ch 4: interest rates

b. a unit of measurement for the interest rate the compounding frequency is a unit of measurement. the frequency with which interest is paid may be different from the compounding frequency used for quoting the rate.

The compounding frequency for an interest rate defines a. the frequency with which interest is paid b. a unit of measurement for the interest rate c. the relationship between the annual interest rate and the monthly interest rate d. none of the above

B. decrease of $2,500 when yields increase bond prices decrease. the proportional decrease is the modified duration times the yield increases. in this case, it is 5 * .0005 = .0025. the decrease is therefore .0025 * 1,000,000 or $2,5000

The modified duration of a bond portfolio worth $1 million is 5 years. By approximately how much does the value of the portfolio change if all yields increase by 5 basis points? a. increase of $2,500 b. decrease of $2,500 c. increase of $25,000 d. decrease of $25,000

a. 5.79% the equivalent rate with continuous compounding is ln(1.06)= 0.0583 = 5.83%

an interest rate is 6% per annum with annual compounding. what is the equivalent rate with continuous compounding? a. 5.79% b. 6.21% c. 5.83% d. 6.18%

d. 9 years the duration of the first bond is 5 years and the duration of the second bond is 10 years. the duration of the portfolio is weighted average with weights corresponding to the amounts invested in the bonds. it is .2 * 5 + .8 * 10 = 9 years

A company invests $1,000 in a 5- year zero coupon bond and $4,000 in a ten-year zero coupon bond. what is the duration of the portfolio? a. 6 years b. 7 years c. 8 years d. 9 years

c. the rate implicit in a transaction where securities are sold and bought back later at a higher price a repo transaction is one where a company agrees to sell securities today and buy them back at a future time. it is a form of collateralized borrowing. the credit risk is very low.

A repo rate is a. an uncollateralized rate b. a rate where the credit risk is relative high c. the rate implicit in a transaction where securities are sold and bought back later at a higher price d. none of the above

a. 11.83% the equivalent rate per quarter is square root 1.06 - 1 = 2.956% the annualized rate with quarterly compounding is four times this or 11.83%

An interest rate is 12% per annum with semiannual compounding. what is the equivalent rate with quarterly compounding? a. 11.83% b. 11.66% c. 11.77% d. 11.92%

a. 5.06% the equivalent rate with semiannual compounding is 2 * (e^ .05/2 - 1) = 0.0506 or 5.06%

An interest rate is 5% per annum with continuous compounding. what is the equivalent rate with semiannual compounding? a. 5.06% b. 5.03% c. 4.97% d. 4.94%

b. working from short maturity instruments to longer maturity instruments determining zero rates at each step Bootstrapping is a way of constructing the zero coupon yield curve from coupon-bearing bonds. It involves working from the shortest maturity bond to progressively longer maturity bonds making sure that the calculated zero coupon yield curve is consistent with the market prices of the instruments.

Bootsrapping involves a. calculating the yield on a bond b. working from short maturity instruments to longer maturity instruments determining zero rates at each step c. working form long maturity instruments to shorter maturity instruments determining zero rates at each step d. calculation of par yields

d. $8.63 the value of the FRA is the value of receiving an extra 0.5* (.08- .06) * 1000= $10 in 2.5 years this is 10/ (1.03^5)= $8.63

The yield curve is flat at 6% per annum. What is the value of an FRA where the holder receives interest at the rate of 8% per annum for a six month period on a principal of $1,000 starting in two years? all rates are compounded semiannually a. $9.12 b. $9.02 c. $8.88 d. $8.63

d. Z is less than Y which is less than X the forward rate accentuates trends in the zero curve. the par yield shows the same trends but in a less pronounced way.

The zero curve is downward sloping. Define X as the 1-year par yield, Y as the 1-year zero rate and Z as the forward rate for the period between 1 and 1.5 years. Which of the following is true? a. X is less than Y which is less than Z b. Y is less than X which is less than Z C. X is less than Z which is less than Y d. Z is less than Y which is less than X

a. X is less than Y which is less than Z When the zero curve is upward sloping, the one year zero rate is higher than 1-year par yield and the forward rate corresponding to the period between 1.0 and 1.5 years is higher than the one year zero rate.

