Why is it that when the yield on a Treasury bond increases (because people are selling their bonds, I believe), mortgage rates increase as well?

Is there any sort of inherent connection between them? Why do banks increase the rates they loan money at when people sell bonds?

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: 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) **cite investopedia

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.

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    Very nice, comprehensive answer. Welcome to Money.SE, I hope you hang around a while. – JoeTaxpayer Aug 18 '13 at 14:55
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    I really appreciate the answer, but I do have some more follow up questions. A) Why are banks going off the 10 year treasury bonds instead of the 30 year? Is it because most people will not hold loans for that long? B) Is it the general rule of thumb that investors are going to pay less for a bond when more risk is perceived in the future? C) Is this all done to curb something like inflation? For instance, the Treasury will issue bonds with higher interest rates in order to 'remove money' from the system. D) Why does the Treasury set coupon rates at the rate they do? – Jon Aug 23 '13 at 6:47
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    E) What is the reason for the current bond sell off? I know it's due to the fed tapering their purchases, but why is this causing people to sell their bonds? Is it because the Fed has created artificial demand which has kept yields low and bond prices high? Are people selling off because they will be able to get more money for the bonds now, because once the Fed stops purchasing bonds prices will fall lower due to decreased demand? – Jon Aug 23 '13 at 6:50
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    I just got the chance to see this, and will work on posting another answer here to try to address your follow-ups. Great questions, btw. disclaimer though, I'm no econ PhD... I went for making money instead :) So, my answers might not be perfectly right but I'll give you my perspective. – THEAO Aug 23 '13 at 8:55
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    @Jon If I write these all in the same answer/comment it would end up being a good sized chapter to put in a Macroeconomics/Monetary Theory textbook. Do you want to split out the questions in your comment into individual Money.SE questions? I will be glad to go through and answer them all... They fill some pretty good holes in terms of "google-able" questions, too – THEAO Aug 28 '13 at 20:20

The yield on treasury bond indicates the amount of money anyone at can make at virtually zero risk.

So lets say banks have X [say 100] amount of money. They can either invest this in treasury bonds and get Y% [say 1%] interest that is very safe, or invest into mortgage loans [i.e. lend it to people] at Y+Z% [say at 3%]. The extra Z% is to cover the servicing cost and the associated risk. (Put another way, if you wanted only Y%, why not invest into treasury bonds, rather than take the risk and hassle of getting the same Y% by lending to individuals?)

In short, treasury bond rates drive the rate at which banks can invest surplus money in the market or borrow from the market. This indirectly translates into the savings & lending rates to the banks' customers.

  • So, as the bond yield increases, banks have to lend at a higher rate because it doesn't make sense for them to lend at the same rate as the bond yield increase? Is this the real reason they raise interest rates? – Jon Jul 8 '13 at 13:40
  • Banks are out to make money, thus whichever way they can make that money is what they will do. The yields on Treasuries on controlled by a number of factors,e.g. foreign investors, the Fed, and others that buy these new bonds that may be at higher rates if the Fed raises rates. The bank is merely trickling down what the Fed is telling them to do in a sense. – JB King Jul 8 '13 at 16:04
  • I'm realizing that I really do not understand how bonds work. The current yield of the 10 year that I see on CNBC, what is that yield representing? How is it calculated? – Jon Jul 8 '13 at 16:41
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    treasury.gov/resource-center/data-chart-center/interest-rates/… would be my suggestion for learning about Treasury yields. Generally it is the % in interest you'd make on the bond but the link would have more details. – JB King Jul 8 '13 at 19:20

yield on a Treasury bond increases

This primarily happens when the government increases interest rates or there is too much money floating around and the government wants to suck out money from the economy, this is the first step not the other way around. The most recent case was Fed buying up bonds and hence releasing money in to the economy so companies and people start investing to push the economy on the growth path.

Banks normally base their interest rates on the Treasury bonds, which they use as a reference rate because of the probability of 0 default. As mortgage is a long term investment, so they follow the long duration bonds issued by the Fed. They than put a premium on the money lent out for taking that extra risk. So when the governments are trying to suck out money, there is a dearth of free flowing money and hence you pay more premium to borrow because supply is less demand is more, demand will eventually decrease but not in the short run.

Why do banks increase the rates they loan money at when people sell bonds?

Not people per se, but primarily the central bank in a country i.e. Fed in US.

