# Interest Rates and Money - PowerPoint PPT Presentation

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Interest Rates and Money. 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

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Interest Rates and Money

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## Interest Rates and Money

### 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)

• 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

### 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:

• Fiat Money:

• Paper currency decreed by local governments as legal tender, but not convertible into precious metals.

• Trust

• Government will always accept as taxes