Bond Price and Yield Calculation

PRICE

The price paid for a bond is based upon the general level of interest rates at the time of purchase. When a security is issued, the coupon rate will be reflective of the current interest rate environment, and the price will typically be at or close to par (100.00% of face value). After the bond is issued, if interest rates go down, the price of the bond will go up (to more than 100.00% of face value). This happens because a new bond issued in the lower interest rate environment would have a lower coupon rate, and trade at or close to par. The investor selling the older bond (with a higher coupon rate) would demand a higher price (a “premium”). for the bond (it has a higher coupon, pays more interest and, therefore is more valuable). Conversely, after a bond is issued, if interest rates go up, the price for the security will decline (to a “discount”) because its coupon will be less valuable. Of course, no investor is obligated to sell a bond prior to maturity regardless of whether interest rates rise or fall.

YIELD


The price paid by the buyer will equate to an “effective yield” to the bond’s stated maturity. The effective yield to maturity is calculated using a mathematical combination of the price paid, the coupon interest rate and the remaining term to maturity.

How To Sell Bonds

Mortgage Backed Securities, CMO Bonds and Yield

Mortgage backed securities offer the best alternative to decreased loan demand. Pass throughs, CMO’s and adjustable rate MBS’s are paid to the bank just like a loan that the banks has made for a mortgage. If a person takes out a $250,000 mortgage, the customer is paying back the bank monthly with principle and interest. As you know, if you own a home, your initial payments are mostly INTEREST in the early years. A mortgage backed security, if it is a new issue will operate the same way. As you learned in the product section, the payments on MBS’s are based on the average coupon of the underlying mortgages. If the Weighted Average Coupon (WAC) is low, the payments will be slower because people will not be refinancing as much.

Geography also plays a part. You want to know where the mortgages are, that the agency is issuing the bond off of. California and New York for instance, has more people moving than states like Nebraska or Alabama, where the population is more settled. The more transient a state, the faster the bond will pay.

Length of the outstanding mortgages, or current face of the mortgages are a factor. “Seasoned pools”, as they are called, are mortgage pools that have had several years of payment on them. They have more predictable payments and duration. They will normally pay better because of that. Seasoned pools are usually what banks are looking for. They are generally interested in better cash flow and predictable cash flow.

The compensation or mark up potential is good in mortgage backed bonds. They are priced above treasuries because, although they are AAA rated, they are not absolute in their pay off and the payments fluctuate. Since they are usually 15-30 years in duration, they allow for price mark up. Where treasuries and straight agency debt allow for a few ticks to a .25, MBS’s can create spreads between buying and selling them up to a ½ or ¾ of point. This can translate to a $5,000 commission on a $1 million sale. Remember, a million dollars in one bond is not unusual for most institutions, and for banks over $500 million in assets, it’s normal.

CMO Bonds

Bank CD Yield

Selling CD’s and taking advantage of loan demand


Banks and other institutions buy CD’s offered by other banks. If you have banks that buys CD’s, and you have a bank that needs money, you can earn from that. Lets say your investing bank is looking for a 3% 5 year CD (don’t be alarmed by the low rates, as of this printing, interest rates are at all time lows), The bank that is looking for money is offering a rate of 3.25%. You can approach the deposit bank with providing them a $100,000 deposit, not to exceed their total cost of 3.25%. You ask them if they pay for deposits, if they do, you tell the bank to issue the CD to your bank at 3%, and then you bill the deposit bank the .25 point spread between their cost and the CD rate you are giving to your customer. A .25 point for a 3 year CD is $750. What if you had 10 banks interested in 3 year CD’s? That’s $7500. Your client banks would wire the money in. Each deposit is fully insured, the bank sends them a receipt, and your done.

You also could do this with banks that are not as loaned out, but are looking to make a spread between their deposit rates, and a higher fixed income investment that you have. Let’s say there is a 4% corporate bond for 3 years that is available, and the deposit bank is paying 3.25% for 3 year deposit CD’s. If you can provide the bank with a CD at a total cost of 3.25%, and then take that money and invest it in a corporate bond, you made a spread for the bank, and you made money on both ends. The deposit spread, and the mark up on the corporate bond trade. These kinds of trades are simple to present and execute. The one objection you will encounter from some is the bank does not accept “Brokered Deposits”. Brokered Deposits are large time deposits that are listed as “brokered”, meaning, it was arranged through a broker. Some banks only consider deposits as brokered if they pay a fee for the deposit. Remember how we explained providing a jumbo CD to a bank and using their gross rate?, we provided the CD to a depositor and charged the bank a .25 point. Now, the bank never paid more for the deposit than if it issues it directly to our investor, we never exceeded their cost, but the bank is paying you a .25 point fee. For some reason, banks may not want to do that.

