# Bond Values

Could someone intuitively explain why if interest rates fall bond prices go up? (Yes sorry this is actually a real question!) But say you own a bond and interest rates fall…are you in a better position now because you likely are receiving a higher interest rate on that bond than what would be the interest rate on a similar bond that is currently issued in the market?

bonds are a series of cash flows. Since you value a bond today you take the future cash flows and divide them by 1 + the corresponding interest rate. So, since interest rates are in the denominator, as they rise, the value of the respective cash flow gets smaller. That’s why bond prices fall when rates rise and rise when rates fall. As for the 2nd part of your question that’s not as easy to answer as it depends on many factors. There’s the interest rate risk and reinvestment risk tradeoff. And i don’t really feel like lookign that up again to ensure i’m not giving you a false definition and example of the trade offs between the two.

Basically, the idea is that all bonds (of the same risk characteristics) generate the same yield, no matter what the coupon rate listed on the bond actually is. This can be called the market yield. If a bond has zero risk of default, and its coupon rate is equal to the market interest rate, then it sells at its par value, which means that all of its cash flows and principal repayments, discounted at that rate, sum up to par. How do all bonds pay at the same yield? Their prices adjust. So a 5% bond might sell for 100 (par value) if the market yield is also 5%, but a 10% bond with otherwise identical characteristics (payment schedule, time to maturity, risk of default, etc.) would sell at a higher value so that someone paying today’s price will get a 5% return on the investment (because that’s the market rate, and all bonds in the market return the same rate). If you are holding a bond that pays more than the market rate, you can think of it in two ways. 1) you can say that it is worth more than currently issued bonds because the coupons are higher than one can get on newly issued stuff with similar characteristics. Alternately, 2) you can say that these payments are still the same, but now discounted at a lower rate so their present value sums to a higher number. If interest rates go up, then your bonds have to go down in price in order to generate a higher yield with the same set of fixed payments. Although you might think that you haven’t really lost money if you’re just holding to maturitiy, the truth is that if you sold just before interest rates changed, and bought just after, you would be getting a higher return than you get by staying with the same bonds. After the interest rate change, you can’t sell and buy for any net benefit, and you’re likely to pay transaction costs. So you do lose money on bonds you hold if interest rates rise, even though you may not feel it the same way that you would feel it if the stock price dropped.

So much for an intuitive explanation… Austin wants to pay money now in order to get payments later (buy a bond). Danny Boy wants to receive money now and give payments later (sell a bond). Danny Boy is going to sell a bond that will have payments of \$100 each year for five years. How much should Austin pay for this bond? If the interest rate is zero, then \$100 today is going to be worth \$100 tomorrow. So, if the interest rate is zero the price of the bond should just be \$500. If the interest rate was high, like 20%, then \$83 today will turn into \$100 one year from now. The amount that Austin wants to pay today, in return for Danny Boy paying pack over the next five years, will be low. If Austin paid \$299 dollars today, then Danny Boy could earn 20% interest on that money and give Austin the \$100 he wanted every year for five years. So, at zero interest the price would be \$500. At 20% interest the price would be 299. Interest rates go up, bond prices go down.