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Title: Markets and Institutions bonds story problem Post by: Nicole1858 on Oct 2, 2022 1. Question 1 (corporate bond seniority). Please note that the stated interest rate does not necessarily
equal expected returns for bonds that may default. Consider one-year bonds issued by Pineapple Inc. If the company does not default, the bond will pay the stated interest plus principal back in one year. If the company does default — which happens with a 10% probability — then the company defaults on all bonds, and bond investors only get R fraction of the principal back (and none of the coupon). R is known as the “recovery rate”. Suppose the company issues two types of bonds: senior and junior bonds. If bankruptcy happens, senior bondholders have higher recovery rates (a) Suppose investors require an expected (average) rate of return of 5%.3 Suppose the recovery rates for senior and junior bonds are R= 70% and R= 30%, respectively. Assume bond interest rates are determined such that all bonds’ expected returns exactly equal 5%.4 What will be the stated interest rates of the senior and junior bonds, respectively? (b) In general, do you expect the stated interest rate on senior bonds to be higher than, equal to, or lower than that of junior bonds? Why? Please justify your answer using explicit arguments. Show your work Title: Re: Markets and Institutions bonds story problem Post by: mononofu_id on Oct 2, 2022 a) 5% = 0.7( x%) + 0 3( x %+ 0.05)
Where x % = returns of the senior bonds And returns for junior bonds will be 5% hihger than senior bonds , so that overall returns to be 5% 5% = x % + 1.5 % ( on exapnsion of brackets) X = 3.5% = return on senior bonds. Return on junior bonds = 3.5 % + 5% = 8.5% This is one of the solution In fact we fix returns of junior bonds is k % higher than that of senior bonds. We get the equation 5 = 0.7 x + 0.3( x + k) 5 = x + 0.3 k By fixing the values of k we get different values for x If we take k = 5 , we get x = 3.5 Since expected returns are 5 % , to counter effect the price fluctuations we can take k = 5 a) Senior bonds have lower returns than junior bonds Senior bonds have higher recovery rate on default , it's returns will be lower than that of junior bonds . It may so happen that senior bonds rates are invested in high security investments, like government bonds , whose returns are low , but capital security is more. So senior bonds have high security of the capital and lower returns and consequently higher recovery rate . Junior bonds have invested in low security investments and there fore it's recovery rate will be low . So it's returns will be higher than that of senior bonds . Title: Re: Markets and Institutions bonds story problem Post by: xcluzive on Oct 4, 2022 Hello, can you show how you got 5 = 0.7x + 0.3(x+k) to 5 = x +0.3k? I am a little confused about part A on what exactly the rates for the senior and junior bonds would be? Thank you!
Title: Re: Markets and Institutions bonds story problem Post by: bio_man on Oct 4, 2022 5% = 0.7(x%) + 0.3(x% + 5)
5 = 0.7x + 0.3x + 1.5% 5 = 1x + 0.15 \(\therefore 5 = x + 1.5\) |