Problem: An investor is considering one of the newly issued 10 year AAA corporat

Question

Problem: An investor is considering one of the newly issued 10 year AAA corporate bonds of $100 face value shown in the following table (bonds pay coupons annually): Description Coupon Rate Price PuttablePut Price XYZ RST 4.00% 4.00% 100 nputtable 100 N/A 98 Currently puttable A: Suppose that market interest rates increase by 100 basis points (1%). Contrast the effect of this increase on the price of each bond B: Should the investor prefer the RST bond over the XYZ bond when rates are expected to rise or to fall? C: What would be the effect, if any, of an increase in the volatility of interest rates on the prices of cnch boad?

Explanation / Answer

If price is same as par value, ytm must be the coupon rate,i.e, 4%

Now lets say rates rise by 100 bps to 4+1=5%

C1=C2=C3=C4=C5=C6=C7=C8=C9=C10=Coupons=100*4%=4

FV=100

So, Price of XYZ=4/1.05+4/1.05^2+4/1.05^3....+4/1.05^9+104/1.05^10=92.27

Price of RST would be max(98,92.27)=98 because if interest rates rise, future value of coupons will become less valuable and investor can sell the bonds back to issuer & can lend/reinvest elsewhere at a higher rate. So, price of XYZ will fall more than RST because RST will have a lower limit of selling price of 98

In case of rate rise, there would be no difference in both but in case of rates fall, XYZ would fall more than RST hence in case of rate rise, investor is indifferent but in case of rae fall, investor would prefer RST

Puttable Bond=Straight Bond+Put option

As put option would increase in value with increase in volatility, so price of pttable bond,i.e,RST would increase. But there would be no effect of volatility on straight bond ,i.,, XYZ

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