Why would I buy a bond with a negative yield?
It would be preferable to purchase a bond with a negative yield if the negative yield was the smallest compared to similar financial securities. The purchase or sale of a security is rarely a mutually exclusive event.  An individual may have personal reasons or a desire to contribute to the activity the bond is financing.  To an entity, the negative yield bond may be part of a cost averaging plan, diversification strategy, a single leg of a multi-leg transaction, or possibly to aid certainty as a hedge in a pairs trade.  And of course there may be other unique situations specific to the entity. Said another way, is the Queen of Spades a good card?  It depends on the game being played and what is in your hand. Perhaps something else comes with the bond so it is a convertible security. Buffett's Negative-Interest Issues Sell Well from 2002 would be an example from more than a decade ago: Warren E. Buffett's new negative-interest bonds sold rapidly   yesterday, even after the size of the offering was increased to $400   million from $250 million, with a possible offering of another $100   million to cover overallotments. The new Berkshire Hathaway securities, which were underwritten by   Goldman, Sachs at the suggestion of Mr. Buffett, Berkshire's chairman   and chief executive, pay 3 percent annual interest. But they are   coupled with five-year warrants to buy Berkshire stock at $89,585, a   15 percent premium to Berkshire's stock price Tuesday of $77,900. To   maintain the warrant, an investor is required to pay 3.75 percent each   year. That provides a net negative rate of 0.75 percent. The question in my view is going into Opinion and economics. Why would I buy a bond with a negative yield? I guess you have answered yourself; Although the second point is more relevant for high net worth individual or large financial institutions / Governments where preserving cash is an important consideration. Currently quite a few Govt Bonds are in negative as most Govt want to encourage spending in an effort to revive economy.
Next year, the Fed plans on unwinding the Bonds and MBS.  They'll ramp up to $50 billion a month.  At the same time we'll be selling Bonds on the market to finance the debt at a rate of $70 billion a month.  I wonder who's going to have the cash to buy the Toxic MBS and the low yield Bonds they'll be unloading on top of the usual Bonds for future debt.  Those Bonds will have to pay double digit rates before anyone will buy them.  Future generations will just get even more screwed the way the Fed has it planned. "The answer is yes. And the reason is if today's interest rates are lower than the interest rate (coupon) at which the bond was issued. The bond's ""lifetime value"" is 100 cents on the dollar. That's the principal repayment that the investor will get on the maturity date. But suppose the bond's coupon rate is 4% while today's interest rate is 3%. Then, people who bought the bond at 100 would get 4% on their money, while everyone else was getting 3%. To compensate, a three year bond would have to rise to almost 103 so that the so-called yield to maturity"" would be 3%. Then there would be a ""capital loss"" (from almost 103 to 100) that would exactly offset the extra interest, that is 1% ""more"" for three years. If today's interest rates are negative (as they were from time to time in the 1930s, and in the present decade), the ""negative"" interest rates will prevent the buyer from getting the ""lifetime value"" (as defined by the OP) of principal plus interest over the original life of the bond. This happens in a ""flight to quality"" situation, where people are willing to take a (small) capital loss on Treasuries in order to prevent a large possible loss from bank failures like those that took place in 2008." 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) **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. The reason for these low interests is that the Japanese central bank is giving away money at negative interests to banks. Yes, negative. So, short of opening your own bank, you'll have to either choose less liquid investments or more risky ones. Get Japanese government bonds. Not a great interest, band not that liquid, but for a 5 years bond you'll do better than the bank can. Get Japanese corporate bonds. Still not great, and a bit more risky, it's better than nothing. Get a Japanese mutual fund. I can't recommend any though. Buy Japanese stock. Many Japanese stock have interesting kickbacks. For example if you buy enough stock of Book-Off you'll get some free books every month. it's risky though because I believe the next NIKKEI index crash is imminent. "[...] are all bonds priced in such a way so that they all return the same amount (on average), after accounting for risk? In other words, do risk premiums ONLY compensate for the amount investors might lose? No. GE might be able to issue a bond with lower yield than, say, a company from China with no previous records of its presence in the U.S. markets. A bond price not only contains the risk of default, but also encompasses the servicability of the bond by the issuer with a specific stream of income, location of main business, any specific terms and conditions in the prospectus, e.g.callable or not, insurances against default, etc. Else for the same payoff, why would you take a higher risk? The payoff of a higher risk (not only default, but term structure, e.g. 5 years or 10 years, coupon payments) bond is more, to compensate for the extra risk it entails for the bondholder. The yield of a high risk bond will always be higher than a bond with lower risk. If you travel back in time, to 2011-2012, you would see the yields on Greek bonds were in the range of 25-30%, to reflect the high risk of a Greek default. Some hedge funds made a killing by buying Greek bonds during the eurozone crisis. If you