You can get around the bank paying the fee if your investor pays the fee. If a bank is offering 4% for 1 year, and the going rate on CD’s is 3.50%, you can offer the CD to your investor at 4%, bill THEM (investor) the .25 point and still net them 3.75% overall. Not all institutional investors pay fees, but they should if you are consistently showing them better rates than what they are seeing locally or directly.

Doing CD business is nice and easy, but you won’t make that much money. Bank deposits are only insured up to $100,000 per account, so your investor can only buy one $100,000 CD at any one bank. There are ways to capitalize on this market though if you do or have one of the following:

Have an institutional investor that only buys CD’s and has millions to put out at different banks

Represent a deposit bank exclusively, or at least be one of a few other brokers. You can then offer the rate to other brokerage firms and you get a cut on every deposit

Have a bank investor who also manages trust accounts. This way, your investing bank will call you with different customers of theirs that are looking for CD’s. They will give you the name of the customer and you just give the bank the wiring instructions and details to them. Trust departments may also buy other bonds; Municipals, treasuries, etc.

www.brokerjobs.com

Commercial Banks and Bond Yield

Banks generally “beat to their own drum”. Unlike credit unions, which tend to be “clicky”, banks will do what is only best for them and each bank is different. If a commercial bank is open, it is investing continuously and has existing broker relationships. That is a certainty. Banks are in business for one thing - to earn more money. Generating greater returns on their loans and their investments is what they are in business for. Loan demand is your biggest objection. Banks feel obligated to push for greater loan demand from their customers. Mortgages, car loans and other loans generate income for long periods of time.

The available funds not used for loans are used for investments. Banks will keep a certain amount of money in Federal Funds or “Fed Funds”, as they are usually called. Fed funds is an overnight bank to bank lending rate. Banks with excess money can sell fed funds to their banks. Banks with low liquidity will borrow through it. Either way, it is a formidable competitor for bond brokers. The ease of fed funds allows for quick and easy, overnight rate of returns. However, the fact that fed funds is overnight, presents a problem too. Banks should not have an over abundance of money in overnight accounts, simply because it does not allow them a chance to “lock in” a fixed rate if interest rates decline. They will just “drift” downward as interest rates decline. Simply put, fed funds should be for reserves and convenience, but not a long term investment policy. If the bank is going to hedge themselves against interest rates rising (which brings bond prices down), then they need to move some money out of there.

Banks can buy almost any debt (bonds, notes CD’s). Most will not buy low grade corporate bonds, but pretty much everything else is open. What they each buy depends on a few things:

Asset size
Current investments
Loan demand
How educated they are


Asset size of a bank is important when determining whether you should contact them. Your best chance for success, if you are looking to work independently, or for a firm is Banks with assets between $100 million - $700 million. A bank with $100 million in assets may have $15 million in investments for instance. Portfolio sizes of $15 million to $100 million should be your target. You want to stay away from pursuing accounts much smaller than that, because the amount of time and work you put in trying to get them to work with you will not be worth the payout. Banks that are over 1 billion in assets are simply too big for most. Not for the reason you may think. They are not that much more

complicated, but they have in-house direct investment officers that do it themselves. You may get lucky where they call you back and buy something, but you will be working so “thin” (price/mark up), that it will be hard to make money. Bonds are based on “mark ups”, if a firm is offering the bond to you at $97 ($970 per $1000 bond), you can mark the bond up in price from their. ¼ of a point to a ½ a point is a normal mark up for most bonds. With the bigger banks, it will be hard to get that much into the bond. They are usually being called by a lot of brokers, and may be seeing the same thing. You don’t want to be showing a bond that is overly marked up in price. He may not want to talk to you anymore. So, the rule with the big banks ($1 billion+) is, work thin, don’t overwork, and just hope that he calls you back on occasion over the “other guy”.

Smaller to medium size banks are passed over by the large primary brokerage firms. So, not only, can you get in easier, it is more potentially rewarding. These banks can be educated, they won’t have a “team” of investment pros at the bank, so your suggestions and education presentations may pay off. It is also rewarding in that these smaller banks will put more “Stock” in personal relationships. You won’t get a lucky 2nd phone call trade, like you could get with a big bank buying everyday, but once they are opened, you can bring them into your philosophy and strategy. Personal relationships have a much better chance to grow, and your chances of always being undercut on price from other brokers, won’t happen as often. The smaller banks do not have the time to talk to 10 brokers every day. What you want, and this applies to any institution, is to be either their only broker (not likely in the beginning), or be one of three that he is dealing with. A sophisticated bank will spread the trades so that all of you get something.

