https://www.reddit.com/r/explainlikeimfive/comments/lin66/why_do_bond_prices_fall_when_interest_rates_rise/
I'm exasperated with trying to comprehend the relationship of bond prices to interest rates/coupon rates/yields.
To my simple mind, the mentioned interest rates are set by the government (or are they the interest rates on the bonds themselves?), the coupon rates come fixed with the bonds, and the yields... well, I don't know how yields fit into this current context because aren't they similar to returns (i.e. the coupon rate returns)?
I would appreciate some very basic calculation examples too, if possible.
We'll start out with a 0 coupon bond so that you can see how it works, because coupons basically work the same way as the final yield.
A T-Bill is issued that promises to pay $100 in 91 days (3 months). Note that it doesn't matter what the interest rate is - 91 days after issue, the bond is going to pay out $100.
The person purchasing the T-Bill will pay whatever the price is - which is the yield ($100) multiplied by (1- the yield rate on a per period basis). So if the annual yield rate is 2.5%, and you're purchasing a 2.5% APY T-Bill for 91 days, it's going to be yielding about .619% over the duration.
The price of the 91 day T-Bill is therefore going to be 100*(1-.00619)=$99.38.
Now let's say that immediately after you buy your 91 day T-Bill, the interest rate changes. It goes up to 5% APY. Suddenly you can buy a T-Bill that will yield $100 in 91 days for only 100*(1-.0123)=$98.77.
In short, it's because bonds lock in what you're going to be paid on the coupon dates and the final payment dates. Bonds don't care what the current interest rate is other than what you're buying them for. Thus the only thing about them that changes is their pricing, not their payments (an 8% coupon bond is going to pay 8% of face value if the market rate is 2% or 10%, it doesn't matter).
Thus, due to the inverse relation of interest rates to price, is why you get the results you see. It's not a 5 year old explanation, but that's the best I can do right now.
Great post.
Just to elaborate a little further using your example:
2.5% APY | Bond Price = $99.38
5% APY | Bond Price = $98.77
If you bought a bond when APY was 2.5%, and the APY went up to 5%, then you have 2 scenarios.
The reason you can only sell your 2.5% bond for a loss is because why would anyone pay you $99.38 for a 2.5% gain when they can go out into the market and buy a 5% bond and pay $98.77 for a 5% gain.