University:
California State University, Northridge
Course:
FIN 462 | Fixed Income Securities
Academic year:

2024
Views:

247

Pages:

15
Author:

Zander Ortega

FIXED INCOME CONCEPTS Key Features of a Bond  Par value – face amount of the bond, which is paid at maturity (assume $1,000).  Coupon interest rate – stated interest rate (generally fixed) paid by the issuer. Multiply by par to get dollar payment of interest.  Maturity date – years until the bond must be repaid.  Issue date – when the bond was issued.  Yield to maturity - rate of return earned on a bond held until maturity (also called the “promised yield”)  Some bonds are callable  Call provision: Allows issuer to refund the bond issue if rates decline (helps the issuer, but hurts the investor) What is the value of a 10-year, 10% annual coupon bond, if rd (discount rate)= 10%? 0 VB = ? rd 1 2 100 100 ... n 100 + 1,000 $100 $100 $1,000 + ... + + VB = 1 10 (1.10) (1.10) (1.10)10 VB = $90.91 + ... + $38.55 + $385.54 VB = $1,000 Fixed Income Security Risk  Default risk, or credit risk, is the possibility that a borrower will be unable to repay principal and interest as agreed upon in the loan document.  Reinvestment rate risk refers to the possibility that the cash coupons received will be reinvested at a rate different from the bond’s stated rate.  Interest rate risk refers to the chance of loss because of adverse movements in the general level of interest rates. What is the Yield-to-Maturity or cost of debt capital?  A discount rate (rd )/cost of debt capital and the expected return for the debt holder if the investor holds the bond until the maturity rd = r* + IP + MRP + DRP + LP r* = real risk free rate IP = inflation premium (rate) MRP = maturity risk premium DRP = credit risk premium LP = liquidity premium What is interest rate (or price) risk?  Interest rate risk is the concern that rising rd will cause the value of a bond to fall. % change +4.8% -4.4% 1 yr $1,048 $1,000 $956 rd 5% 10% 15% 10yr $1,386 $1,000 $749 % change +38.6% -25.1% The 10-year bond is more sensitive to interest rate changes, and hence has more interest rate risk. What is reinvestment rate risk?  Reinvestment rate risk is the concern that kd will fall, and future CFs will have to be reinvested at lower rates, hence reducing income. EXAMPLE: Suppose you just won $1,000,000 playing the lottery. You intend to invest the money and live off the interest.  If you choose to invest in series of 1-year bonds, that pay a 8% coupon you receive $80,000 in income and have $1,000,000 to reinvest. But, if 1-year rates fall to 3%, your annual income would fall to $30,000.  If you choose a 30-year bond that pay a 10 % coupon you receive $100,000 in income; you can lock in a 10% interest rate, and $100,000 annual income for 30 years Interest Rate Risk : Malkiel’s Theorems  Malkiel’s theorems are a set of relationships among bond prices, time to maturity, and interest rates.  Theorem One : Bond prices move inversely with yields.  Theorem Two : Long-term bonds have more risk.  Theorem Three : Higher coupon bonds have less risk. Interest Rate Risk : Malkiel’s Theorems  Bond A : matures in 8 years, 9.5% coupon Bond B : matures in 15 years, 11% coupon Which price will rise more if interest rates fall?  Apparent contradictions can be reconciled by computing a statistic called duration. Duration  For a noncallable security, duration is the weighted average time until a bond’s cash flows are received.  Duration is not limited to bond analysis. It can be determined for any cash flow stream.  Duration is a direct measure of interest rate risk. The higher it is, the higher is the risk. Duration Measures  Macaulay duration is the time-value-of-moneyweighted, average number of years necessary to recover the initial cost of the security. N ∑ D= Ct t = 1(1 + R) P t ×t where D = duration Ct = cast flow at time t R = yield to maturity (per period) P = current price of bond N = number of periods until maturity t = period in which cash flow is received Duration Measures  Modified duration measures the percentage change in bond value associated with a one-point change in interest rates. 2C 2 dP 1 NC N  1 − 1  C1 ⋅ ⋅ = + ++  N  1 2 dR P (1 + R )  (1 + R ) (1 + R ) (1 + R )  P Dmodified DMacaulay = 1+ R 2 ( ) price Problems with Duration  yield to maturity The bond price - bond yield relationship is not linear.  Graphically, duration is the tangent to the current point on the price-yield curve. Its absolute value declines as yield to maturity rises.  Duration is a first derivative statistic. Hence, when the change is large, estimates made using the derivative alone will contain errors. Convexity  Convexity measures the difference between the actual price and that predicted by duration, i.e. the inaccuracy of duration.  The more convex the bond price-YTM curve, the greater is the convexity. 1 N t (t + 1)C t N ( N + 1)F + Convexity = ∑ t +2 N +2 P t =1 (1 + R ) (1 + R ) bond price Using Convexity yield to maturity  No matter what happens to interest rates, the bond with the greater convexity fares better. It dominates the competing investment.

Fixed Income Concepts

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