Let’s say that an investor has purchased a 6-year 8% semi-annual coupon bond. Bond details are, Settlement date 01/Feb/2016, Maturity 01/Jan/2022,Bond Face Value 83,000/=,Purchase yield 10.1737%. Basis-actual/360. I want to check whether my calculation steps are in order and answers for below 3 situations in order to understand the reinvestment risk properly. Calculation steps, PRICE = 90.50002 ----> PRICE(01/Feb/2016,01/01/2022,8%,10.1737%,100,2,1) Number of coupons = 6*2=12 Coupon Income = 83000*4%*12 = 39,840/= Future dollar value of all cash flows= 83,000*(1+0.04)^12 = 132,886/= This value is made up of 83,000/= principal return and 49,886/= (132,886-83,000) of the total dollar return from coupon and reinvestment income. If there was no reinvestment income then the coupon income would be 39,840/=. Then the balance 10,046/= (49886-39,840) is earned from reinvestment income. Therefore this is the money which is earned by investing the periodic coupon payments. 1.At what rate this 10,046/= is earned? 8% ? 2.Suppose after one year 5 year market interest rates have come down to 2%, how much is the reinvestment risk? 3.Suppose now the market yield is 13% then whats the impact to reinvestment risk from marking to market loss?
Just a quick point (rather than answering your questions one by one) is that reinvestment income is gained at the rate prevailing in the market at the time…which sounds like the 10.17%…the coupons aren’t reinvested at the coupon rate.
So you ned to calculat the value of an 8% semi-annual coupon, reinvested at the 10.17% rate available in the market. If the reinvestment rate falls to 2%, obviously those cash flows will be worth less, but the price of the bond will have risen to potentially offset the loss in reinvestment income.
The reinvestment risk is the difference in price between the cash flows reinvested at different prevailing market rates. Price risk is the change in price of the bond experienced due to those changes in prevailing market rates.
Hi S666,Thanks I got your point, Yes you are correct,10.17% is the market rate at the time of purchasing the bond.
Can I consider the net of following 1 & 2 as reinvestment risk,
difference between money received by investing all future coupons at 10.17% and 2% -----(1)
capital gain/loss arisen due to decrease/increase in mkt yields-----(2)
But in this example increase in bond price due to decrease in mkt rates will offset the losses arising from investing coupons at 2%.
But if I keep the bond untill maturity,there will not be any capital gain/loss, Then there will only be reinvestment risk due to investing at lower 2% rate.am i right?
Can I consider investing coupons at 10.17% untill maturity as ordinary annunity to calculate the money received ?