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## Interest Rates and Money

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**Treasury Bills**• Government sells t-bills to raise cash. • Issued through an auction • Short term zero-coupon bond • Maturities of 28, 91, and 182 days issued weekly • Highly liquid • Exempt from all state and local taxes • Taxable at the Federal level • Virtually free of default risk • Treasury/Agency issues (WSJ)**Bonds and Yields**• When the coupon rate =YTM • Bond Price = Face Value (Par) • When the coupon rate > YTM • Bond price > Face Value (Par) • When the coupon rate < YTM • Bond Price < Face Value (Par)**Bid and Ask Prices**• T-bills are bought and sold through dealers. • Ask Price: The lowest price at which any dealer stands ready to sell. • Bid Price: The highest price at which any dealer stands ready to buy • As a market participant (not a dealer) at which price do you buy/sell? • Which price is higher?**Treasury Bill Quotations**• The WSJ (Sept 13, 2006) gave the following quotes for Treasury bills expiring on December 7**Treasury Bill Quotations**• Numbers under “bid” and “asked” are not prices • These numbers are discount yields, quoted in hundredths.**Treasury Bill Quotations**• Quotes of T-bills are expressed using bank-discount yields and are expressed in %. • yBD is the bank discount yield • P is the price of a T-bill • F is the face value • n is the number of days until maturity.**Treasury Bill Quotations**• Assume a face value of 10,000 • The bid price is the price at which a customer can sell the bill to a dealer. • PB=10,000[1-0.0482(86/360)] = $9884.86 • The ask price is the price at which a customer can buy the bill from a dealer. • PA=10,000[1-0.0481(86/360)] = $9885.09 • The “Chg” in the WSJ is the change in the asked bank discount yield from the previous day.**Treasury Bill Quotations**The “Ask Yld” in the WSJ is the Bond Equivalent Yield or APR of a T-bill: How would you find the EAR?**EAR**• The total return over the next 86 days for this bond is • This is the “86 day growth rate” • We want an annual growth rate • How many 86-day periods are in a year? • 365/86 • The effective annual return is therefore**Bond Quotes**• Treasury bonds often pay coupons semi-annually • Coupon rates are quoted as APRs • If coupon rate is stated as 8%, bond pays 4% of face value every 6 months.**Treasury Bond Quotes**• The WSJ quoted on Jan 13, 2006 the following T-bond • What does this mean?**Treasury Bond Quotes**• The bond expires in August 2009. • This bond pays an interest rate of 6.000%. • An investor receives interest semi-annually. • Thus, the interest is $3 every February and August. • The price quotes are given in 32nds as a percentage of face value • The bid price is 100(105+13/32)(.01)=$105.41 • The ask price is 100(105+14/32)(.01)=$105.44 • The price increased by 5/32 of the face value on January 12, 2006 • The bond equivalent ask-yield (APR) is 4.34%.**Inflation**Inflation: A general rise in the price level • Fixed-weight Index - CPI • CPI in 1992: 139.7 • CPI in 2005: 197.6 • Gas in 1992: $1.12 per gallon • Holding relative prices constant, what should be the price of gas today?**Inflation**• CPI has increased by a factor of 1.41 • 197.6/139.7 = 1.41 • If relative prices are constant, price of gas today should be 1.12(1.41) = $1.58**Inflation Example**• CPI 1976: 56.8 • CPI 2005: 197.6 • If the average house cost $60,000 in 1976, what would the average house cost in 2005 assuming relative prices are constant?**Inflation Example**• CPI increased by factor of 197.6/56.8 = 3.48 • Average house today should cost 60,000(3.48) = 208,000**Inflation**• CPI tends to be biased upward: • Quality change and new product bias • Substitution bias • Outlet substitution bias See page 31 of Cecchetti for more info**Real Returns**• Beginning of year: • pizza is $10.00. • You have $100 in cash. • You could buy 10 pizzas • Instead, you invest the $100 in a long term gov. bond. The return on the bond is 5%. • Inflation over the year is 3%.**Real Returns**• The investment provides you a nominal income at year end of 100(1.05) = $105. • At year end, the cost of a pizza is 10.00(1.03)=$10.30. • At year end, you could buy 10.19 pizzas (105/10.3)=10.19. • Your real return is therefore only ____?% 1.9%**Real Returns**• C = amount of cash at beginning of period • P = price of a good at beginning of period • rn = nominal return, • rr = real return • i = inflation rate • The real (gross) rate of return was found above by solving the following equation**Example: Real Returns**• The rate of return on a t-bill is 8% • Inflation over the next year is 4% • What is your real return? • 1.08/1.04 = 1.038 = 1+r • r = 3.8% • approximately 4% = t-bill - inflation**Bond Returns**• If I own a bond and rates change why should I care? • I may need to sell the bond before it matures. • When rates increase bond prices go down. • When rates decrease, bond prices go up. • The return I get from owning the bond depends on what rates are when I sell the bond.**Example: Zero Coupon Bonds**• Annual Bond • Beginning of year • Matures 10 years • YTM=10% • Coupon Rate=10% • FV=1000 • Price=? • End of year • YTM=11% • Price=?**Example: Zero Coupon Bonds**• Return from buying and selling: • 944.63/1000-1 = -5.54% • Prices of long term bonds are more sensitive to interest rate changes than short-term bonds**Bond Returns**• If I own a bond and I plan on holding it to maturity and rates change why should I care? • Opportunity Cost of funds invested • For example, when rates go up, I am losing out • Inflation is higher and my real return is lower and/or • I am missing out on a higher real return**Chapter 2 of Cecchetti**Money and the Payments System**Money**Money • Money is an asset that is generally accepted as payment for goods and services or repayment of debt. 1. A means of payment. • Transferability • Information 2. A unit of account • Allocation of resources • Relative prices 3. A store of value • Liquidity**Money and Value**• What makes money valuable? • Gold Regime: • Government stands ready to trade gold for dollars • Fiat Money: • Paper currency decreed by local governments as legal tender, but not convertible into precious metals. • Trust • Government will always accept as taxes