Question 1 - Introduction to the bond market and bonds & Pricing of bonds

a)

(i) Explain why the amortization feature increases the reinvestment risk of a bond issue.

Reinvestment risk is the possibility of a decrease in future market interest rates and hence the intermediate cashflows being reinvested at a lower interest rate than the  initial yield of the bond.

In an amortizing bond, the bondholder will be paid a coupon as well as part ofthe      principal (face value) as the periodic cash flow during the life of the bond. Also, the    periodic cash flows will be on monthly basis rather than on semi-annual basis with a non-amortizing bond. Therefore, the need to reinvest monthly and the need to invest larger periodic cashflows increases the reinvestment risk of an amortizing security.

(2 marks)

(ii) Explain credit-spread risk and its impact on a bond portfolio?

The credit-spread is the difference in the yield of a corporate bond over and above the   yield of a treasury bond of the same maturity. This yield spread will compensate for the credit risk of the corporate bond issuer. Credit-spread risk is the possibility of a               widening of the credit-spread of a corporate bond due to a decline in the credit quality  of the bond after the issuance.

If the credit-spread widens, the corporate bond yield will increase and this will lead to a decrease in the value of the bond portfolio.

(2 marks)

b) What is the advantage of a put provision for the bondholder?

A put provision gives the bondholder the right to sell the bond back to the issuer at par value on designated dates. When market interest rates are higher, the bondholder can  sell an existing issue with a lower yield and can buy a new issue with a higher yield       (market price is lower).

(2 marks)

c)  Consider a bond selling at par  ($1,000) with a  coupon rate  of 8%  p.a. paid semi- annually and 15 years to maturity.

(i) What is the current yield of this bond?

Current yield = 8%

(1 mark)

(ii) Calculate the bond price if the yield changes to 12%.

FV= $1,000, PMT= $40, N=30, i=6% → Price of the bond (PV)= $ 724.70

(2 marks)

(iii) What could be the reason for the change in the bond yield?

i.           Market interest rates would have increased.

ii.          The credit quality of the bond would have decreased. I.e., the credit-spread of the bond has increased.

(1 mark) (Total 10 marks)

Question 2 - Measuring Yield

a) Consider the following cash flows in relation to a debt obligation whose current market

price is $12,560. Calculate the yield offered by this debt obligation.

The yield offered by this debt obligation is the discount rate (r) which satisfies the following equation.

12,560 =   +  +  +  +

Therefore, yield = 11.81 % p.a.

(3marks)

b) Consider a bond that pays 10% semi-annual coupons, has a $100 par value, 30 years to maturity and a price of $110. The bond is callable in 10 years at $105. Calculate the following on bond equivalent basis.

(i) Yield to maturity

FV= $100, PMT= $5, N=60, PV = -$110 → i/2 = 4.51%

Yield to maturity (on BE basis) = 4.51*2 = 9.02%

(2 marks)

(ii) Yield to call

FV= $105, PMT= $5, N=20, PV = -$110 → i/2 = 4.40%

Yield to first call (on BE basis) = 4.40*2 = 8.80%

(2 marks)

c) State three components of the total return to a bond investor.

i. Periodic coupon income

ii. Coupon reinvestment income

iii. Capital gain/loss realized when the bond matures, is sold or called before maturity.

(3 marks) (Total 10 marks)

Question 3 - Bond Price Volatility

a) Explain why you agree or disagree with the following statements:

(i)  Bond price volatility is higher in a low-interest rate  environment than in a high- interest rate environment.

Agree

This is due to the convexity in the relationship between the bond price and yield changes. For the same amount of yield change, the change in the bond price is larger when interest rates are lower, than when interest rates are higher.

(2 marks)

(ii) For a given term to maturity and initial yield, the price volatility of a bond is greater, the greater the coupon rate.

Disagree

When the bond has large early cashflows, its price sensitivity is lower. This can also be explained by the duration of a bond which is a measurement of bond price volatility. The duration of a bond is smaller when the bond has large early cashflows. Therefore, the price volatility of a bond is lower, the greater the coupon rate.

(2 marks)

b) Bond X has a $1,000 par value, 9% semi-annual pay coupons, a maturity of 5 years and a yield to maturity of 8%. Calculate the following for Bond X.

(i)  Price value of a basis point (PVBP)

Current price of the bond

FV = $1,000, PMT= $45, N=10, i/2=4%  → Price = $ 1,040.55

Price of the bond if yield increases by 1 bp,

FV = $1,000, PMT= $45, N=10, i/2=4.005%  → Price = $ 1,040. 14

Therefore, PVBP = 1,040.55 – 1,040. 14 = $ 0.41 (for $1,000 par value)

(2 marks)

Assume the bond pays an annual coupon for parts (ii) and (iii).

(ii) Macaulay Duration

New bond price:

FV = $1,000, PMT= $90, N=5, i=8%  → drice = $ 1,039.93

Macaulay Duration =  [                        ]

=  4.26

(3 marks)

(iii) Modified Duration

Modified Duration = 4.26/ (1.08) = 3.94

(1 mark) (Total 10 marks)

Question 4 - Factors affecting bond yields and the term structure of interest rates

a) Explain the following terms.

(i) Yield curve

The yield curve is the graphical depiction of the relation between the yield on bonds of the same credit quality but different maturities.

(ii) Theoretical spot rate curve

This is the graphical depiction of the relationship between the yield on a zero-coupon treasury and its maturity.

Because there are no zero-coupon Treasury debt issues with a maturity greater than     one year, it is not possible to construct such a curve solely from observations of market activity on Treasury securities.

Rather, it is necessary to derive this curve from theoretical considerations as applied to the yields of the actually traded Treasury debt securities.

(iii) Par coupon curve

This is the graphical depiction of on-the-run treasury yield necessary to make the issue trade at par, and the maturity ofthe issue.

(3 marks)

b) Explain why you agree or disagree with the following statements.

(i) The benchmark spread of a higher rated bond is always less than a lower-rated bond.