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Thread: Questions about Bonds

  1. #1
    Actuary.com - Level I Poster
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    Questions about Bonds

    I don't think I'm fully getting the idea of bonds (and how they are paid out)--


    My idea of bonds-
    Person1 buys a 10,000 par bond, coupon (G) 15% for 5 years.
    This means that the cash flows will looks like:
    -10,000, year 1: 1500, year 2: 1500, year 3: 1500, year 4: 1500, year 5: 11,500
    And so Person1's total would be 17,500 (=1500x4+11500)

    And if, instead, I just invested (i) that at 10%, I would've only got:
    10,000(1.1^5)= 16,105.00

    Which means I would get 1,395 more if I invest in a bond (=17500-16105)

    It says -AS A GENERAL RULE- that if i<G, then the bond will cost more. Which makes sense. I would be willing to pay up to 1,394 dollars more (even though if that was the case I'd only make a dollar profit) (1395-1394=1).

    But that doesn't make sense- because if i=14%, then 10,000(1.14^5)= 19,254
    (and in this case i>G)

    Which is more than how much you would earn with the bond.. So NOW you would want to pay less for the bond...which goes against the GENERAL RULE...? No? Am I missing something?

  2. #2
    Actuary.com - Posting Master
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    So you are not discounting coupon payments or the final cash value at all?

  3. #3
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    DON'T FORGET ABOUT TIME MONEY VALUE (TMV)

    To get this cash flow you should invest some amount at time 0 (PV or bond price)
    PV=1500*v + 1500*v^2 + 1500*v^3 + 1500*v^4 + 11500*v^5.

    You can check that, for
    i=10% PV=11895.3934; (bond price is more that 10000)
    i=15% PV=10000; (bond price is equal that 10000)
    i=20% PV=8504.6939 (bond price is less that 10000)

    You can see that this investment matches with 10,000 only when interest rate equals coupon rate. Why?

    What is bond? It is money lending.
    Let say you lend 10000 at i=15%. Bond pays your interest every year.
    year 1: 1500, year 2: 1500, year 3: 1500, year 4: 1500, year 5: 1,500 + return your 10,000. Everybody is happy.

    Let say i=20%, you should get as interest 2000, but bond still pays you every year 1500. Of course, you don't want this deal, so you want pay less.

    Let say i=10%, you should get as interest 1000, but bond still pays you every year 1500. Now, bond owner doesn't want this deal, so you should pay more.

    Therefore, general rule about interest rate and coupon rate.

  4. #4
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    So much for the socratic method...

  5. #5
    Actuary.com - Level I Poster
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    Quote Originally Posted by SerOga View Post
    DON'T FORGET ABOUT TIME MONEY VALUE (TMV)

    To get this cash flow you should invest some amount at time 0 (PV or bond price)
    PV=1500*v + 1500*v^2 + 1500*v^3 + 1500*v^4 + 11500*v^5.

    You can check that, for
    i=10% PV=11895.3934; (bond price is more that 10000)
    i=15% PV=10000; (bond price is equal that 10000)
    i=20% PV=8504.6939 (bond price is less that 10000)

    You can see that this investment matches with 10,000 only when interest rate equals coupon rate. Why?

    What is bond? It is money lending.
    Let say you lend 10000 at i=15%. Bond pays your interest every year.
    year 1: 1500, year 2: 1500, year 3: 1500, year 4: 1500, year 5: 1,500 + return your 10,000. Everybody is happy.

    Let say i=20%, you should get as interest 2000, but bond still pays you every year 1500. Of course, you don't want this deal, so you want pay less.

    Let say i=10%, you should get as interest 1000, but bond still pays you every year 1500. Now, bond owner doesn't want this deal, so you should pay more.

    Therefore, general rule about interest rate and coupon rate.
    So right as soon as you get paid for a Bond- they assume you put it in something that is earning, i, interest?
    (Just as if you weren't putting it in the Bond- you'd be putting the money in a bank that earns i interest..)

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