Question 1

The value of a bond measured at a duration date will vary with a change in the yield.

Accepted Answer

Duration is a measure of the 'pivotal time to maturity' of a bond,or bond portfolio.Assuming the yield curve is flat,and allowing a one-off parallel shift in the yield curve,the value of the bond measured at the duration time will not vary with the shift in the yield curve.

Question 2

Given a bond with a duration measure of 2 and a convexity measure of 3.5,then the approximate percentage change in price predicted from a proportional change in 1 plus the yield of 0.005 (i.e.(1 + y))is 0.991%.

Accepted Answer

Using equation 6.12,page 178,the percentage change in bond price ² = -0.00991 or 0.991%.Hence the answer is true.

Question 3

Index-linked bonds are necessarily linked to the Consumer Price Index.

Accepted Answer

CPI-linked bonds work by giving protection against inflation to investors by providing a set level of real return.The most common form of these securities is capital-indexed bonds.

Question 4

Calculate the price of a coupon-paying bond maturing in 15 years,where the bond has a face value of $100 000,yield of 7% p.a.and coupon rate of 9% p.a.Assume interest rates are paid half yearly.

Accepted Answer

Using the bond pricing formula,equation 6.1,with N = 30 periods,i = 3.5%,c = 4.5% and FV = $100 000,gives a value of $118,392.

Question 5

Suppose a two-year 9% p.a.bond with a face value of $100 000 has a yield of 8% p.a.What is the price of this bond provided it pays semi-annual coupons?

Accepted Answer

According to equation 6.1,,the price of the bond mentioned in the question can be found as follows: P = 4500/(1.04)+ 4500/(1.04)² + 4500/(1.04)³ + 104500/(1.04)⁴ = $101 814.95.

Question 6

What is the purchase price of a bond bought on 1 March 2005,paying semi-annual coupons of 6.0% p.a.and maturing on 15 June 2007? The coupons are paid on 15 June and 15 December each year,and each compounding period has 181 days.The bond has a face value of $100 000 and a yield of 7% p.a.

Accepted Answer

Using equation 6.6,and the information provided in the question,we can find the purchase price of this bond as follows: [3000/(1.035)+ 3000/(1.035)² + 3000/(1.035)³ + 3000/(1.035)⁴ + 1033000/(1.035)⁵] F1F1F1S1F1F1F10 (1.035)^75/181 = $99145.75.

Question 7

Calculate the price of a coupon-paying bond maturing in two years,where the bond has a face value of $100 000,yield of 6% p.a.and coupon rate of 8% p.a.Assume interest rates are paid half yearly and the last coupon payment has just been made.

Accepted Answer

The price is the sum of the present value of four coupon payments of $4000,plus a single payment of $100 000 after four periods.The PV of each period's cash flows is $3883,$3770,$3661,$92403 = $103717.Note: The periodic discount rate is 3%.

Question 8

Calculate the convexity (measured in six-monthly periods)for a coupon-paying bond maturing in two years,where the bond has a face value of $100 000,yield of 5% p.a.and coupon rate of 7% p.a.Assume interest rates are paid half yearly and the last coupon payment has just been made.

Accepted Answer

Using equation 6.11,we can find the convexity of the bond.The bond will have periodic cash flows of $3500 for three periods,the last cash flow being $103 500 in period four.The weights of the PV of these cash flows are 0.0329,0.0321,0.0313 and 0.904.Multiplying each by t (t + 1)periods and then halving the obtained value gives a convexity of 9.35.

Question 9

Bond A has a price of $97 635 and a duration of 1.93.Bond B has a price of $54 696 and has a duration of 3.46.Calculate the duration of a portfolio comprised of one of Bond A and one of Bond B.

Accepted Answer

The duration of the portfolio is the market value weights of each bond F1F1F1S1F1F1F10 the duration of each bond.In this case,the market value of the bond portfolio is (97635 F1F1F1S1F1F1F10 1)+ (54696 F1F1F1S1F1F1F10 1)= $152331.The weight of the Bond A holding is 97635/152331 = 0.6409,and the weight of the Bond B holding is 54696/152331 = 0.3591.The duration of the portfolio is therefore 0.6409 F1F1F1S1F1F1F10 1.93 + 0.3591 F1F1F1S1F1F1F10 3.46 = 1.2369 +1.2425 = 2.4794.

