestic Product) is the total of
  goods and services produced in the U.S.
• Preliminary announcement of GDP comes about a
  month after the end of the quarters followed by
  two revisions over the next several weeks to
  incorporate the final month of the quarter more
  accurately
• A recession is generally defined as two
  consecutive quarters of negative GDP growth

37
U.S. Employment Figures

• Compiled and reported by the Bureau of Labor
  Statistics (BLS) at the U.S. Department of Labor
• Usually released at 830 AM on the first or
  second Friday of the month
• Figures are compiled during the middle of the
  previous month
• Currently, the market focuses on changes in
  nonfarm payroll and tends to ignore the
  unemployment number

38
U.S. Consumer Inflation Rate Percent Change in
CPI, CPI-U and Core CPI

• Also compiled and reported by the BLS
• Numbers are released at various times during the
  middle of the month
• There are many CPIs
• The headline CPI is the most general
• Core CPI removes volatile food and energy prices
• CPI-U (urban CPI) is used for inflation-index
  Treasury securities and is preferred by some
  economists

39
U.S. Producer Inflation Rate Change in PPI and
Core PPI for Finished Goods

• Also compiled and reported by the BLS
• Numbers are released at various times during the
  middle of the month, usually before CPI
• Can provide an early warning of impending
  inflation
• PPI is more volatile than CPI (bounces around
  more), and not all changes in producer prices are
  passed along to consumers

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Why Not Target Inflation Directly?

• Swedens central bank does this
• Their inflation meter is pictured above
• The target rate is 2 plus or minus 1
• The rest of Europe also likes inflation targeting
• The new Fed chairman could also adopt it as part
  of U.S. monetary policy

41
Inflation and Interest Rates

• Let us suppose that you can get a 4.3 APY on a
  1-year bank CD
• 10,000 invested now generates 10,430 in one
  year
• Problem Inflation eats away some of that value
• Suppose that expected inflation is 3 over that
  year
• Then it takes 10,300 in a year to buy the same
  amount as 10,000 now
• 10,430/10,300 1.0126, so the real return is
  then r 1.0126 1 1.26

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Fisher equation

• Real interest rate Nominal interest rate
  Expected inflation
  rate
• The current fed funds rate is 3.5 and a
  reasonable guess at expected inflation is 3
  (roughly what it was for the past year)
• This means the real fed funds rate is 0.5
• This compares with a historical average of
  between 2 and 3
• This indicates the Fed may still increase it

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The Fisher Equation Done Right

• (1Real interest rate) (1Nominal interest
  rate)
  (1Expected inflation rate)
• In the notation of BKM p. 138 and 139

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A Big Problem With the Fisher Equation

• It is difficult to estimate the expected rate of
  inflation
• There are financial instruments (TIPS, futures
  contracts) that provide a clue, but these clues
  cannot be completely trusted for several reasons
• They may not use the right inflation index
• They are subject to intentional or unintentional
  temporary or permanent market distortions
• It is also difficult to statistically test the
  accuracy of such clues because expectations are
  abstract

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One Last Bit of Bad News

• Taxes also eat into the return provided by
  interest
• The exact amount of this bite is determined by
  ones marginal tax rate
• Taxes are so depressing that finance textbooks
  generally ignore them (and they will only receive
  occasion mention in this course)
• There are, however, a variety of legal ways to
  eliminate or reduce the taxes on investments

46
Fed Watcher Caroline Baum

• Columnist for Bloomberg who focuseson the
  actions of the Federal Reserveand related
  economic issues
• Her column is educational and influences Wall
  Street
• The only fixed-income commentator with comparable
  clout is bond manager Bill Gross

47
How Might We Predict Future Levels of the Fed
Funds Rate?
48
Chicago Board of Trade (CBOT)Fed Funds Futures
Contracts

• Is basically a bet on what the average 30-day fed
  funds rate will be over a given future month
• They trade at a discount to 100, so a fed funds
  rate of 3.5 (the current rate) would be
  equivalent to a futures price of 1003.5096.50
• To professional investors, especially those who
  trade fixed-income securities, this is among the
  most important financial securities out there

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Fed Funds Futures Details

• Useful References
• From CBOT
• From the Cleveland Fed
• Futures (and forward) contracts have two sides
• Long You take delivery and benefit when the
  price goes up (and the fed funds rate goes down)
• Short You make delivery and benefit when the
  price goes down (and the funds rate goes up)

50
More Fed Funds Futures Details

• Nothing is ever delivered with this contract
• Main reason Only banks can do fed funds
  transactions, but the futures are available to
  anyone with a commodities trading accout
• Using margin (more on that later) money is made
  and lost on a daily basis, rather than at the end
• Fed fund futures, like most of high finance
  exist in what can be viewed as a fantasy land

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Some Final (Gory) Fed Funds Details

• A 1-bip change the futures contract is worth
  41.67 per 5 million contract (the weird number
  is the result of using a 360-day year)
• A 1-bip increase is equivalent to prices going up
  and rates going down, so the long side profits
• A 1-bip decrease is equivalent to prices going
  down and rates going up, so the short side
  profits
• Under many circumstances, one can reverse
  engineer the markets expectations of what the
  Fed will do from the fed funds futures

