finance material

8/7/2019 Finance Material

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Topics covered in this document:

Overview (Types of Investments)

Stocks

Bonds

Options

Futures

Risk and Diversification

Duration

Convexity

Overview (for more info, have a look at

http://www.investopedia.com/university/20_investments/ )

Investment objectives will almost always change for every investor throughout theirlives. Capital appreciation might be more important while you are young, meanwhileentering your golden years might place a greater emphasis on providing income.Whatever your objective, knowing what investment options are out there is extremelyimportant.

Furthermore, if there is one consistent idea is that diversification is king. A diversifiedportfolio will not only reduce unwanted risk but also contributes to a winning portfolio. Awell-diversified portfolio doesn't necessarily mean just buying more than one stock.Instead branching out into other areas of investment could be a viable alternative.Without further ado, here are 20 Investments that we feel every investor should be awareof:

20 Investments Investors Should Know

1. American Depository Receipt - ADR2. Annuity3. Closed-End Investment Fund4. Collectibles5. Common Stock6. Convertible Securities7. Corporate Bond8. Futures Contract9. Life Insurance
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10. Money Market Securities11. Mortgage Backed Securities - MBS12. Municipal Security - Munis13. Mutual Fund14. Options

15. Preferred Stock16. Real Estate and Property17. Real Estate Investment Trust - REIT18. Treasuries (Government Securities)19. Unit Investment Trust - UIT

20. Zero Coupon Securities

Stock Basics: What Are Stocks?

The Definition of a StockPlain and simple, stock is a share in the ownership of a company. Stock represents aclaim on the company's assets andearnings. As you acquire more stock, your ownershipstake in the company becomes greater. Whether you say shares,equity, or stock, it allmeans the same thing.

The importance of being a shareholder is that you are entitled to a portion of thecompanys profits and have a claim on assets. Profits are sometimes paid out in the formofdividends. The more shares you own, the larger the portion of the profits you get. Yourclaim on assets is only relevant if a company goesbankrupt. In case ofliquidation, you'll

receive what's left after all the creditors have been paid. This last point is worth repeating:the importance of stock ownership is your claim on assets and earnings. Without

this, the stock wouldn't be worth the paper it's printed on.

Dividend: Distribution of a portion of a company's earnings, decided by the board ofdirectors, to a class of its shareholders. The amount of a dividend is quoted in the amounteach share receives or in other words dividends per share.

Liquidation

1. When a business or firm is terminated or bankrupt, its assets are sold and the proceeds

pay creditors. Any leftovers are distributed to shareholders.

2. Any transaction that offsets or closes out a long or short position.

Creditors liquidate assets to try and get as much of the money owed to them as possible.They have first priority to whatever is sold off. After creditors are paid, the shareholders

get whatever is left with preferred shareholders having preference over common

shareholders.
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Stock Basics: What Causes Prices To Change?

Stock prices change everyday by market forces. By this we mean that share prices changebecause ofsupply and demand. If more people want to buy a stock (demand) than sell it(supply), then the price moves up. Conversely, if more people wanted to sell a stock than

buy it, there would be greater supply than demand, and the price would fall.

That being said, the principal theory is that the price movement of a stock indicates whatinvestors feel a company is worth. Don't equate a company's value with the stock price.The value of a company is its market capitalization, which is the stock price multiplied bythe number ofshares outstanding.

The most important factor that affects the value of a company is its earnings. Earnings aretheprofita company makes, and in the long run no company can survive without them.

Stock Basics: How To Read a Stock Table/Quote

Any financial paper has stock quotes that will look something like the image below:

Columns 1 & 2: 52-Week Hi and Low - These are the highest and lowest prices atwhich a stock has traded over the previous 52 weeks (one year). This typically does notinclude the previous day's trading.

Column 3: Company Name & Type of Stock - This column lists the name of thecompany. If there are no special symbols or letters following the name, it is commonstock. Different symbols imply different classes of shares. For example, "pf" means theshares arepreferred stock.

Column 4: Ticker Symbol - This is the unique alphabetic name which identifies thestock. If you watch financial TV, you have seen theticker tape move across the screen,quoting the latest prices alongside this symbol. If you are looking for stock quotes online,you always search for a company by the ticker symbol.Column 5: Dividend Per Share - This indicates the annualdividend payment per share.If this space is blank, the company does not currently pay out dividends.

Column 6: Dividend Yield - This states the percentage return on the dividend, calculated
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as annual dividends per share divided by price per share.

Column 7: Price/Earnings Ratio - This is calculated by dividing the current stock priceby earnings per share from the last four quarters. For more detail on how to interpret this,see ourP/E Ratio tutorial.

Column 8: Trading Volume - This figure shows the total number of shares traded forthe day, listed in hundreds. To get the actual number traded, add "00" to the end of thenumber listed.

Column 9 & 10: Day High & Low - This indicates the price range at which the stockhas traded at throughout the day. In other words, these are the maximum and theminimum prices that people have paid for the stock.

