Question

•Describe the price-yield relationship of a fixed rate bond. Illustrate your explanation using changes in yields and the effect on bond prices.

•Explain the concept of duration and convexity. Discuss how bond features like coupon rates, maturities, credit risks, yields, duration, convexity and prices are related.

•What are the limitations of duration and convexity? Suggest ways that can mitigated or overcomethe limitation(s). How do they work?

•What are the types of treasury issues, the term structure of interest rate, risk-free rate, spot rate, forward rate and default or credit risk? How do they affectbond prices

Answer 1

You have asked multiple unrelated questions in the same post. I have addressed the first one. Please post the balance questions separately one by one.

•Describe the price-yield relationship of a fixed rate bond. Illustrate your explanation using changes in yields and the effect on bond prices.

The Price Yield relationship:

The price of the bond is present value of all its future coupon payment and par value repayment at the end of term. The present value is calculated using YTM (yield to maturity) as the discount factor.

An investor part away with the money equal to the price of bond and in turn gets periodic interest payment and a final bullet repayment on maturity.

1. It is a simple three step process:
   1. Estimate all the cash flows expected on a security
   2. Determine the appropriate discount rate
   3. Calculate the present value of the estimated cash flows
2. Formula for finding value of a bond:

where, C_N = coupon payment for year N, YTM = yield to maturity (interest rate), PAR = Face Value of the bond. In case the coupon payment is semi-annually, the coupon rate in the numerator should be halved and the time period used for compounding in the denominator should be doubled.

Alternatively, this can also be written as:

Where: V_B = Value of the Bond; I = Interest received over the course of the bond; PVIFA = PV interest factor annuity; K = discount rate; N = No. of periods; F = Principal or face value of the bond; PVIF = PV interest factor.

Relation between Price & Yield:

• Value of bond moves inversely with the market interest rate or discount rate. If Interest Rates Increase, Price of a Bond Decreases. If Interest Rates Decrease, Price of a Bond Increases.
• Relationship between coupon rate and discount rate:

Sl. No.	Relationship	Valuation
1.	Discount Rate = Coupon Rate	Value of bond = Face Value
2.	Discount Rate < Coupon Rate	Value of bond > Face Value
3.	Discount Rate > Coupon Rate	Value of bond < Face Value

• The longer the time until maturity, the more sensitive the bond price is to changes in interest rates
• In practice most bonds pay interest semi-annually, so we have to find the appropriate semi-annual rate and adjust coupon payments
• The rate of return that the owner of and instrument would earn by holding the instrument until maturity is called the yield to maturity (YTM). YTM of a bond is the discount rate which equates the price of a bond with the PV of its expected future cash flow.
• Bond valuation is the determination of the fair price of a bond. As with any security or capital investment, the theoretical fair value of a bond is the present value of the stream of cash flows it is expected to generate.
• Magnitude of change in market interest rate also influences the value of bond. Greater the change in market interest rate, greater the swing in bond prices.
• Whether the bond is trading at a premium or at a discount, as a bond approaches maturity, its value converges to the par value. As the bond approaches its maturity date, value of bond also approaches its par value (“Convergence” or “Pull to Par”). Pull to Par is the effect in which the price of a bond converges to par value as time passes. At maturity the price of a debt instrument in good standing should equal its par or face value.
• Change in market interest rate also leads to Reinvestment Risk as the interest received from the bonds may invest at a lower coupon rate due to movement in market interest rates.