You’ve really got three or four questions going here… and it’s clear that a gap in understanding one component of how bonds work (pricing) is having a ripple effect across the other facets of your question. The reality is that everybody’s answers so far touch on various pieces of your general question, but maybe I can help by integrating. So, let’s start by nailing down what your actual questions are:
1. Why do mortgage rates (tend to) increase when the published treasury bond rate increases? I’m going to come back to this, because it requires a lot of building blocks.
2. What’s the math behind a bond yield increasing (price falling?)
This gets complicated, fast. Especially when you start talking about selling the bond in the middle of its time period. Many people that trade in bonds use financial calculators, Excel, or pre-calculated tables to simplify or even just approximate the value of a bond. But here’s a simple example that shows the math.
Let’s say we’ve got a bond that is issued by… Dell for $10,000. The company will pay it back in 5 years, and it is offering an 8% rate. Interest payments will only be paid annually. Remember that the amount Dell has promised to pay in interest is fixed for the life of the bond, and is called the ‘coupon’ rate.
We can think about the way the payouts will be paid in the following table:
As I’m sure you know, the value of a bond (its yield) comes from two sources: the interest payments, and the return of the principal. But, if you as an investor paid $14,000 for this bond, you would usually be wrong. You need to ‘discount’ those amounts to take into account the ‘time value of money’. This is why when you are dealing in bonds it is important to know the ‘coupon rate’ (what is Dell paying each period?). But it is also important to know your sellers’/buyers’ own personal discount rates. This will vary from person to person and institution to institution, but it is what actually sets the PRICE you would buy this bond for.
There are three general cases for the discount rate (or the MARKET rate). First, where the market rate == the coupon rate. This is known as “par” in bond parlance. Second, where the market rate < the coupon rate. This is known as “premium” in bond parlance. Third, where the market rate > coupon rate. This is known as a ‘discount’ bond.
But before we get into those in too much depth, how does discounting work? The idea behind discounting is that you need to account for the idea that a dollar today is not worth the same as a dollar tomorrow. (It’s usually worth ‘more’ tomorrow.) You discount a lump sum, like the return of the principal, differently than you do a series of equal cash flows, like the stream of $800 interest payments.
The formula for discounting a lump sum is:
Present Value=Future Value* (1/(1+interest rate))^((# of periods))
The formula for discounting a stream of equal payments is:
Present Value=(Single Payment)* (〖1-(1+i)〗^((-n))/i)
(i = interest rate and n = number of periods)
So let’s look at how this would look in pricing the pretend Dell bond as a par bond. First, we discount the return of the $10,000 principal as (10,000 * (1 / 1.08)^5). That equals $6,807.82.
Next we discount the 5 equal payments of $800 as (800* (3.9902)). I just plugged and chugged but you can do that yourself. That equals $3,192.18. You may get slightly different numbers with rounding.
So you add the two together, and it says that you would be willing to pay ($6,807.82 + $3,192.18) = $10,000. Surprise! When the bond is a par bond you’re basically being compensated for the time value of money with the interest payments. You purchase the bond at the ‘face value’, which is the principal that will be returned at the end.
If you worked through the math for a 6% discount rate on an 8% coupon bond, you would see that it’s “premium”, because you would pay more than the principal that is returned to obtain the bond [10,842.87 vs 10,000]. Similarly, if you work through the math for a 10% discount rate on an 8% coupon bond, it’s a ‘discount’ bond because you will pay less than the principal that is returned for the bond [9,241.84 vs 10,000].
It’s easy to see how an investor could hold our imaginary Dell bond for one year, collect the first interest payment, and then sell the bond on to another investor. The mechanics of the calculations are the same, except that one less interest payment is available, and the principal will be returned one year sooner… so N=4 in both formulae.
Still with me? Now that we’re on the same page about how a bond is priced, we can talk about “Yield To Maturity”, which is at the heart of your main question.
Bond “yields” like the ones you can access on CNBC or Yahoo!Finance or wherever you may be looking are actually taking the reverse approach to this. In these cases the prices are ‘fixed’ in that the sellers have listed the bonds for sale, and specified the price. Since the coupon values are fixed already by whatever organization issued the bond, the rate of return can be imputed from those values.
To do that, you just do a bit of algebra and swap “present value” and “future value” in our two equations.
