Question 1

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?

Accepted Answer

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.

Question 2

Which of following describes forward rates?

Accepted Answer

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

Question 3

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?

Accepted Answer

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.

Question 4

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?

Accepted Answer

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.

Question 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 rates are continuously compounded.

Accepted Answer

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

Question 6

Which of the following is NOT a theory of the term structure

Accepted Answer

Maturity preference theory is not a theory of the term structure.The other three are.

Question 7

The compounding frequency for an interest rate defines

Accepted Answer

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.

Question 8

Bootstrapping involves

Accepted Answer

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.

Question 9

Under liquidity preference theory,which of the following is always true?

Accepted Answer

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 long periods forward rates are raised relative to what expected future short rates would predict.

Question 10

Which of the following is true?

Accepted Answer

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.

Question 11

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?

Accepted Answer

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.

Question 12

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.

Accepted Answer

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.

Question 13

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?

Accepted Answer

To find the one-year continuously compounded zero rate, we first need to determine the bond's yield to maturity using the given price and coupon rate. Then, convert this yield to a continuously compounded rate. The bond's cash flows are discounted using the semiannual zero rate to find the yield, which is then converted to a continuously compounded rate.

Question 14

An interest rate is 5% per annum with continuous compounding.What is the equivalent rate with semiannual compounding?

Accepted Answer

The equivalent rate with semiannual compounding is 2×(e^0.05/2−1)= 0.0506 or 5.06%.

Question 15

A repo rate is

Accepted Answer

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.

Question 16

An interest rate is 12% per annum with semiannual compounding.What is the equivalent rate with quarterly compounding?

Accepted Answer

The equivalent rate with quarterly compounding is 11.83%. This is because the effective annual rate is the same regardless of the compounding frequency. The effective annual rate is calculated as (1 + (nominal rate / number of compounding periods))^number of compounding periods - 1. In this case, the nominal rate is 12%, the number of compounding periods is 2 (for semiannual compounding) or 4 (for quarterly compounding), and the effective annual rate is (1 + (0.12 / 2))^2 - 1 = 12.25% or (1 + (0.12 / 4))^4 - 1 = 12.25%.

Question 17

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?

Accepted Answer

The forward rate accentuates trends in the zero curve.The par yield shows the same trends but in a less pronounced way.

Question 18

An interest rate is 6% per annum with annual compounding.What is the equivalent rate with continuous compounding?

Accepted Answer

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

Question 19

Which of the following is true of LIBOR

Accepted Answer

LIBOR is a rate used for interbank transactions.

Question 20

Which of the following is true of the fed funds rate

Accepted Answer

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 what is termed the fed funds rate to rectify this.

Quiz 4: Interest Rates