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. |
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