CH4

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 rates are continuously compounded. A. 6.75% B. 7.0% C. 7.25% D. 7.5%

D: The forward rate for the third year is (3×0.065−2×0.06)/(3−2) = 0.075 or 7.5%.

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. 11.83% The equivalent rate per quarter is 1.06 1 2.956% . The annualized rate with quarterly compounding is four times this or 11.83%.

The six month and one-year rates 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%

A. The six month rate is 1.5% per six months. The one year rate is 2% per six months. The one year par yield is the coupon that leads to a bond being worth par. A is the correct answer because (3.99/2)/1.015+(100+3.99/2)/1.022 = 100. The formula in the text can also be used to give the par yield as [(100-100/1.022)×2]/(1/1.015+1.022)=3.99.

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%

A. The equivalent rate with semiannual compounding is 2×(e0.05/2−1) = 0.0506 or 5.06%.

Which of 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 (or 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

A. Interest rates implied by current zero rates for future periods of time

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 year. Which of the following is true? A. XislessthanYwhichislessthanZ B. YislessthanXwhichislessthanZ C. X is less than Z which is less than Y D. Z is less than Y which is less than X

Answer: A When the zero curve is upward sloping, the one-year zero rate is higher than the one-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 correct answer is therefore A.

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%

Answer: C The equivalent rate with continuous compounding is ln(1.06) = 0.0583 or 5.83%.

Bootstrapping 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 from long maturity instruments to shorter maturity instruments determining zero rates at each step D.The calculation of par yields

B. Working from short maturity instruments to longer maturity instruments determining zero rates at each step

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. A unit of measurement for the interest rate

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

B. Decrease of $2,500 When yields increase bond prices decrease. The proportional decrease is the modified duration times the yield increase. In this case, it is 5×0.0005=0.0025. The decrease is therefore 0.0025×1,000,000 or $2,500.

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

B. It is an overnight interbank rate

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%

C. If the rate is R we must have R = ln(1/0.9137) = 0.0902 or 9.02%.

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 U.S.

C. It is a rate used when borrowing and lending takes place between banks

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

C.The rate implicit in a transaction where securities are sold and bought back later at a higher price

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. The value of the FRA is the value of receiving an extra 0.5×(0.08−0.06)×1000 = $10 in 2.5 years. This is 10/(1.035) = $8.63.

A company invests $1,000 in a five-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

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 a weighted average with weights corresponding to the amounts invested in the bonds. It is 0.2×5+0.8×10=9 years.

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. Forward rates are unbiased predictors of 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.

D. Forward rates are higher than expected future spot rates.

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

D. Maturity preference theory

.Which of the following is true? A. When interest rates in the economy increase, all bond prices increase B. As its coupon increases, a bond's price decreases C. Longer maturity bonds are always worth more that shorter maturity bonds when the coupon rates are the same D. None of the above

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 therefore wrong. As coupons increase a bond becomes more valuable because higher cash flows will be received. B is therefore wrong. When the coupon is higher than prevailing interest rates, longer maturity bonds are worth more than shorter maturity bonds. When it is less than prevailing interest rates, longer maturity bonds are worth less than shorter maturity bonds. C is therefore not true. The correct answer is therefore D

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 year. Which of the following is true? A. XislessthanYwhichislessthanZ B. YislessthanXwhichislessthanZ C. X is less than Z which is less than Y D. Z is less than Y which is less than X

D. Z is less than Y which is less than X