The zero curve is upward sloping. Define X as the 1-year par yield, Y as the 1-year zero rate and Z as the forward rate for the period between 1 and 1.5 years. which of the following is true? a. X is less than Y which is less than Z b. Y is less than X which is less than Z c. X is less than Z which is less than Y d. Z is less than Y which is less than X

d. forward rates are higher than expected future spot rates liquidity preference theory argues that individuals like their borrowings to have a long maturity and their deposits to have a short maturity. to induce people to lend for the long periods forward rates are raised relative to what expected future short rates would predict.

Under liquidity preference theory, which of the following is always true? a. the forward rate is higher than the spot rate when both have the same maturity b. forwards rates are unbiased predictors expected future spot rates c. the spot rate for a certain maturity is higher than the par yield for that maturity d. forward rates are higher than expected future spot rates

a. interest rate implied by current zero rates for future periods of time the forward rate is the interest rate by the current term structure for the future periods of time. for example, earning the zero rate for the period between one and two years gives the same result as earning the zero rate for the two years.

Which of the following describes forward rates? a. interest rates implied by current zero rates for future periods of time b. interest rate earned on an investment that starts today and last for n-years in the future without coupons c. the coupon rate that causes a bond price to equal its par (principal) value d. a single discount rate that gives the value of a bond equal to its market price when applied to all cash flows

C. liquidity preference theory maturity preference theory is not a theory of the term structure. the other three are

Which of the following is NOT a theory of the term structure a. expectations theory b. market segmentation theory c. liquidity preference theory d. maturity preference theory

c. it is a rate used when borrowing and lending takes place between banks libor is a rate used for interbank transactions

Which of the following is true of LIBOR? a. the libor rate is free of credit risk b. a libor rate is lower than the treasury rate when the two have the same maturity C. it is a rate used when borrowing and lending takes place between banks d. it is subject to favorable tax treatment in the us

b. it is an overnight interbank rate at the end of each day some banks have surplus reserves on deposit with the federal reserve others have deficits. they use overnight borrowing and lending at which is termed the fed funds rate to rectify this.

Which of the following is true of the fed funds rate? a. it is the same as the treasury rate b. it is an overnight interbank rate c. it is a rate for which collateral is posted d. it is a type of repo rate

d. none of the above when interest rates increase the impact of discounting is to make future cash flows worth less. bond prices therefore decline. A is wrong. as coupons increase a bond becomes more valuable because higher cash flows will be received. b is wrong. when the coupon is higher than prevailing interest rates, longer maturity bonds are worth less than shorter bonds. makes c wrong.

Which of the following is true? a. when interest rates in the economy increase, all bond prices increase b. as its coupon increases, a bonds price decreases c. longer maturity bonds are always worth more than shorter maturity bonds when the coupon rates are the same. d. none of the above

a. 3.99% 6-month rate is 1.5% per 6 months. 1 year rate is 2% per six months. 1 year par yield is the coupon that leads to a bond being worth par. A is correct bc (3.99/2)/1.015 + (100+ 3.99/2)/ 1.02^2= 100. the formula in the text can also be used to give the par yield as [(100 -100/ 1.02^2)*2] / (1/1.015 + 1.02^2)= 3.99

the six month and one year rate are 3% and 4% per annum with semiannual compounding. Which of the following is closest to the one-year par yield expressed with semiannual compounding? a. 3.99% b. 3.98% c. 3.97% d. 3.96%

c. 9.02% if the rate is R we must have (3/1.04) + 103e^-R*4= 97 or e^-R = (97-(3/1.04))/ 103= .9137 so that R= ln(1/ .9137) = .0902 or 9.02%

the six month zero rate is 8% per annum with semiannual compounding. the price of a one year bond that provides a coupon of 6% per annum semiannually is 97. what is the one year continuously compounded zero rate? a. 8.02% b. 8.52% c. 9.02% d. 9.52%

D. 7.5% the forward rate for the 3rd year is [(3 * .065) - (2* .06)] / (3-2) = .075 or 7.5%

the two-year zero rate is 6% and the three-year zero rate is 6.5%. What is the forward rate for the third year? All rate are continuously compounded. a. 6.75% b. 7.0% c. 7.25% d. 7.5%