YTM/ YTC

Market Price of Bond

1. Determined by the demand and supply of a bond 2. Demand and supply are affected by the state of the economy, nature of the borrower, taste of the investor, etc

current yield ignores

1. The current yield calculation takes into account only the coupon interest and no other source of return that will affect an investor's yield. 2. The time value of money is also ignored. 3. Interest on interest from reinvesting coupon payments is ignored

The yield-to-call measure is subject to the same problems as the yield to maturity because it assumes that the:

1. bond will be held until the first call date 2. coupon interest payments will be reinvested at the yield to call

The YTM is a promised yield because at the time of purchase ONLY IF

1. the coupon payments can be reinvested at the yield-to-maturity 2. The risk that an investor faces is that future reinvestment rates will be less than the yield-to-maturity at the time the bond is purchased, i.e., reinvestment risk. -- the bond is held to maturity. -- If the bond is not held to maturity, investors may face interest-rate risk.

YTM for Zero Coupon Bond

A zero-coupon bond is characterized by a single cash-flow resulting the yield y=([CFn/p]^(1/n))-1 where y is the yield, CFn is the cash flow that occurs in n periods, and P is today's value and n is the number of periods.

if example is done semi annually, then

C($)=30 FV=1000 NPER=36 Price=700.89 then multiply by 2

example: The YTM for an 18-year, 6% coupon bond selling for $700.89 per $1,000 par value is

C($)=60--> 0.06x1000 FV= 1000 NPER= 18 Price= 700.89 =rate(nper,pmt,-pv,fv) = rate(18, 60, -700.89,1000) pmt= coupon rate x face value

We computed the current yield and yield-to-maturity for an 18-year, 6% coupon bond selling for $700.89. Suppose that this bond is first callable in five years at $1,030. The cash-flows for this bond if it is called in five years are

EXCEL: RATE(10,30,-700.89,1030)=7.6% the yield-to-call on a bond-equivalent basis is 15.2%=7.6%*2

YTM (zero coupon) excel formula

On the coupon dates: Use the Rate() function On any other date: Use the Yield() function. YIELD(settlement,maturity,rate,pr,redemption,frequency,basis)

yield to call (YTC)

The yield to call assumes that the issuer will call the bond at some assumed call date and the call price is specified in the call schedule. P= (C/1+y)+ (C/((1+y)^2)).... (CF/((1+y)^n*))+(M/((1+y)^n*)) where M * = call price (in dollars) and n* = number of periods until the assumed call date (number of years times 2)

YTM

The yield to maturity is the interest rate that will make the present value of the cash flows equal to the price (or initial investment). P= (CF/1+y)+ (CF/((1+y)^2))+ (CF/((1+y)^3)).....

Difference between rate equations in YTM and YTC

YTM---> =rate(nper,pmt,-pv,fv) YTC---> =rate(nper where bond is called, pmt,-pv, fv when bond is called) the only things that change are number of periods and future value

The current yield, The yield to maturity, Yield to call,Yield to worst.

are all expressed as a percent

The yield-to-maturity for a zero-coupon bond selling for $274.78 with a maturity value of $1,000, maturing in 15 years, is

calculate the rate: C($)= 0-- bc its zero coupon FV= 1000 Price= -274.78 NPER= 30-- not 15 bc it is semi =rate(nper,pmt,pv,fv) =rate(30,0,-274.48,1000)= 4.41% multiply by 2 to get annual-- 4.41x2= 8.81

Yield to Worst

compute the yield-to-call and yield-to-maturity for a callable bond selling at a premium, and select the lower of the two as a measure of potential return. out of YTM and YTC, whichever one has lower return is YTW

Current yield relates the annual coupon interest to the market price.

current yield = annual dollar coupon interest/price

example of current yield: The current yield for an 18-year, 6% coupon bond selling for $700.89 per $1,000 par value is

current yield=(0.6 ×1000)/700.89 =0.0856, 8.56% per year

YTM Finra Example

settlement date= 2/15/19 maturity date= 11/15/22 rate= 9.455% price=121.838-- doesn't need to be negative redemtion= 100--- always 100 frequency= 2---- semi basis= 0 =YIELD(settlement,maturity,rate,pr,redemption,frequency,basis) =yield(settle,maturity,9.455,121.838,100,2,0)= 3.22