If you own a 10-year bond paying annual 4% with face of $1000 and the bond is called after five years, prepayment is the risk of this action occurring and you now having to potentially reinvest the principal at lower rates.

So are you making less in the event of prepayment simply bc you might now potentially have to reinvest at lower rates or bc you are missing out on the future interest for years 6-10 ($200 in total interest). Are those two statements one in the same?

However, you still earned 4% annually during the first five years, no?

You have lost the opportunity to collect interest for the last 5 years of the bond. Because of the incentives involved, you can be pretty certain that the present value of the interest payments is more than the $1000 paid back to you – that is, the bond’s market value is more than $1000. Thus, you incur a loss of market value - $1000. Remember that losses include opportunity costs. You earned 4% for the first 5 years, but that’s not really good enough – you bought a 10 year bond for a reason, and you were entitled to 10 years of payments but for the call option.

Your second paragraph is sort of saying the same thing but you need both elements: you’re making “less” relative to the guaranteed 4% payments for the next 5 years.

If rates have increased after the first 5 years and the bond gets called so you reinvest principle at 6% coupon instead of 4% do you really care that the bond was called?

But if rates have gone up over the first 5 years does the issuer have any incentive to call the bond and refinance at a higher rate?

What’s the difference in value between a bond that has a 5 year maturity paying 4% and a 10 year bond paying 4%? And which one is this?

If rates are going up over the first 5yrs the price of the bond will be declining…and the issuer will have no incentive to call back the bond that he is short…therefore your risk exposure to prepayment is minimal,. If rates are dropping and the bond price goes up through the call price the issure has incentive to call the bond back and re-issue the bond in a lower interest rate envirnoment, since the issuer is borrowing money and the bond buyer is lending money…i think if you understand that concept then u will be ok as far as 'Simple" prepayment goes…

So it’s not necessarily that you’re losing out on the final five years worth of interest that means you’re getting less/losing out. It’s that you might have to reinvest at potenitally lower rates and instead of receiving something greater than the face of $1000 (which is its worth in the mkt due to lower prevailing rates) all you get is a thousand…??

Just trying to generally grasp. When somone calls your bond early/pays off debt early, is the investor actually getting less than anticpated/ making less of a return ?? this is due to potentially lower reinvestment returns (now getting less than initial rate) and less than market return on face??

Think about every period as its own loan. Say I lend you $5,000 at 10% interest. One period later, you owe me $500 immediately, and you still owe me the $5,000 to pay back whenever. So let’s say you pay me $1,000 of that $5,000. You’ve given me $1,500, and you owe me another $4,000. The next period, you owe me $400 no matter what, but you can elect to pay more than that again. So let’s say you do, and you give me $4,400 to clear your debt. At no point was I making less than 10% on the money I lent you, but I made 10% on $4,000 the second period, and I don’t get to collect interest from you anymore. So, I’ve collected $900 in interest, but I originally gave you $5,000. I had to do something with the $1,500 you paid me in the first period which includes a prepayment. If I didn’t invest it, or I invested it at less than 10%, I’m not making 10% on all my money anymore. I’m still getting 10% on whatever you haven’t paid off, but I want 10% on all my money.

Now apply the same concept to a bond. You invest your money in a bond because you like getting the coupons at whatever interest rate. But now the bond issuer takes back the bond and just gives you cash. You made the coupon rate on the face value of the bond for as long as you held it, but the party’s over once he calls the bond, and you have to put your money elsewhere. Elsewhere, though, isn’t as attractive as the first bond you bought, so now you’re making a smaller return over the rest of the life of the bond compared to what you otherwise would have. Are you getting “less than anticipated”? Yes, because you anticipate that the bond won’t be called (or will be called with probability less than 1). Is your holding period return less than the coupon rate? No, because you get the rate for as long as the bond is yours. The difference now is your holding period is reduced, so your future investment isn’t going to be as good as the deal you already had, and therefore your total return over the maximum life of the bond is going to be less than the return of holding the bond the whole time.

your last comment is assuming that any reinvestment opportunities are less than what your prior interest rate was, right? If your bond gets called early, and you’re fortunate enough to find a similar investment that returns 12%, then you actually make more, no?

Aaron, thanks for the example and your help. Much obliged!

Prepayment option is with the home owner.

Call option is with the bond issuer.

guess that got messed up in all the above.

There are very few reasons for the issuer of a Bond to call said bond if Interest rates are higher. Unless they are using excess cash to reduce debt because they have no other profitable use for that capital. But yes, if a bond was called and Interest rates are higher than you should be pretty excited.

I wonder if anyone has tried to model the chance of a call be exercised when interest rates are rising, due to exogenous factors? Probably not considering it would reduce the value of the option and would just be a really rare occurence.

Yes, you’re correct that the assumption is that you can’t find a better deal. It’s entirely possible that interest rates fall in credit markets, the bond issuer exercises the call option and pays you the face value today, and then you turn that money into a personal loan for your friend who is willing to pay more than the prevailing market rates for good borrowers. Granted, you’re presumably taking on more risk, so your risk-adjusted return might actually be lower, but you also don’t know the actual risk that your friend defaults (if you could figure it out, you would make trillions). Risk adjustments aside, it’s entirely possible that you end up with a better return on your reinvestment. The trick here is that you won’t get a better return in the same market – if you bought a different bond of the same quality and characteristics, you’re definitely getting a lower return.

The theoreticals are good to be conscience of (i.e. taking your money elsewhere with better returns), but it’s also important to remember the kind of mentality expected of you on the exams. Unless a problem says so, it’s expected that you would reinvest your money in an identical security, which is where the lower return conclusion comes from.