  • What do you mean that is the first step? I thought yield on the bonds increase because investors are selling them. – Jon Jul 8 '13 at 13:38
  • @Jon - Ask yourself why would somebody sell a perfectly good and non-defaulting, in theory atleast, bond. It wouldn't happen unless and until there is some adverse warning or circumstances. yield on the bonds increase because investors are selling them That is wrong. Yield is related to how interest rates are moving, which affects the bond price, not to investors buying or selling bonds. The buying or selling is an after effect of the changes in interest rates. – DumbCoder Jul 8 '13 at 13:57
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    DC has it right. When the Gov wishes to remove money from the system, they sell bonds. Selling drives the price down and the rate up. – JoeTaxpayer Jul 8 '13 at 14:10
  • I'm very new to all of this, so just bear with me hear. What has caused the increase in the yield of the 10 year treasury bond? – Jon Jul 8 '13 at 16:06
  • Can you walk me through a step by step process of how this currently works, perhaps with some math thrown in. I just don't get why the yield on the 10 year has gone up recently. I thought yields go up when bond prices go down, which happens when people sell bonds. – Jon Jul 8 '13 at 16:08

The simple answer is that, even though mortgages can go for 10, 15, 20 and 30 year terms in the U.S., they're typically backed by bonds sold to investors that mature in 10 years, which is the standard term for most bonds. These bonds, in the open market, are compared by investors with the 10-year Treasury note, which is the gold standard for low-risk investment; the U.S. Government has a solid history of always paying its bills (though this reputation is being tested in recent years with fights over the debt ceiling and government budgets).

The savvy investor, therefore, knows that he or she can make at least the yield from the 10-year T-note in that time frame, with virtually zero risk. Anything else on the market is seen as being a higher risk, and so investors demand higher yields (by making lower bids, forcing the issuer to issue more bonds to get the money it needs up front). Mortgage-backed securities are usually in the next tier above T-debt in terms of risk; when backed by prime-rate mortgages they're typically AAA-rated, making them available to "institutional investors" like banks, mutual funds, etc.

This forms a balancing act; mortgage-backed securities issuers typically can't get the yield of a T-note, because no matter how low their risk, T-debt is lower (because one bank doesn't have the power to tax the entire U.S. population). But, they're almost as good because they're still very stable, low-risk debt.

This bond price, and the resulting yield, is in turn the baseline for a long-term loan by the bank to an individual. The bank, watching the market and its other bond packages, knows what it can get for a package of bonds backed by your mortgage (and others with similar credit scores). It will therefore take this number, add a couple of percentage points to make some money for itself and its stockholders (how much the bank can add is tacitly controlled by other market forces; you're allowed to shop around for the lowest rate you can get, which limits any one bank's ability to jack up rates), and this is the rate you see advertised and - hopefully - what shows up on your paperwork after you apply.

Different bonds (and securitized mortgages are bonds) that have similar average lives tend to have similar yields (or at least trade at predictable yield spreads from one another). So, why does a 30 year mortgage not trade in lock-step with 30-year Treasuries?

First a little introduction:

Mortgages are pooled together into bundles and securitized by the Federal Agencies: Fannie Mae, Freddie Mac, and Ginnie Mae.

Investors make assumptions about the prepayments expected for the mortgages in those pools. As explained below: those assumptions show that mortgages tend to have an average life similar to 10-year Treasury Notes.

100% PSA, a so-called average rate of prepayment, means that the prepayment increases linearly from 0% to 6% over the first 30 months of the mortgage. After the first 30 months, mortgages are assumed to prepay at 6% per year. This assumption comes from the fact that people are relatively unlikely to prepay their mortgage in the first 2 1/2 years of the mortgage's life.

See the graph below.

enter image description here

The faster the repayments the shorter the average life of the mortgage. With 150% PSA a mortgage has an average life of nine years. On average your investment will be returned within 9 years. Some of it will be returned earlier, and some of it later. This return of interest and principal is shown in the graph below:

enter image description here

The typical investor in a mortgage receives 100% of this investment back within approximately 10 years, therefore mortgages trade in step with 10 year Treasury Notes.

Average life is defined here:

The length of time the principal of a debt issue is expected to be outstanding. Average life is an average period before a debt is repaid through amortization or sinking fund payments. To calculate the average life, multiply the date of each payment (expressed as a fraction of years or months) by the percentage of total principal that has been paid by that date, summing the results and dividing by the total issue size.

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