vania-janet/multiturn-rag-retrieval-data huggingface dataset:
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.
Remember the fundamental principle here; money now is worth more than money later, because of what you can do with money between now and later. You do realize a lower overall yield from this investment, but you get returns from it quickly which you can turn around and reinvest to make more money. As such, you're usually willing to tolerate a lower rate of return, because of the faster turnaround and thus the higher present value. The ""Income Yield %"" from your table is also referred to as the ""Flat Yield"". It is a very crude measure, a simple function of the coupon rate, the current quote price and the face value (R/P * V). For the first bond in your list, the flat yield is (.04/114.63 * 100) = 3.4895%. This is a very simple measure that is roughly analogous to what you would expect to make on the bond if you held it for one year, collected the coupon payment, and then sold the bond for the same price; you'd earn one coupon payment at the end of that year and then recoup the principal. The actual present value calculation for a period of 1 year is PV = FV/(1+r), which rearranges to r = FV/PV - 1; plug in the values (present value 114.63, future value 118.63) and you get exactly the same result. This is crude and inaccurate because in one year, the bond will be a year closer to maturity and will return one less coupon payment; therefore at the same rate of return the present value of the remaining payout of the bond will only be $110.99 (which makes a lot of sense if you think about it; the bond will only pay out $112 if you bought it a year from now, so why would you pay $114 for it?). Another measure, not seen in the list, is the ""simple APY"". Quite simply, it is the yield that will be realized from all cash flows from the bond (all coupon payments plus the face value of the bond), as if all those cash flows happened at maturity.
"Even though the article doesn't actually use the word ""discount"", I think the corresponding word you are looking for is ""premium"". The words are used quite frequently even outside of the context of negative rates. In general, bonds are issued with coupons close to the prevailing level of interest rates, i.e. their price is close to par (100 dollar price). Suppose yields go up the next day, then the price moves inversely to yields, and that bond will now trade at a ""discount to par"" (less than 100 dollar price). And vice versa, if yields went down, prices go up, and the bond is now at a ""premium to par"" (greater than 100 dollar price)"
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.
Why does the rising price of a bond pushes it's yield down? The bond price and its yield are linked; if one goes up, the other must go down. This is because the cash flows from the bond are fixed, predetermined. The market price of the bond fluctuates. Now what if people are suddenly willing to pay more for the same fixed payments? It must mean that the return, i.e. the yield, will be lower. Here we see that risk associated with the bonds in question has   skyrocketed, and thus bonds' returns has skyrocketed, too. Am I right? The default risk has increased, yes. Now, I assume that bonds' price is determined by the market (issued by   a state, traded at the market). Is that correct? Correct, as long as you are talking about the market price. Then who determines bonds' yields? I mean, isn't it fixed? Or - in the   FT quote above - they are talking about the yields for the new bonds   issued that particular month? The yield is not fixed - the cash flows are. Yield is the internal rate of return. See my answer above to your first question.
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’.
The 10yr bond pays coupons semi annually.  The yield % is what you would get annually if you hold the bond to full term.  The coupon payment won't be exactly 1.65%/2 because of how bond pricing and yields work.  The yield commonly quoted does not tell you how much each interest payment is.  You have to look at the price and coupon of a specific individual bond.  The rate you see is the market equilibrium yield at the present.      Example, I offer two different people two different bonds.  Joe buys a 10yr bond paying 5% coupons semi annually at a par value of $1000.  I charge him $1000.  Bob wants to buy a 10yr bond paying 10% coupons semi annually at a par value of $1000.  I charge him $1500 for this.   The yield is similar between the two (not equal due to math details but lets assume).  So at the end of 10 yrs, the two have roughly the same total amount of $.  Bob's paid more each year but he paid more up front.    This is why the federal govt can issue bonds with diff coupons and the market prices them so the yield rises/falls to the market clearing yield.
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.
Say you buy a bond that currently costs $950, and matures in one year, at $1000 face value. It has one coupon ($50 interest payment) left. The coupon, $50, is 50/950 or 5.26%, but you get the face value, $1000, for an additional $50 return. This is why the yield to maturity is higher than current yield. If the maturity were in two years, the coupons still provide 5.26%, and the extra 1000/950 is another 5.26% over 2 years, or (approx) 2.6%/yr compounded, for a total YTM of 7.86%. This is a back-of envelope calculation, the real way to calculate is with a finance calculator. Entering PV (present value) FV (future value) PMT (coupon payment(s)) and N (number of periods). With no calculator or spreadsheet, my estimate will be pretty close.
