# Interest Rates and Money

## Presentation on theme: "Interest Rates and Money"— Presentation transcript:

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.

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[ (86/360)] = \$ The ask price is the price at which a customer can buy the bill from a dealer. PA=10,000[ (86/360)] = \$ 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? 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? The US Department of Labor's Bureau of Labor Statistics (BLS) is responsible for calculating the CPI Based on individual prices for a fixed market basket of goods and services. Collects prices each month for thousands of goods and services from thousands of outlets.

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 Quality change and new product bias, the largest source of bias, arises because the CPI does not immediately take into account either improvements in the quality of goods and services or the introduction of new products. To the extent that the CPI fails to account for changes in quality, the index will not reflect "true" changes in prices. And new products need to be incorporated into the CPI on a timely basis, so that the early declines in price that are a normal part of the product life cycle are captured. Example: a VCR in 1980 cost somewhere around \$600. A VCR in 2006 cost \$30. So technology has caused the prices of VCRs to go down. What the CPI would not take into account is that the VCR bought in 2006 is about 10 times better than the VCR produced in A VCR of the same quality may only cost \$5. DVD players need to be incorporated early. Otherwise early declines in price won’t be captured. Substitution bias occurs because the formula used for CPI calculations assumes that consumers purchase a constant mix of various goods and services despite changes in their relative prices. In actuality, if the price of one good rises relative to that of another good, consumers will tend to substitute cheaper goods for higher-priced ones. Because the weights of goods in the CPI are adjusted infrequently (about once every 10 years), substitution is not taken into account. Example: Suppose gas prices shot out the window - \$1000 per gallon. People would substitute away from using cars, and start using bicycles. CPI would reflect change in gas prices. If you were to adjust wages according to the CPI index, you would pay people enough so that they could still afford the same amount of gas as before. But even if people were paid enough to afford the same amount of gas as before, they probably wouldn’t buy gas. They’d invest more in thie homes or other things, so the impact would be that people would be better off than before. Outlet substitution bias occurs because the CPI does not adequately take into account the extent to which new discount stores have offered lower prices and enticed consumers away from the traditional outlets that tend to be more fully represented in the CPI market basket. For example, as more Walmarts become available, people will start buying more of their products from Walmart rather than from expensive grocery stores.

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 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+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%

Example: Zero Coupon Bonds
Return from buying and selling: 944.63/ = -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

Money and the Payments System
Chapter 2 of Cecchetti Money and the Payments System

Money Money 1. A means of payment. 2. A unit of account
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 Means of payment – money eliminates the need to know anything about the other party Need something that is easy to transfer, and whose value is easily verified. Store of value – must have value for sellers to accept We use other things as a store of value What is the big advantage of money? - Liquidity Unit of account – think if we didn’t have money how many prices do we need? Prices act as a signal to markets What matters are relative prices. When one product suddenly increases in price, this acts as a signal That investors should invest more money to develop that product.

Money and Value What makes money valuable? Gold Regime: Fiat Money:
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 Before, people used assets with intrinsic value as money: silk, butter, salt, cigarettes