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Interest Rates and Money

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  1. Interest Rates and Money

  2. 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)

  3. 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)

  4. 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?

  5. Treasury Bill Quotations • The WSJ (Sept 13, 2006) gave the following quotes for Treasury bills expiring on December 7

  6. Treasury Bill Quotations • Numbers under “bid” and “asked” are not prices • These numbers are discount yields, quoted in hundredths.

  7. 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.

  8. 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.

  9. 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?

  10. 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

  11. 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.

  12. Treasury Bond Quotes • The WSJ quoted on Jan 13, 2006 the following T-bond • What does this mean?

  13. 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%.

  14. 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?

  15. 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

  16. 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?

  17. Inflation Example • CPI increased by factor of 197.6/56.8 = 3.48 • Average house today should cost 60,000(3.48) = 208,000

  18. 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

  19. 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%.

  20. 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%

  21. 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

  22. 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

  23. 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.

  24. 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=?

  25. 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

  26. 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

  27. Chapter 2 of Cecchetti Money and the Payments System

  28. 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

  29. 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