Column 11: Close - The close is the last trading price recorded when the market closedon the day. If the closing price is up or down more than 5% than the previous day's close,

the entire listing for that stock is bold-faced. Keep in mind, you are not guaranteed to getthis price if you buy the stock the next day because the price is constantly changing (evenafter the exchange is closed for the day). The close is merely an indicator of pastperformance and except in extreme circumstances serves as a ballpark of what youshould expect to pay.

Column 12: Net Change - This is the dollar value change in the stock price from theprevious day's closing price. When you hear about a stock being "up for the day," itmeans the net change was positive

Summary

Stock means ownership. As an owner, you have a claim on the assets and earningsof a company as well as voting rights with your shares.

Stock is equity, bonds are debt. Bondholders are guaranteed a return on theirinvestment and have a higher claim than shareholders. This is generally whystocks are considered riskier investments and require a higher rate of return.

You can lose all of your investment with stocks. The flip-side of this is you canmake a lot of money if you invest in the right company.

The two main types of stock are common and preferred. It is also possible for a

company to create different classes of stock.

Stock markets are places where buyers and sellers of stock meet to trade. TheNYSE and the Nasdaq are the most important exchanges in the United States.

Stock prices change according to supply and demand. There are many factorsinfluencing prices, the most important being earnings.
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getting paid back. For example, the U.S. Government is far more secure than anycorporation. Theirdefault risk--the chance of the debt not being paid back--is extremelysmall, so small that the U.S. government securities are known asrisk free assets. Thereason behind this is that a government will always be able to bring in future revenuethrough taxation. A company on the other hand must continue to make profits, which is

far from guaranteed. This means the corporations must offer a higheryield in order toentice investors--this is the risk/return tradeoffin action.

Thebond rating system helps investors distinguish a company's credit risk. Think of abond rating as the report card for a company's credit rating.Blue-chip firms, which aresafer investments, have a high rating while risky companies have a low rating. The chartbelow illustrates the different bond rating scales from the major rating agencies in theUnited States: Moody's, Standard and Poor's, and Fitch Ratings:

Bond RatingGrade RiskMoody's S&P/ Fitch

Aaa AAA Investment Highest Quality

Aa AA Investment High Quality

A A Investment Strong

Baa BBB Investment Medium Grade

Ba, B BB, B Junk Speculative

Caa/Ca/C CCC/CC/C Junk Highly Speculative

C D Junk In Default

Notice that if the company falls below a certain credit rating, its grade changes frominvestment quality to junk status. Junk bonds are aptly named: they are the debt ofcompanies in some sort of financial difficulty. Because they are so risky they have tooffer much higher yields than any other debt. This brings up an important point: not allbonds are inherently safer than stocks. Certain types of bonds can be just as risky, if notmore risky, than stocks.

Yield, Price, and Other Confusion

The price fluctuation of bonds is probably the most confusing part. In fact, many newinvestors are surprised to learn that a bond's price, just like that of any other publicly-

traded security, changes on a daily basis! Here's the thing: so far we've talked aboutbonds as if everybody held them to maturity. It's true that if you do this, you'reguaranteed to get your principal back; however, a bond does not have to be held tomaturity. At any time a bond can be sold in the open market, where the price canfluctuate, sometimes dramatically. We'll get to how price changes in a bit. First we needto introduce the concept of yield.

Measuring Return with Yield
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Yield is a figure that shows the return you get on a bond. The simplest version of yield iscalculated by the following formula: yield = coupon amount/price. When you buy a bondat par, yield is equal to the interest rate. When the price changes, so does the yield.

Yield to Maturity (YTM): The rate of return anticipated on a bond if it is held until the

maturity date. YTM is considered a long-term bond yield expressed as an annual rate.The calculation of YTM takes into account the current market price, par value, couponinterest rate and time to maturity. It is also assumed that all coupons are reinvested at thesame rate. Sometimes this is simply referred to as "yield" for short.

Putting It All Together: The Link Between Price and Yield

The yield's relationship with price can be summarized as follows: when price goes up,yield goes down and vice versa. Technically you'd say the bond's prices and its yield areinversely related.

Reading a Bond Table

Column 1: Issuer - This is the company, state (or province), or country that is issuing the

bond.

Column 2: Coupon - The coupon refers to the fixed interest rate that the issuer pays tothe lender.

Column 3: Maturity Date - This is the date on which the borrower will pay the investorstheir principal back. Typically only the last two digits of the year are quoted, 25 means2025, 04 is 2004, etc.


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Column 4: Bid Price. This is the price someone is willing to pay for the bond. It isquoted in relation to 100, no matter what the par value is. Think of the bid price as apercentage: a bond with a bid of 93 means it is trading at 93% of its par value.

Column 5: Yield. The yield indicates annual return until the bond matures. Usually thisis the yield to maturity, not current yield. If thebond is callable it will have a "c--" wherethe "--" is the year the bond can be called. For example c10 means the bond can be calledas early as 2010.

Callable bond: A bond that can be redeemed by the issuer prior to its maturity. Usually apremium is paid to the bond owner when the bond is called. Also known as a"redeemable bond".

