fin 410 chp 9

Simple Interest Basis

- Another method to quote interest rates. - Calculated just like annual percentage rates (APRs). - Used for CDs.

several different ways market participants quote interest rates

- Bank Discount Basis - Bond Equivalent Yields (BEY) - Annual Percentage Rates (APR) - Effective Annual Rates (EAR)

Market Segmentation Theory

- Debt markets are segmented by maturity, so interest rates for various maturities are determined separately in each segment - The U.S. government borrows at all maturities

Maturity Preference Theory

- Long-term interest rates contain a maturity premium necessary to induce lenders into making longer term loans. - U.S. government borrows much more heavily short-term than long-term

Expectations Theory

- The term structure of interest rates reflects financial market beliefs about future interest rates. - almost always upward sloping, but interest rates have not always risen.

Pure Discount Security

- an interest-bearing asset: - It makes a single payment of face value at maturity. - It makes no payments before maturity

Fixed income securities

- securities include long-term debt contracts from a wide variety of issuers - have a maturity of greater than one year.

APR can be converted to an EAR

1+EAR = (1+(APR/m))^m

BEY Formula

= (365*DY)/(360-DTM*DY)

STRIPS formula

= FV / (1+(YTM/2))^2m

Present Value formula

= FV / (1+r)^n

Banker's acceptance

A postdated check on which a bank has guaranteed payment. Commonly used to finance international trade transactions

T Bill

A short-term U.S. government debt instrument issued by the U.S. Treasury.

if the rate on a car loan is 1 percent per month, then the APR is

APR=interest rate*#periods 12%=.01*12

uppose the ask discount rate on a T-bill with 170 days to maturity is 3.22 percent. What is the bond equivalent yield?

Book * BEY=(365*DY)/(360-DTM*DY) .03315=(365x.0322)/(360-170x.0322)

on our 12 percent APR car loan, the EAR can be determined by:

Book* 1+EAR=(1+(APR/m))^m 12.68%=1+EAR=(1+(.12/12))^12

A typical credit card may quote an APR of 18 percent. On closer inspection, you will find that the rate is actually 1.5 percent per month. What annual interest rate are you really paying on such a credit card? With 12 periods in a year, an APR of 18 percent is converted to an EAR

Book* 1+EAR=(1+(APR/m))^m 19.56%=1+EAR=(1+(.18/12))^12

Suppose you wanted to buy a T-bill with 85 days to maturity and a face value of $5,000,000. How much would you have to pay if the ask discount is 3.41 percent?

Book* Ask Price=FV(1-(DTM/360)*DY) 4959743=5000000(1-(85/360)*.341)

Suppose a T-bill has 45 days to maturity and an ask discount of 5 percent. What is the bond equivalent yield?

Book* BEY=(365*DY)/(360-DTM*DY) .05101=(365x.05)/(360-45x.05)

A money market instrument with 60 days to maturity has a quoted ask price of 99, meaning $99 per $100 face value. What are the banker's discount yield, the bond equivalent yield, and the effective annual return?

Book* Current Price=FV(1-(DTM/360)*DY) 99=100(1-(60/360)*DY)........*DY=6%* BEY=(365*DY)/(360-DTM-DY) *6.145*=(365*.06)/(360-60*.06) 1+EAR=(1+(APR/m))^m 1+EAR=(1+(.06145/6.0833))^6.0833 m=(365/60)=6.0833

Suppose you have $1,000 to invest and you can invest at an annual rate of 3.5 percent per year. If you invest for three years (N = 3), the amount you will have in three years is

Book* FV=PV(1+r)^n 1108.72 = 1000(1+.035)^3

Suppose you invest $500 for 4 percent for six years. How much money will you have at the end of six years?

Book* FV=PV(1+r)^n 632.66 = 500(1.04)^6

you will be getting $800 in four years. What is an equivalent amount today if you discount at 3.7 percent?

Book* PV=FV/(1+r)^n 691.79=800/(1+.037)^4

suppose a banker's acceptance has a face value of $1 million that will be paid in 90 days. If the interest rate, quoted on a discount basis, is 5 percent, what is the current price of the acceptance?

Book* Current Price=FV(1-(DTM/360)*DY) 987,500=1000000(1-(90/360)*.05)

The rate on a particular money market instrument, quoted on a discount basis, is 4 percent. The instrument has a face value of $100,000 and will mature in 71 days. What is its price? What if it had 51 days to maturity?

Book* Current Price=FV(1-(DTM/360)*DY) 99,211.11=100,000(1-(71/360)*.04)

Bank Discount Basis Equation

Current Price=FV*(1-(DTM/360)*DY)

Federal Funds Rate

Interest rate that banks charge each other for overnight loans of $1 million or more

London Interbank Offer Rate

Interest rate that international banks charge one another for overnight Eurodollar loans

Interest Rate Risk

Long-term bond prices are much more sensitive to interest rate changes than short-term bonds

Suppose a banker's acceptance that will be paid in 71 days has a face value of $100,000. If the discount yield is 4%, what is the current price of the banker's acceptance?

NOTES* 99,211.11

The ask quote is 99.93, or $99.93. The ask YTM is 0.14%. Matures in about 6 months (½ Year) from the time of the quote. what is the strip

NOTES* = FV / (1+(YTM/2))^2m = 100 / (1+(.0014/2))^2(1/2)

Real Interest Rate formula

Nominal rate - Inflation Rate

Let's verify the price of the November 2012 Strip. The ask quote is 99.93, or $99.93. The ask YTM is 0.14%. Matures in about 6 months (½ Year) from the time of the quote

Notes * 99.93

Commercial Paper

Short-term, unsecured debt issued by the largest corporations.

Prime Rate

The basic interest rate on short-term loans that the largest commercial banks charge to their most creditworthy corporate customers.

Call Money Rate

The interest rate brokerage firms pay for call money loans from banks. This rate is used as the basis for customer rates on margin loans.

CDs

The interest rate on certificates of deposit, which are large-denomination deposits of $100,000 or more at commercial banks

Discount Rate

The interest rate that the Fed offers to commercial banks for overnight reserve loans.

Euro Dollar

U.S. dollar denominated deposits in banks outside the United States

Consider a STRIPS maturing in six years with an ask price of 73.031. Its yield to maturity is

YTM=2*(((FV/STRIPS)^2m)-1) 5.31%=2*(((100/73.031)^(2*6))-1)

Bank Discount Basis

a method of quoting interest rates on money market instruments, such as T-bills and banker's acceptances

Real Interest Rates

adjusted for inflation effects.

Forward rate

an expected on short term security that is to be originated at some point in the future

Hibor

an interest rate based on Hong Kong dollars. It is the interest rate among banks in the Hong Kong interbank market.

EURIBOR

an interest rate that also refers to deposits denominated in euros. However, it is based largely on interest rates from the interbank market for banks in the European Union

Bond Equivalent Yield (BEY)

another way to quote an interest rate.

Fisher Hypothesis

asserts that the general level of nominal interest rates follows the general level of inflation...interest rates are, on average, higher than the rate of inflation

Nominal Interest Rates

interest rates as they are observed and quoted, with no adjustment for inflation.

structure of interest rates

is the relationship between time to maturity and the interest rates for default-free, pure discount instruments.

Treasury

plot of Treasury yields against maturities.

STRIPS

pure discount instruments created by "stripping" the coupons and principal payments of U.S. Treasury notes and bonds into separate parts, which are then sold separately.

Euro LIBOR

refers to deposits denominated in euros—the common currency of 16 European Union countries