You purchase a three year, $1,000 face value, semi-annual coupon bond for $950.

Question

You purchase a three year, $1,000 face value, semi-annual coupon bond for $950. The annual coupon rate is 6%. Exactly one year later, you have received two coupons and then sell the bond for $1,050. Coupons receive a 0% reinvestment rate and the timing of the sale occurs so that there is no accrued interest in the price. Assuming that your capital gains tax rate is 15% and your interest income tax rate is 30%, what is the one year, after-tax holding period return for this bond?

You calculate modified duration for a bond to be 6. You then witness a price decline in the market value of this bond to be -1.4% with a corresponding increase in yield of 25 basis points. Find the approximate market derived convexity of this bond.

Explanation / Answer

holding period return= (Price gain + coupon payment) / Purchase price

here the capital gain for 2 bonds is $200 and interest income is $120 @6% per annum

tax on capital gains is 15% and tax on interest earinings is 30%

then the return is

= 200 - (15%)+ 120 - (30%)/ $950

=($170 + $84)/950

= $254/ 950

= 0.267 or 26.7%

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