Duration is the weighted average time until all the cash flows of a fixed income security are received. There are a few different measures of duration but generally, duration measures the sensitivity of the price of a fixed income asset to a change in the yield of that asset. If you're familiar with calculus, duration is the first derivative of price with respect to yield.  Convexity is the sensitivity of the duration of bond with respect to changes in yield, or the second derivative.   The first chart [here](http://www.investopedia.com/terms/c/convexity.asp#axzz1x4F075zM) will help. Convexity measures the curvature of the blue or pink line, the steeper the curve the higher the convexity.   The more cash flows there are in a bond (higher or more frequent coupon) the lower the duration, because you are receiving more of your investment earlier as opposed to later (think time value of money). If a bond has one cash flow, meaning you get paid back only at maturity (zero coupon) then any changes in interest rates will have a greater impact on the price of the bond since you are discounting only one cash flow in the future. Think of buying a bond with no coupons and a 5% yield that matures in 5 years, or a bond with similar yield and maturity buy pays a coupon. If interest rates rise, the zero coupon bond's price will fall more than the bond with coupons. Why? Because if you own the zero coupon bond you have to wait 5 years to get your money back and reinvest it at the higher rate, while if you have the bond that pays coupons you can reinvest those incremental cash flows at the higher rate, even though at purchase they had the same yield and maturity.  These are both tough concepts that took me a fair amount of time to really understand. If you're investing in bonds or any fixed income asset, these topics are crucial to understanding interest rate risk.
"Just to confirm, you don't pay interest when holding a bond, the issuer of the bond pays you interest. The idea of calculating ""present value"" is as you suggest. You discount future payments using an appropriate rate. These future payments include both the coupon payments you receive through the life of the bond and the principal repayment at the maturity of the bond - each should be discounted from the due date of the payment to today's date. A typical rate to use would be the interest you yourself could earn by investing elsewhere (this gives you some idea of how much it would cost to get those payments another way), or perhaps some standard rate, for example the interbank rates such as LIBOR or FEDFUNDS."
In this case the market interest rate is the discount rate that sets equal the market price (current value) of the bond to its present value. To find the market interest rate which is also referred to as promised yield YTM you would have solve for the interest rate in the bond price formula A market price of bond is the sum of discounted coupons and the terminal value of the bond. Most spreadsheet programs and calculators have a RATE function that makes possible finding this market interest rate. First see this for finding a coupon paying bond price The coupon payments are discounted so is the par value of the bond and sum of such discounts is the market price of the bond. The TVM functions in Excel and calculators make this possible using the following equation Let us take your data, 9% $100,000 coupon with 5 years remaining to maturity with market interest rate of 10%. Bonds issued in the US mostly pay two coupons per year. Thus we are finding the present value of 10 coupons each worth $4500 and par value of $100,000. The semi-annual market interest rate is 10%/2 or 5% The negative sign indicate money going out of hand Now solving for RATE is only possible using numerical methods and the RATE function is programmed using Newton-Raphson method to find one of the roots of the bond price equation. This rate will be the periodic rate in this case semi-annual rate which you have to multiply by 2 to get the annual rate. Do remember there is a difference between annual nominal rate and an annualized effective rate. To find the market interest rate  If you don't have Excel or a financial calculator then you may opt to use my version of these financial functions in this JavaScript library tadJS
IMHO bonds are not a good investment at this present time, nor generally. Appreciate for a moment that the yield of an investment is DIRECTLY related to the face/trading value. If a thing (bond/stock) trades for $100 and yields 3%, it pays $3.  In the case of a bond, the bond doesn't pay a % amount, it pays a $ amount.  Meaning it pays $3. SO, for the yield to rise, what has to happen to the trading price?  It has to decrease. As of 2013/14 bonds are trading at historically LOW yields.  The logical implication of this is if a bond pays a fixed $ amount, the trading price of the bond has to have increased.  So if you buy bonds now, you will see a decrease in its face value over the long term. You may find the first tool I built at Simple Stock Search useful as you research potential investments.
Yield can be thought of as the interest rate you would receive from that investment in the form of a dividend for stocks or interest payments on a bond.  The yield takes into account the anticipated amount to be received per share/unit per year and the current price of the investment.   Of course, the yield is not a guaranteed return like a savings account.  If the investment yield is 4% when you buy, it can drop in value such that you actually lose money during your hold period, despite receiving income from the dividend or interest payments.
