Week 10 Bonds Flashcards
What is YTM?
- Defined as the interest rate that makes the present value of a bond’s payments equal to its price –> a measure of the average rate of return that will be earned on a bond if it’s bought new and held to maturity
- YTM is a 6-month rate
- YTM is the average per period return if the bond is held to maturity and if the coupons are reinvested a the YTM
Current Yield vs. Coupon Rate vs. YTM
- coupon rate: interest rate paid to bondholder
- current yield: the return you will earn if you hold for a period of one year
- YTM: the return you will earn if you hold a bond until it matures. The YTM assumes all coupon payments are reinvested at YTM
Coupon Rate < YTM
Discount to Face Value
Let’s say interest rates rise, the fixed coupon rate will be less valuable as it isn’t commensurate with the higher interest rate risk level, causing price to go down and trade at a discount.
Coupon Rate > YTM
Premium to Face Value
How are long-term ZCBs created?
Longer term ZCB are commonly created from coupon bearing notes and bonds. A bond dealer who purchases a Canada coupon bond and separates the cash flows into a series of independent securities, where each security is a claim to one of the payments of the original
What is the YTM of a ZCB?
YTM is the spot rate
What is the spot rate?
- The rate that prevails today for a time period corresponding to the zero’s maturity
- if you know the spot rate, you can price any set of diskless cashflows
P = CF1/(1+r1) + CF2/1+r2^2 + CF3/1+R3^3
What is the yield curve
plots the YTM of ZCB as a function of bond maturity
Flat yield curve
Period of strong global economic growth and tightening of monetary policy
Steep upwards yield curve
Banks kept short-term rates low to stimulate growth, emerging from recession
Normal upward slope yield curve
More normal, banks removed monetary stimulus and increased short-term rates
Inversion
Negative slope, investors might be selling off their stocks and moving money to bonds; lost confidence in the economy and believe the merger returns of bonds offer better opportunity than losses of stocks
What determines the slope of the yield curve?
- the upward sloping yield curve is evidence that short-term rates are expected to be higher next year than they are now
- yield curve reflects the markets assessment of coming interest rates
- the yield or spot rate on a long-term bond reflects the path of short rates anticipated by the market over the life of the bond
What is the forward rate?
- The forward rate is the rate that you can contract on today to lend in the future
- It is the break-even future interest rate that would equate the total return from a rollover strategy to that of a longer term zero coupon bond
Two primary explanations of the upward sloping yield curve
- expectations hypothesis
- liquidity premium hypothesis
What is the expectations hypothesis?
- The theory states that the forward rate equals the market consensus expectation of future short-term rates
- the slope of the yield curve is due entirely to expectations about future interest rates –> if the yield curve is upward sloping it must be because investors believe future interest rates will rise
- under expectations hypothesis, forward rates equal expected future interest rates
- the long-term yield of a financial instrument is the average of the short-term yields that are expected to occur over the life
(1+y2)^2 = (1+r1)(1+E(r2))
What is the liquidity premium hypothesis?
- the liquidity preference theory maintains that short-term investors dominate the market; thus, in general, the forward rate exceeds the expected short-term rate. In other words, investors prefer to be liquid vs. illiquid and will demand a premium to go long-term.
- readily explains upward sloping yield curve, BUT not other shapes
- short term investors unwilling to hold LT bonds unless the f2>E(r2). LT investors unwilling to hold short term bonds unless E(r2) > f2. Both groups of investors requires a premium to hold bonds with different maturities from their investment horizons. Advocates believe short-term investors dominate the market, f>E(r), excess is the liquidity premium
Duration
Duration measures the average maturity of the bonds promised cash flows
Macaulay’s Duration
the weighted average of the times to receive all payments –> the weight associated with each payment should be related to the “importance” of that payment to the value of the bond
5 Duration Rules
1: duration of a ZCB is its maturity
2: holding maturity constant, a bond’s duration is lower when the coupon rate is higher
3: holding coupon rate constant, a bond’s duration is higher when it’s TTM is higher
4: holding all constant, a higher YTM decreases maturity. Duration of a coupon bond is higher when the bond’s YTM is lower
5: duration of a perpetuity is. (1+y)/y
