You buy a bond, reinvesting coupons at the Yield to Maturity. How much do you pay? Bond Value = B { 1/(1+R)N + (Cr/R) (1 - (1+R/m)-mN)} Years to Maturity:   N = years Annual Coupon Rate:   Cr = %   as a percentage of the Maturity Value Coupons per Year:   m = Bond Value at Maturity:   B = $ Current Yield:   R = %   expressed as a percentage Bond Value = $

You buy a bond for a particular price, reinvesting coupons at the Yield to Maturity. What IS the YTM? Current Price = B { 1/(1+R)N + (Cr/R) (1 - (1+R)-N)} ... solved for R (which ain't easy) Years to Maturity:   N = years Annual Coupon Rate:   Cr = %   assuming a single annual coupon Bond Value at Maturity:   B = $ Current Price = $ Yield to Maturity:   R = %

You buy a bond for a particular price $A, reinvesting coupons at some arbitrary rate I. What is your annualized return? A(1+R)N = B {1 + (Cr/I) ((1+I)N - 1} ... solved for R (which is easy, this time) Years to Maturity:   N = years Annual Coupon Rate:   Cr = %   assuming a single annual coupon Coupons invested at:   I = %   just in case it's something different from the YTM Bond Value at Maturity:   B = $ Bond Price:   A = $ Return on Investment:   R = %

If there's a 1% DECREASE in YTM, what's the percentage INCREASE in Bond Price? (approximately) Macauley Bond Duration: BD = (1+y)/y - {1+y + n(c-y)} / {c[(1+y)n - 1] + y} Yield per coupon period:   y =%   for 2 periods per year, divide annual yield by 2 to get the yield per period !! Number of periods to Maturity:   n =   for 3 periods per year, multiply years to maturity by 3 to get the number of periods!!! Coupon Rate per period:   c =%   for 4 periods per year, divide the annual coupon rate by 4 to get the rate per period!!!! Macauley Duration =   which gives the (approximate) percentage increase in Bond Price for a 1% decrease in Yield

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See also Bond Stuff