Question 10

Duration is a concept that is useful in assessing a bond's credit risk.

Accepted Answer

Duration is a concept that is useful in assessing a bond's price volatility

Question 11

Duration takes into account the non-linearity in the relationship between bond price and yield.

Accepted Answer

Duration is essentially the negative of the elasticity of bond price with respect to yield,and so the duration measure can also be used to estimate the effect on the bond price by a change in yield.The level of accuracy decreases with the size of the change in the yield because the relationship between price and yield is not linear,while the elasticity approximation assumes that this relation is linear.

Question 12

Consider a bond with a current price of $98 320,a duration measure of 2 and a convexity measure of 3.5.The approximate dollar change in price predicted from proportional change in 1 plus the yield (i.e.(1 + y))of 0.005 is more than $1000.

Accepted Answer

Using equation 6.12,page 178,the percentage change in bond price ² = -0.00991 or 0.991%.The dollar change in the price is $98320 F1F1F1S1F1F1F10 0.00991 = $974.35.Since this is less than $1000,the statement is false.

Question 13

The common type of bonds involves varying coupon payments over time.

Accepted Answer

Bonds such as indexed bonds provide an example of coupon payments that change with changes in the CPI.However,the more common type of bond involves fixed coupon payments,and for these bonds the quoted yield is the internal rate of return for the bond.

Question 14

Calculate the price of a coupon-paying bond maturing in two years,where the bond has a face value of $100 000,yield of 7.5% p.a.and coupon rate of 7.5% p.a.Assume interest rates are paid half yearly and the last coupon payment has just been made.

Accepted Answer

The price is the sum of the present value of four coupon payments of $3750,plus a single payment of $100 000 after four periods.The PV of each period's cash flows is $3614,$3484,$3358,$89544 = $100000.Note: The periodic discount rate is 3.75%.

Question 15

When estimating a price change for a bond due to a change in the yield,incorporating convexity does not improve the estimate.

Accepted Answer

The characteristic of convexity arises from the non-linear relationship between yield and prices.Knowledge of convexity increases the accuracy of price change prediction given changes in the yield.

Question 16

For index-linked bonds,which of the following changes in alignment with the CPI?

Accepted Answer

CPI-linked bonds tend to be issued by government authorities,and work by giving protection against inflation to investors by providing a set level of real return.The most common form of these securities is the capital-indexed bonds.Each year,the redemption or face value of the bond is indexed upward by the rate of inflation.As coupons are paid on the face value of the bond,the coupons are similarly indexed upward.

Question 17

Calculate the duration (measured in six-monthly periods)for a coupon-paying bond maturing in two years,where the bond has a face value of $100 000,yield of 7% p.a.and coupon rate of 9% p.a.Assume interest rates are paid half yearly and the last coupon payment has just been made.

Accepted Answer

According to equation 6.9,we can determine the duration of the bond.The bond will have periodic cash flows of $4500 for three periods,the last cash flow being $104 500 in period four.The weights of the PV of these cash flows are 0.041,0.039,0.038 and 0.839.Multiplying each by the time period each occurs gives a duration of 3.48.

Question 18

Call risk refers to the uncertainty associated with future reinvestment rates.

Accepted Answer

Reinvestment risk refers to the uncertainty associated with future reinvestment rates.Call risk refers to the likelihood that the call provision,found in corporate bond issues,will be exercised.

Question 19

The following statement,"investors must forgo some yield when compared with straight bonds because of the lower risk,and the market should price these accordingly",refers to index-linked bonds.

Accepted Answer

CPI-linked bonds tend to be issued by government authorities,and work by giving protection against inflation to investors by providing a set level of real return.The most common form of these securities is the capital-indexed bonds.Each year,the redemption or face value of the bond is indexed upward by the rate of inflation.

Question 20

Suppose a 5 year 8% p.a.bond with a yield of 6.5% and principal of $100 000 pays coupon payments semi-annually.What is the present value of this bond?

Accepted Answer

Using equation 6.4,and the information provided in the question,the present value of this bond is P = 4000[(1-(1.0325)^-¹⁰)/0.0325] + 100 000/(1.0325)¹⁰ = $106,316.80.

Quiz 6: Bonds