Question

Define and discuss the followings:

a) YTM vs. HPR

b) Call provision vs. Sinking fund provision

c) Nominal yield, current yield, YTM, and YTC

d) Price-yield relationship

e) How to annualize a bi-weekly return?

f) Bond Duration and types of Duration

g) Features of Macaulay’s Duration Measure

h) Term Structure of Interest Rate and Term Structure Theory

i) Convexity of a Bond

j) Convexity of a Callable Bond[hint: see RB textbook]

k) Immunization Strategy

l) Zero-coupon bond vs. Perpetuity and their duration measures

Answer 1

a) Yield to maturity (YTM) is the total return anticipated on a bond if the bond is held until it matures. Yield to maturity is considered a long-term bond yield but it is expressed as an annual rate. In other words, it is the internal rate of return (IRR) of an investment in a bond if the investor holds the bond until maturity, with all payments made as scheduled and reinvested at the same rate.

Holding period return is the total return received from holding an asset or portfolioof assets over a period of time, generally expressed as a percentage. Holding period return is calculated on the basis of total returns from the asset or portfolio (income plus changes in value). It is particularly useful for comparing returns between investments held for different periods of time.

b) A call provision is a provision on a bond or other fixed-income instrument that allows the original issuer to repurchase and retire the bonds. If there is a call provision in place, it typically comes with a time window under which the bond can be called, with a specific price to be paid to bondholders, and any accrued interest defined within the provision.

A provision in some bond indentures requiring the issuer to put money aside to repay bondholders at maturity. Inbonds with such a provision, a fund or account is set up into which an issuer deposits money on a regular basis torepay the bond when it matures.

c) A nominal yield is the coupon rate on a bond. The nominal yield is the interest rate (to par value) that the bond issuer promises to pay bond purchasers. This rate is fixed, applies to the life of the bond, and is sometimes referred to as nominal rate, coupon yield or coupon rate.

Current yield is an investment's annual income (interest or dividends) divided by the current price of the security. This measure looks at the current price of a bond instead of its face value. Current yield represents the return an investor would expect if the owner purchased the bond and held it for a year, but current yield is not the actual return an investor receives if he holds a bond until maturity.

d) This is why the famous statement that a bond’s price varies inversely with interest rates works. When interest rates go up, bond prices fall in order to have the effect of equalizing the interest rate on the bond with prevailing rates, and vice versa. Another way of illustrating this concept is to consider what the yield on our bond would be given a price change, instead of given an interest rate change. For example, if the price were to go down from $1,000 to $800, then the yield goes up to 12.5%. This happens because you are getting the same guaranteed $100 on an asset that is worth $800 ($100/$800). Conversely, if the bond goes up in price to $1,200, the yield shrinks to 8.33% ($100/$1,200)