Here is one from a Bloomberg partnership, it is free. To get the end of day prices, you may need some programming done. PM me if you need help with that. Getting bond quotes and general information about a bond issue is considerably more difficult than researching a stock or a mutual fund. A major reason for this is that there is not a lot of individual investor demand for the information; therefore, most bond information is available only through higher level tools that are not accessible to the average investor. Read more: Where can I get bond market quotes? | Investopedia http://www.investopedia.com/ask/answers/06/bondquote.asp#ixzz3wXVwv3s5
A bond fund has a 5% yield. You can take 1/.05 and think of it as a 20 P/E.  I wouldn't, because no one else does, really. An individual bond has a coupon yield, and a YTM, yield to maturity. A bond fund or ETF usually won't have a maturity, only a yield.
"It is important to distinguish between cause and effect as well as the supply (saving) versus demand (borrowing) side of money to understand the relationship between interest rates, bond yields, and inflation. What is mean by ""interest rates"" is usually based on the officially published rates determined by the central bank and is referenced to the overnight lending rate for meeting reserve requirements.  In practice, what the means is, (for example) in the United States the Federal Reserve will have periodic meetings to determine whether to leave this rate alone or to raise or lower the rate.  The new rate is generally determined by their assessment of current and forecast national and global economic conditions and factors in the votes of the various Regional Federal Reserve Presidents.  If the Fed anticipates economic weakness they will tend to lower and keep rates lower, while when the economy seems to be overheated the tendency will be to raise rates. Bond yields are also based on the expectation of future economic conditions, but as determined by market participants.  At times the market will actually ""lead"" the Fed in bidding bond prices up or down, while at other times it will react after the Fed does.  However, ignoring the varying time lag the two generally will track each other because they are really the same thing.  The only difference is the participants which are collectively determining what the rates/yields are. The inverse relationship between interest rates and inflation is the main reason for fluctuating rates in the first place.  The Fed will tend to raise rates to try to slow inflation, and lower rates when it feels inflation is too low and economic growth should be stimulated.  Likewise, when the economy is doing poorly there is both little inflationary pressure (driving interest rates down both in terms of what savers can accept to keep ahead of inflation and at) and depressed levels of borrowing (reduced demand for money, driving down rates to try to balance supply and demand), and the opposite is true when the economy is booming. Bond yields are thus positively correlated to inflation because during periods of high inflation savers won't want to invest in bonds that don't provide them with an acceptable inflation adjusted yield.  But high interest rates tend to have the effect or reining in inflation because it gets more costly for borrowers and thus puts a damper on new economic activity. So to summarize,"
Mortgage rates tend to track the yield on the 10-year Treasury note. The CBOE Interest Rate 10-Year T-Note, TNX, is a security directly related to this rate. Divide the CBOE price of TNX by 10 to get the yield.  One can also track the  10Y T-Note yield at yahoo finance using ticker symbol (^TNX).   One can also track the  10Y T-Note yield at yahoo finance using ticker symbol (^TNX).
Bonds have multiple points of risk: This is part of the time value of money chapter in any finance course.  Disclaimer - Duff's answer popped up as I was still doing the bond calculations. Similar to mine but less nerdy.
It refers to the risk free rate of a particular country. Because all other rates are usually pegged to the risk free rate. In US,it is the 30 day treasury rate. In England, it is the LIBOR In Canada, it is the overnight rate at which banks lend money to each other. All of these come under the category of risk free rate.
Let's say today you buy the bond issued by StateX at 18$. Let's say tommorow morning the TV says that StateX is going towards default (if it happens it won't give you back not even the 18$ you invested). You (and others that bought the same bond like you) will get scared and try to sell the bond, but a potential buyer won't buy it for 18$ anymore they will risk maximum couple of bucks, therefor the price of your bond tomorrow is worth 2$ and not 18 anymore. Bond prices (even zero coupon ones) do fluctuate like shares, but with less turbolence (i.e. on the same period of time, ups and downs are smaller in percentage compared to shares) EDIT: Geo asked in the comment below what happens to the bond the FED rises the interest. It' very similar to what I explained above. Let's say today you buy the bond just issued by US treasury at 50$. Today the FED rewards money at 2%, and the bond you bought promised you a reward of 2% per year for 10 years (even if it's zero coupon, it will give you almost the same reward of one with coupons, the only difference is that it will give you all the money back at once, that is when the bond expires). Let's say tommorow morning the TV says that FED decided to rise the interest rates, and now on it lends money rewarding a wonderful 4% to investors. US treasury will also have to issue bonds at 4%. You can obviously keep your bond until expiration (and unless US goes default you will get back all your money until the last cent), but if you decide to sell your bond, you will find out that people won't be willing to pay 50$ anymore because on the market they can now buy the same type of bond (for the same period of time, 10 years) that give them 4% per year and not a poor 2% like yours. So people will be willing to pay maximum 40$ for your bond or less.