STAT2032 Chap.6 Fixed Interest Securities
Fixed Interest Securities
A fixed interest security is valued from promised cash flows, not from its label. A coupon bond combines a level coupon stream with a redemption payment, each discounted at a yield expressed for the coupon period. Price, face value and redemption value can differ, and their roles must remain distinct.
The chapter uses the inverse price-yield relationship to diagnose premium and discount results, then considers valuation between coupon dates, optional redemption, inflation-linked amounts and tax-adjusted receipts without losing the underlying cash-flow schedule.
Face value determines coupon amount, redemption value is paid at maturity and price is what the investor pays now. Yield discounts the promised receipts.
When coupon and yield are quoted on different bases, convert yield to the coupon period before counting discount powers. For a bond redeemable at par, a required yield above the coupon rate produces a discount price; a required yield below the coupon rate produces a premium. This direction should be predicted before evaluating an annuity expression.
Dates between coupons require an explicit fraction of a coupon period.
Start with the value just after the previous coupon and accumulate across the elapsed fraction, while keeping any clean or dirty convention separate. Optional redemption creates several possible schedules, so an investor protecting a minimum yield compares the prices associated with every permitted issuer choice.
Tax and inflation alter the actual receipts or the valuation basis and should be written into the cash-flow row before discounting. Running yield, gross redemption yield and net yield answer different questions and cannot be substituted merely because each is reported as a percentage.
What this chapter covers
- 01
Coupon and redemption cash flows
- 02
Yield per coupon period
- 03
Premium and discount bonds
- 04
Valuation between coupon dates
- 05
Optional redemption dates
- 06
Inflation and tax adjustments
Worked example · free
Price a bond at a required yield
- 1The half-year yield is (1.07)^(1/2) - 1 = 0.034408.
- 1There are ten coupons of $30 and a final redemption of $1,000.
- 1Write P = 30a for ten periods at j + 1000v^10.
- 1Evaluation gives P = $963.23.
- 1The periodic yield exceeds the coupon rate, so a price below par is expected.
Key terms
- Face value
- The reference amount used to calculate coupon payments under the stated coupon rate.
- Redemption value
- The amount repaid by the issuer at the applicable maturity or redemption date.
- Coupon rate
- The rate applied to face value to determine the coupon paid in each stated period.
- Yield to maturity
- The periodic or annualized return that equates price with the value of promised coupons and redemption.
Fixed Interest Securities FAQ
Why does a higher yield produce a lower bond price?
The promised coupons and redemption do not change when the required yield changes. A higher yield applies stronger discounting to each positive future cash flow, so their present values fall and the price falls. The relationship is inverse and curved because cash flows at different dates receive different powers of the discount factor.
How can I identify a premium bond before calculating?
For redemption at par with ordinary positive coupons, compare the coupon rate per payment period with the required yield for that same period. A coupon rate above yield makes the cash flows attractive relative to the market requirement, so price is above par. A coupon rate below yield implies a discount.
What changes when redemption is optional?
Each permitted redemption date creates a different cash-flow schedule and therefore a different price at the required yield. If the issuer controls the date, protect the investor's target by considering the date that is least favourable to the investor under the contract. Do not average maturities or treat the option as a change to coupon rate.
Why are face value and price different quantities?
Face value is the reference amount used to calculate coupons, while price is the present value paid by the investor for all promised receipts. Market yield can place price above or below face. Redemption value is a third quantity and must also be stated rather than assumed to equal either of the others.
Exam move
Write bond questions as literal cash-flow lists before compressing them into annuity notation. Separate face value, coupon amount, price and redemption amount on the page so one symbol cannot silently change meaning. Convert the quoted yield to the coupon period and count coupon intervals, not calendar labels. Predict premium, par or discount from the coupon-yield comparison, then use that prediction to audit the result.
Reprice the same bond at three yields to observe the inverse curved relationship. For a date between coupons, state the exact valuation instant and distinguish the full value from any accrued-interest convention used in the exercise. When redemption is optional, write one schedule for each allowed date. Add tax or inflation by changing actual receipts first, rather than applying a vague adjustment to the final price.
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