How To Sell Bonds To Banks and Other Institutions

Where is the money in the bond market or any fixed income area? Institutions. Institutions are the “life blood” of the bond market and the primary income source for bond brokers. Commercial Banks, Savings Banks, Credit Unions, Insurance Companies, and Municipalities (City, County, and other local government authorities). We will look deep inside this misunderstood area of investments. We will examine each type of institution, what they historically buy, who they buy from, which dealers to use, how to request and examine a portfolio, who to ask for and much more.

The benefits of dealing with institutions, especially banks and credit unions, is that you are not dealing with the personal money of the person you are talking to. Meaning, in most financial prospecting situations, you are usually working with an individual looking to invest HIS money. Institutions do not work that way of course. You are dealing with people who are hired to manage the portfolio for the benefit of the institution. This person will not have the paranoia that can set in with retail investors when brokers call them. The institutional manager will judge you in other ways for sure, but he will look at you based on service and need you can provide, plus he is not allowed to buy risky investments anyway.

Public institutions (banks, credit unions, municipal authorities) do not buy stock or other equities, The risk the principal itself in fixed income is minimal. There is price risk and market risk even with the safest investments though. Banks usually, or should have a pretty balanced portfolio. Treasury securities, agencies, mortgage backed securities, bank CD’s, and municipal bonds primarily. We will discuss this in detail when looking at banks specifically.

Credit Unions are also a major factor in the fixed income market. Credit unions need to be handled a little differently. Credit unions are “not for profit” institutions. They do not pay taxes. However, they do look to generate added income for the benefit of their members, which can translate into better services to their membership. Credit unions, especially the smaller ones (under 10 million in assets), are managed by people who have other functions or jobs outside the credit union. Credit unions will buy different fixed income product, but the smaller ones tend to stick with bank CD’s or they invest with their corporate credit union. As with banks, we will dedicate a section just for credit unions.

We will also learn how to market to Municipalities (cities, towns, authorities). These Governments are very limited in what they can invest in. They are obviously dealing with tax money and general revenues from their local area. Straight agencies, treasuries and some CD’s are usually about it. They are limited like I said, but if they buy $20 million dollars worth of an agency bond, that’s pretty good. Municipalities will have their own section later.




There are several areas we will need to get in to. Some are for education, some are for prospecting. All are necessary to maximize your production and to build a long lasting career. We will discuss the following areas and elements of the institutional fixed income market:

Banks
Trust departments
Credit unions
Municipalities
Insurance companies
Other institutions
Prospecting
Reading and analyzing portfolios
Types of fixed income product
Suitability
Competition
Relevant accounting laws
Lead sources
How you get paid
Top firms


You need to understand this market to succeed in it. The people you are going to speak with are professionals who will know if you can bring value to them or not. If you dedicate yourself to learning what you need to know, it is a very lucrative area of the market, where you client list can build steadily, and the money you are advising on can grow infinitely.















All banks own bonds of some sort, and they are buying them from brokers. Our primary bonds are:


• U.S. Treasury obligations (T-bills, T-notes, T-bonds)
• Government Agency Debt (GNMA)
• Private Agency Debt (FNMA, FHLMC, FHLB and others)
• Mortgage Backed Securities (Pass throughs , CMO’s, ARM’s)
• Municipal Bonds
• Investment Grade Corporate Bonds

The institutions that have strict policy guidelines on the bonds that they can buy are Banks, Credit Unions and Municipalities.

The spreads on Treasuries make them difficult to sell or “mark up” more than a few “ticks” to most sophisticated banks and institutions. A tick is 1 point in price. Government bonds are quoted in 32nds.

An example of a treasury bond would be: Bid 101-16 Ask: 101-24. If your client wanted to buy $10,000 of this treasury bond, you would see the price to you at 101-24 (24/32). 24/32 = .75. So the price is really 101.75 or $10,175. Each point represents $10 for every $1000 par bond. For $10,000, each point is worth $100. All bonds trade at a minimum of 1000. Institutions normally buy $250,000 up to tens of millions per trade. So, our example of a $10,000 trade really isn’t realistic and would not be worth your time. A “tick” by the way, is if the price went up to 101-25.

Trading for a few “ticks” on $100,000 would make you very little. If you factor in ticket charges, you might make $100 on the trade. You only present treasuries if it’s non competitive, or if the client is investing at least $1,000,000, otherwise it won’t make you much. If your client deals with 3 other brokers on treasuries, you will all be fighting for very little money. It’s very easy to get a quick quote on treasuries. Every major dealer owns them, and they can be purchased quickly. You or your trader will contact a major brokerage firm (Merrill Lynch, UBS etc.) and buy them. Not much money yes, still, it is assets you are controlling, and it could be used as available money to swap out of into a better investment for the client.