go through the Efficient frontier theory, your argument is a counter statement to it. Same with individual bonds, or a portfolio of bonds. You always want to be compensated for the risk you take. The higher the risk, the higher the compensation, and vice versa. When investors buy the bond at this price, they are essentially buying a ""risk free"" bond [...] Logically yes, but no it isn't, and you shouldn't make that assumption." As well as credit risk there's also interest risk. If a bond has a face value of $100, pays 1% and matures in 20 years' time then you expect to receive a total of $120 from buying it now -- $1 per year for 20 years and $100 at the end. But if you can get a 3% return elsewhere, then if you invest your $80 there instead you will get $2.40 per year for 20 years and then $80 at the end, making a total of $128 (and you also get more of the money sooner). So even $80 for the $100 bond is a bad buy, and you should invest elsewhere. Yield is the term used to describe how much income the bond will generate if the bond was purchased at a particular moment in time. If I pay $100 for a one year, $100 par value bond that pays 5% interest then the bond yields 5% since I will receive $5 from a $100 investment if I held the bond to maturity. If I pay $90 for the same one year bond then the bond yields 17% since I will receive $15 from a $90 investment if I held the bond to maturity. There are many factors that affect what yield creditors will accept: It is the last bullet that ultimately determines yield.  The other factors feed into the creditor’s desire to hold money today versus receiving money in the future.  I desire money in my hand more than a promise to receive money in the future.  In order to entice me to lend my money someone must offer me an incentive.  Thus, they must offer me more money in the future in order for me to part with money I have. A yield curve is a snapshot of the yields for different loan durations.  The x-axis is the amount of time left on the bond while the y-axis is the yield.  The most cited yield curve is the US treasury curve which displays the yields for loans to the US government.  The yield curve changes while bonds are being traded thus it is always a snapshot of a particular moment in time. Short term loans typically have less yield than longer term loans since there is less uncertainty about the near future. Yield curves will flatten or slightly invert when creditors desire to keep their money instead of loaning it out.  This can occur because of a sudden disruption in the market that causes uncertainty about the future which leads to an increase in the demand for cash on hand. The US government yield curve should be looked at with some reservation however since there is a very large creditor to the US government that has the ability to loan the government an unlimited amount of funds. Automatic exercisions can be extremely risky, and the closer to the money the options are, the riskier their exercisions are. It is unlikely that the entire account has negative equity since a responsible broker would forcibly close all positions and pursue the holder for the balance of the debt to reduce solvency risk.  Since the broker has automatically exercised a near the money option, it's solvency policy is already risky. Regardless of whether there is negative equity or simply a liability, the least risky course of action is to sell enough of the underlying to satisfy the loan by closing all other positions if necessary as soon as possible. If there is a negative equity after trying to satisfy the loan, the account will need to be funded for the balance of the loan to pay for purchases of the underlying to fully satisfy the loan. Since the underlying can move in such a way to cause this loan to increase, the account should also be funded as soon as possible if necessary. Accounts after exercise For deep in the money exercised options, a call turns into a long underlying on margin while a put turns into a short underlying. The next decision should be based upon risk and position selection.  First, if the position is no longer attractive, it should be closed.  Since it's deep in the money, simply closing out the exposure to the underlying should extinguish the liability as cash is not marginable, so the cash received from the closing out of the position will repay any margin debt. If the position in the underlying is still attractive then the liability should be managed according to one's liability policy and of course to margin limits. In a margin account, closing the underlying positions on the same day as the exercise will only be considered a day trade.  If the positions are closed on any business day after the exercision, there will be no penalty or restriction. Cash option accounts While this is possible, many brokers force an upgrade to a margin account, and the ShareBuilder Options Account Agreement seems ambiguous, but their options trading page implies the upgrade. In a cash account, equities are not marginable, so any margin will trigger a margin call.  If the margin debt did not trigger a margin call then it is unlikely that it is a cash account as margin for any security in a cash account except for certain options trades is 100%. Equities are convertible to cash presumably at the bid, so during a call exercise, the exercisor or exercisor's broker pays cash for the underlying at the exercise price, and any deficit is financed with debt, thus underlying can be sold to satisfy that debt or be sold for cash as one normally would. To preempt a forced exercise as a call holder, one could short the underlying, but this will be more expensive, and since probably no broker allows shorting against the box because of its intended use to circumvent capital gains taxes by fraud.  The least expensive way to trade out of options positions is to close them themselves rather than take delivery.