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)

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

Maturity Days to Maturity

Bid Asked Chg Ask Yld

Dec 07 06 86 4.82 4.81 0.01 4.93

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.

nF

PFyBD

360

)]360/(1[ nyFP BD

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?

nP

PFy

A

ABEY

365

%93.486

3651

000,10

9885.09BEYy

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

%1625.11000,10

9885.09BEYy

%03.51)011625.1( 86/365

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?

Rate Maturity Bid Asked Chg Ask Yld

6.000 Aug 09n 105:13 105:14 5 4.34

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

ir

PCiPrC

r nr

11

/)1(/)1(

1

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=?

1000

63.944

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

MoneyMoney

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