Treasuries are very safe of course, that’s why they are bought. Only buying treasuries will diminish the rate of return of the entire portfolio, if that is their only or main investment vehicle. Treasuries offer flexibility though. The market values on them will normally hold up well over time. They are very liquid and can be traded instantly. You should sell them only as “time bucket” or maturity gap placing.

If you see the bank has nothing maturing in the first half of a year for instance, you can recommend treasuries there too. Remember, institutions are looking for best price, but also good advice. The medium sized banks ($50 million - $500 million assets) will value good planning and thoughtful recommendations over dealing with 10 brokers all day. The larger institutions are more complicated, and require more price awareness. They think they have the ideas covered and you may have to just be an order taker with them.

Selling Mortgage Backed Securities or CMO's

Mortgage backed securities offer the best alternative to decreased loan demand. Pass throughs, CMO’s and adjustable rate MBS’s are paid to the bank just like a loan that the banks has made for a mortgage. If a person takes out a $250,000 mortgage, the customer is paying back the bank monthly with principle and interest. As you know, if you own a home, your initial payments are mostly INTEREST in the early years. A mortgage backed security, if it is a new issue will operate the same way.

Length of the outstanding mortgages, or current face of the mortgages are a factor. “Seasoned pools”, as they are called, are mortgage pools that have had several years of payment on them. They have more predictable payments and duration. They will normally pay better because of that. Seasoned pools are usually what banks are looking for. They are generally interested in better cash flow and predictable cash flow.

The compensation or mark up potential is good in mortgage backed bonds. They are priced above treasuries because, although they are AAA rated, they are not absolute in their pay off and the payments fluctuate. Since they are usually 15-30 years in duration, they allow for price mark up. Where treasuries and straight agency debt allow for a few ticks to a .25, MBS’s can create spreads between buying and selling them up to a ½ or ¾ of point. This can translate to a $5,000 commission on a $1 million sale. Remember, a million dollars in one bond is not unusual for most institutions, and for banks over $500 million in assets, it’s normal.

Sell Bonds

Bond Price and Yield

When interest rates rise, existing bond prices decline. This inverse price-yield relationship exists because bonds have a fixed nominal yield and the price is based on how attractive or not interest rates are compared to that fixed rate.

If interest rates increase, new bonds will come out at a higher rate - thus the existing bond is now les attractive and will trade at a lower price. If bond yields decrease, existing fixed income investment will increase as those will become more attractive.

Long term bond prices are more volatile than short term bond prices. The lower coupon securities of the same maturity will be more volatile as well.

It is best to invest in long term bonds when interest rates are high or peaked and are expected to drop. This will increase the price.

Investment Articles

Inverted Yield Curve - Bond Curve

When the yield curve is inverted, short term interest rates are higher than long term rates. This normally occurs when interest rates have been targeted to rise based on tightenting by the federal reserve board.

When interest rates are higher on the short term or an inverted bond curve is in place, many investors will polace their money in money market investment securities.

Yield curves can also fluctuate or be flat - where interest rates are fairly equal across several maturities on the curve.

Treasury STRIP Yield - T Strip

A treasury STRIP is a 0 coupon bond issued by the U.S Government and has a yield based on a discount price and the maturity.

Since T Strips are 0 coupon - they do not pay interest, so the overall rate of return is shown in it's yield to maturity. These securities are backed by the US Government and were created from Treasury Notes and Bonds. Strips are not considered new debt, but redeemed bonds re-issued as 0 coupon yield securities.

Maturities are normally long term (over 5 years) and the T Strip yield is figured using the deep discount price (below par), and the years to maturity. This will give the investment a realized overall rate of return or yield to maturity.

http://www.aitraining.com/treasurystrip.htm

Treasury Bond

Yields on Treasury bonds fluctuate just like any other debt security. T Bonds are long term (10-30 years) and pay interest semi-annually.

Because US Treasury Bonds are AAA rated with higher credit quality than corporate bonds or other debt securities, their yields tend to be lower than others. However, they are very liquid and trade very close to the interest rate or yield markets.

http://www.aitraining.com/treasurybond.htm

Yield To Call - Callable Bonds

Many bonds, including corporate and municipal securities are callable and will have a yield to call.

An issuer that puts a call feature on a bond is inserting that date as a way to refinance out early, if they choose to do so. The advantage to the issuer is that if interest rates decline, the municipality or corporation can redeem the higher interest rate bond and replace it with a lower bond rate. If this take place, the investor will realize a yield to call - instead of a yield to maturity.

