Question

You buy an seven-year bond that has a 5.00% current yield and a 5.00% coupon (paid annually. In one year, promised Vields to maturity have risen to 6.00%. What is your holding period return? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Holding period return < Prey 5 of 5 Next ere to search

Answer 1

	Solution:
		Holding Period Return	0.08	%
	Working Notes:
		Since bond current yield is 5% and it annual coupon is also 5%, its current price must be equals to Par value of Bond. But As bond current yields rises to 6%,the bond current price reduces in one year as its yield now becomes greater than its coupon 5%.
		Holding Period Return
		=(coupon + (price in Y1-current price))/current price
		Current price of the bond = Par value of the bond = $1000
		Now we will calculate bond price in one year
		Bond Price = Periodic Coupon Payments x Cumulative PVF @ periodic YTM (for t= to t=n) + PVF for t=n @ periodic YTM x Face value of Bond
		Coupon Rate = 5%
		Annual coupon = Face value of bond x Coupon Rate = 1,000 x 5% = $50
		YTM= 6% p.a (annual) yield rises from 5% to 6%
		n= no.of coupon = No. Of years remaining x no. Of coupon in a year		(remaining years = 7-1=6)
		= 6 x 1 = 6
		Bond Price = Periodic Coupon Payments x Cumulative PVF @ periodic YTM (for t= to t=n) + PVF for t=n @ periodic YTM x Face value of Bond
		=$50 x Cumulative PVF @ 6% for 1 to 6th + PVF @ 6% for 6th period x 1,000
		= 50 x 4.917324326 + 1000 x 0.70496054
		=$950.8267563
		=$950.826756
		Cumulative PVF @ 6 % for 1 to 6th is calculated = (1 - (1/(1 + 0.06)^6) ) /0.06 = 4.917324326
		PVF @ 6% for 6th period is calculated by = 1/(1+i)^n = 1/(1.06)^6 =0.70496054
		Holding Period Return
		=(coupon + (price in Y1-current price))/current price
		Annual coupon = Face value of bond x Coupon Rate = 1,000 x 5% = $50
		Price in one year = $950.826756                               calculated above
		Current price = $1000 par value
		Holding Period Return
		=(coupon + (price in Y1-current price))/current price
		=(50 + ($950.826756 -1000))/1000
		=0.000826756
		0.0826756%
		0.08%
	Hence	Holding Period Return	0.08	%
	Please feel free to ask if anything about above solution in comment section of the question.