52
The September 20, 2005 FOMC Meeting

• What the FOMC does at this meeting will determine
  the fed funds rate for the entire month of
  October 2005
• Two main possibilities
• Rate stays at 3.50, so futures are 96.50
• Rate rises to 3.75, so futures are 96.25
• If the chance to the two possibilities is
  believed by the market to be 50-50 (even odds),
  the futures should trade at the midpoint 96.375

53
Recent Action in the October 2005 Fed Funds
Futures Contract
54
Eurodollars

• U.S. dollar-denominated time deposits at banks
  outside of the United States, known as offshore
  banks
• Free of U.S. regulation, including reserve
  requirements
• These banks do receive credit ratings and require
  an investment grade or higher rating to attract
  depositors

55
3-Month LIBOR

• The London Interbank Offer Rate for 3-month
  Eurodollar time deposits
• It is a rate that one London bank charges another
  and is published each day at 11AM London time by
  the British Bankers Association
• It is a candidate for the most important interest
  rate in the world
• It is just the rate that is offered (posted) by
  banks to other banks wishing to borrow from them

56
3-Month LIBID

• The London Interbank Bid Rate
• It is the rate that one bank is willing to pay to
  receive deposits
• LIBID is less than LIBOR by several bips
• Not an official rate and difficult to find on the
  Internet

57
The Most Important Analytics Slide in
FinanceSECURITIES PRICES ARE A FICTION

• The economic notion of a price implies that both
  buyers and sellers can transact at that price
• Reported prices in the financial media are
  either arrived at by a price-setting process or
  represent the last traded price
• Prices are different depending on whether you are
  buying or selling
• The bid price is what you can sell for
• The ask or offer price is what you can buy for

58
Bid/Ask Spread

• Although it may be difficult to find, almost
  every traded security has a bid/ask spread
• Example Google

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What is a Better Indicator of Googles Price Its
Last Trade or the Bid/Ask Spread?
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And Something To Make Life More Difficult

• Most of the time, interest rates are changing
• First big implication The interest rate that you
  use for discounting depends on the length of the
  time period
• Second big implication The interest rates that
  are fine to use today may not be fine to use
  tomorrow

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Eurodeposits at Maturities Beyond 3 Months
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Fascinating Stuff Hidden in Eurodeposit Rates

• Predicted changes in interest rates, also known
  as forward interest rates
• Predicted changes in the future relative values
  of currencies, also known as forward exchange
  rates

63
Question to Be Answered Next Time

• Why do interest rates vary from currency to
  currency?

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For Next Time

• Get vCard in if you have not already done so
• Follow the links on the slides
• Read the material around these two theorems
• Interest rate parity theorem (BKM p. 822)
• Spot-futures parity theorem (BKM p. 807, we will
  be looking at gold, which does not pay dividends,
  so D0)
• Do the problems on the 6 slides that follow this
  one
• Justify each True-False answer
• For the CD problems 1-3, use a calculator for one
  CD and a calculator or spreadsheet for the rest

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True-False Statements (Page 1 of 2)

• One can make the annual percentage yield from a
  CD as high as one wants by choosing a short
  enough compounding interval.
• At higher stated yields, the compounding interval
  will make more of a difference to the annual
  percentage yield.
• The FOMC is virtually certain to raise the fed
  funds target rate to 3.75 at its September 20
  meeting

66
True-False Statements (Page 2 of 2)

• If the real interest rate on a CD is negative,
  then its future value will be less than its
  present value
• Doubling the interest rate on a CD will double
  its APY
• If two one-year CDs both pay 10,000 at maturity,
  then the one with the lower APY will cost more to
  purchase now
• If one six-month CD has a higher continuously
  compounded interest rate than another six-month
  CD, it will also have a higher APY.

67
Questions about the Following Slide With CD Rates

• Compute the APY (known in the textbook as
  Effective Annual Interest Rate) for each CD.
• Compute the future value at maturity for each CD
  for an investment of 10,000 today.
• Compute the present value of 10,000 received at
  maturity from each CD.
• You are considering the 3-month and 12-month (1
  year) CDs offered by Beal bank. Bank of Miller
  (BoM) is willing to guarantee you a 9-month when
  the 3-month Beal CD matures if you sign with them
  now. What APY must BoM provide you so that after
  a year you will have the same amount you would
  have buying Beals 12-month CD.

68
CD Interest Rates Compiled By Your Assistant on
September 6, 2005
M is monthly compounding (m12) andQ is
quarterly compounding (m4)
69
Questions about the Following Slide With Fed
Funds Futures Prices

• Does the market expect the fed funds rate to
  increase or decrease between September and
  November 2005?
• What is the current expected fed funds rate for
  the month of October 2005?
• Net Chg is the change in price since
  yesterdays close. If you were had a long
  position of 5 contracts in each of the three
  months, how much money would have made made or
  lost since yesterdays close?
• Assuming that the only possibilities for the
  September 20 meeting are for the target fed funds
  rate to stay at 3.50 or to be increased to
  3.75. According to the October futures, what is
  the probability that they will increase?

70
Fed Funds Futures on 9/7/05Note Last 1
(highlighted) is the current price