Whether the YTC is better or worse for the investor will depend on when the redemption takes place and what price the bond is called at. The price is important, as it can be below, the same, or higher than the price the invetor paid. That will determine call yield.

If the bond is called at a higher price than what was paid, the YTC will be higher and vice versa.

The main risk with a bond that is called is it forces the investor to reinvest the money at a lower rate, as bond yields should be lower in the market at that time.

There could be other reasons for calling a bond early such as: rearranging maturities or just having the money to not have to offer the debt anymore. There is no reason to issue bonds if you don't need the money.

http://www.brokerjobs.com/bondyield.htm

Tax Free Yield

One of the yields investors are seeking more and more are tax free yields offered by municipal bonds.

Muni bonds are federally exempt on the interest received. They are subject to state and local tax. The heavier the tax bracket - the better the yield will be.

If a bond was issued at par and had a coupon rate of 4% and the investor is in the 30% tax bracket, the tax free rate of return would be figured out by dividing 4 by 100 - the tax bracket of 30. This would come out to 5.71%

Municipal bonds offer a chance to earn interest without taxation. If you buy a bond issued in your home state, you could be triple tax free.

Rating, coupon rate, geographical area and bracket are the main factors of whether someone should buy a muni bond.

http://www.brokerjobs.com/munibonds.htm

Yield To Maturity Calculate

Calculating yield to maturity under the "rule of thumb" method is not difficult. The concept with it is the YTM is based on the Nominal Yield, Price and the years to maturity. So, the formula or calculation is based on that.

Premium bonds have a lower yield to maturity vs. the nominal rate. That is because the nominal yield only pays to par value. Thus if the bond was bought above par, the premium amount does not earn interest and the premium is not paid at maturity. The investor is losing the above par amount at the end of the term. If the investment was sold beforehand at a profit - the cost would be a profit.

Example

A 5% bond was purchased at $1150 and the maturity is 15 years. Calculating YTM would be based on all of this information. The total premium amount is $150 - divided over 15 years would give you $10 per year. That is the amount that is basically lost each year on the price - if held to maturity.

The way the formula is calculated is you take the yearly real interest - which is $50 and then subtract the lost above par yearly price of $10. This leaves you with a real yearly return of $40. Then divide $40 by the average price of the bond during it's life. Since par ($1000) is the redemption price and $1150 was the price that was paid - the median price would be $1075.

So $40 divided by $1075 would be the YTM = 3.72%

Discount bonds are calculated the same way - except the yearly discount is added on to the nominal interest payments. This would result in a higher YTM calculation.

http://www.aitraining.com/ytm.htm

Current Yield

A bond's current yield can be found by dividing the coupon or nominal by the current market price of the security. It is not an overly important yield to investors - as it is always changing and is most important if someone is pricing the bond to sell. If an investor is holding the security to maturity - then the current yield is not a big concern.

A debt that is priced above par (premium) will have a lower current yield vs. the nominal. A 7% corporate debenture priced at $102 will have a current of 6.86% ($70 divided by $1020). Discounted bonds will have a higher current yield than it's coupon rate.

http://www.aitraining.com/currentyield.htm

Nominal Yield

The fixed interest rate on a bond is known as it's nominal yield or coupon rate. This is the rate that the issuer pays to investors. It is fixed, never changes and is paid to par value only.

Since the nominal yield is fixed, during times of lower current interest rates - bonds with high nominal rates will be priced at a premium. If a 7% bond is trading while interest rates are only 5%, bond brokers and traders will price the bond above par, which will give the security a lower yield to maturity.

High nominal coupons provide good current income, since that is the amount that is paid in internest to the bondholder. However that interest money is only paid to par value - so the nominal yield provides part of a bond's return.

When interest rates are lower, new offerings will come out at lower nominal rates. When yields are higher - new issues come out higher. It is in the secondary market that bonds will normally trade above or below par, based on the interest rate picture on similar bonds and the nominals that they are at.

http://www.aitraining.com/bondyield.htm

Yield Basics

Bonds are priced to offer an effective yield to investors. Since fixed income securites are sold in par value amounts, the pricing of these bonds will effect the overall yield an investor gets.

Although you may receive a high coupon rate paid to par (nominal rate), if a premium was paid, your overall yield to maturity will be lower than the coupon rate. This is normal, as the coupon cannot be changed, but interest rates do change. The only think the market or a bond trader can do is re-price these bonds to current interest rate levels. That adjustment will be reflected in the current and yield to maturity.