Let’s say that Dell has gone private, had an awesome year, and figured out how to make robot unicorns that do wonderful things for all mankind. You decide that now would be a great time to sell your bond after holding it for one year… and collecting that $800 interest payment. You think you’d like to sell it for $10,500. (Since the principal return is fixed (+10,000); the number of periods is fixed (4); and the interest payments are fixed ($800); but you’ve changed the price... something else has to adjust and that is the discount rate.)
It’s kind of tricky to actually use those equations to solve for this by hand… you end up with two equations… one unknown, and set them equal. So, the easiest way to solve for this rate is actually in Excel, using the function =RATE(NPER, PMT, PV, FV). NPER = 4, PMT = 800, PV=-10500, and FV=10000. Hint to make sure that you catch the minus sign in front of the present value… buyer pays now for the positive return of 10,000 in the future.
That shows 6.54% as the effective discount rate (or rate of return) for the investor. That is the same thing as the yield to maturity. It specifies the return that a bond investor would see if he or she purchased the bond today and held it to maturity.
3. What factors (in terms of supply and demand) drive changes in the bond market?
I hope it’s clear now how the tradeoff works between yields going UP when prices go DOWN, and vice versa. It happens because the COUPON rate, the number of periods, and the return of principal for a bond are fixed. So when someone sells a bond in the middle of its term, the only things that can change are the price and corresponding yield/discount rate.
Other commenters… including you… have touched on some of the reasons why the prices go up and down. Generally speaking, it’s because of the basics of supply and demand… higher level of bonds for sale to be purchased by same level of demand will mean prices go down. But it’s not ‘just because interest rates are going up and down’. It has a lot more to do with the expectations for 1) risk, 2) return and 3) future inflation.
Sometimes it is action by the Fed, as Joe Taxpayer has pointed out. If they sell a lot of bonds, then the basics of higher supply for a set level of demand imply that the prices should go down. Prices going down on a bond imply that yields will go up. (I really hope that’s clear by now). This is a common monetary lever that the government uses to ‘remove money’ from the system, in that they receive payments from an investor up front when the investor buys the bond from the Fed, and then the Fed gradually return that cash back into the system over time.
Sometimes it is due to uncertainty about the future. If investors at large believe that inflation is coming, then bonds become a less attractive investment, as the dollars received for future payments will be less valuable. This could lead to a sell-off in the bond markets, because investors want to cash out their bonds and transfer that capital to something that will preserve their value under inflation. Here again an increase in supply of bonds for sale will lead to decreased prices and higher yields.
At the end of the day it is really hard to predict exactly which direction bond markets will be moving, and more importantly WHY. If you figure it out, move to New York or Chicago or London and work as a trader in the bond markets. You’ll make a killing, and if you’d like I will be glad to drive your cars for you.
4. How does the availability of money supply for banks drive changes in other lending rates?
When any investment organization forms, it builds its portfolio to try to deliver a set return at the lowest risk possible. As a corollary to that, it tries to deliver the maximum return possible for a given level of risk.
When we’re talking about a bank, DumbCoder’s answer is dead on. Banks have various options to choose from, and a 10-year T-bond is broadly seen as one of the least risky investments. Thus, it is a benchmark for other investments.
5. So… now, why do mortgage rates tend to increase when the published treasury bond yield rate increases?
The traditional, residential 30-year mortgage is VERY similar to a bond investment. There is a long-term investment horizon, with fixed cash payments over the term of the note. But the principal is returned incrementally during the life of the loan.
So, since mortgages are ‘more risky’ than the 10-year treasury bond, they will carry a certain premium that is tied to how much more risky an individual is as a borrower than the US government.
And here it is… no one actually directly changes the interest rate on 10-year treasuries. Not even the Fed. The Fed sets a price constraint that it will sell bonds at during its periodic auctions. Buyers bid for those, and the resulting prices imply the yield rate. If the yield rate for current 10-year bonds increases, then banks take it as a sign that everyone in the investment community sees some sign of increased risk in the future. This might be from inflation. This might be from uncertain economic performance. But whatever it is, they operate with some rule of thumb that their 30-year mortgage rate for excellent credit borrowers will be the 10-year plus 1.5% or something. And they publish their rates.