Summary:

Bonds are just like IOUs. Buying a bond means you are lending out your money. Bonds are also called fixed-income securities because the cash flow from them is

fixed. Stocks are equity; bonds are debt. The key reason for purchasing bonds is to diversify your portfolio. Issuers of bonds are governments and corporations. A bond is characterized by its face value, coupon rate, maturity, and issuer. Yield is the rate of return you get on a bond. When price goes up, yield goes down and vice versa. When interest rates rise, the price of bonds in the market falls and vice versa. Bills, notes, and bonds are all fixed-income securities classified by maturity. Government bonds are the safest, followed by municipal bonds, and then

corporate bonds. Bonds are not risk free. It's always possible--especially for corporate bonds--for

the borrower to default on the debt payments. High risk/high yield bonds are known as junk bonds. You can purchase most bonds through a brokerage or bank. If you are a U.S.

citizen you can buy through TreasuryDirect. Brokers often don't charge a commission to buy bonds but instead markup the

price.

Options Basics: Introduction

Nowadays, many investors' portfolios include investments such as mutual funds, stocks,and bonds. But the variety of securities you have at your disposal does not end there. Atype of security called an option presents a world of opportunity to sophisticatedinvestors.

The power of options lies in their versatility. They enable you to adapt or adjust yourposition according to any situation that arises. Options can be as speculative or as
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conservative as you want. This means you can do everything from protecting a positionfrom a decline to outright betting on the movement of a market or index.

This versatility, however, does not come without its costs. Options are complex securitiesand can be extremely risky. This is why, when trading options, you'll see a disclaimer

like the following:

Options involve risks and are not suitable for everyone. Option trading can bespeculative in nature and carry substantial risk of loss. Only invest with risk capital.

Options Basics:What are Options?An option is a contract giving the buyer the right, but not the obligation, to buy or sell anunderlying asset at a specific price on or before a certain date. An option, just like a stockor bond, is asecurity. It is also a binding contract with strictly defined terms andproperties.

Still confused? The idea behind an option is present in many everyday situations. Say forexample you discover a house that you'd love to purchase. Unfortunately, you won't havethe cash to buy it for another three months. You talk to the owner and negotiate a dealthat gives you an option to buy the house in three months for a price of $200,000. Theowner agrees, but for this option, you pay a price of $3,000.

This example demonstrates two very important points. First, when you buy an option,you have a right but not the obligation to do something. You can always let the expirationdate go by, at which point the option is worthless. If this happens, you lose 100% of yourinvestment, which is the money you used to pay for the option. Second, an option ismerely a contract that deals with an underlying asset. For this reason, options are called

derivatives, which means an option derives its value from something else. In ourexample, the house is the underlying asset. Most of the time, the underlying asset is astockor an index.

Underlying: 1. In derivatives, the security that must be delivered when aderivative contract, such as a put or call option, is exercised.

2. In equities, the common stock that must be delivered when a warrant is exercised, orwhen a convertible bond or convertible preferred share is converted to common stock.

Security: An instrument representing ownership (stocks), a debt agreement (bonds), or

the rights to ownership (derivatives).

Calls and Puts

The two types of options are calls and puts:

A call gives the holder the right to buy an asset at a certain price within a specific periodof time. Calls are similar to having a long positionon a stock. Buyers of calls hope thatthe stock will increase substantially before the option expires.
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A put gives the holder the right to sell an asset at a certain price within a specific periodof time. Puts are very similar to having ashort positionon a stock. Buyers of puts hopethat the price of the stock will fall before the option expires.

Participants in the Options MarketThere are four types of participants in options markets depending on the position theytake:

1. Buyers of calls2. Sellers of calls3. Buyers of puts4. Sellers of puts

People who buy options are called holders and those who sell options are called writers;furthermore, buyers are said to have long positions, and sellers are said to have short

positions.

Here is the important distinction between buyers and sellers:-Call holders and put holders (buyers) are not obligated to buy or sell. They have thechoice to exercise their rights if they choose.-Call writers and put writers (sellers) howeverare obligated to buy or sell. This meansthat a seller may be required to make good on their promise to buy or sell.

Don't worry if this seems confusing--it is. For this reason we are going to look at optionsfrom the point of view of the buyer. Selling options is more complicated and can thus beeven riskier. At this point it is sufficient to understand that there are two sides of anoptions contract.

The Lingo

To trade options, you'll have to know the terminology associated with the options market.

The price at which an underlying stock can be purchased or sold is called the strike price.This is the price a stock price must go above (for calls) or go below (for puts) before aposition can be exercised for a profit. All of this must occur before the expiration date.

An option that is traded on a national options exchange such as theCBOE is known as alisted option. These have fixed strike prices and expiration dates. Each listed optionrepresents 100 shares of company stock (known as a contract).

For call options, the option is said to be in-the-moneyif the share price is above the strikeprice. A put option is in-the-money when the share price is below the strike price. Theamount by which an option is in-the-money is referred to as intrinsic value.

The total cost (the price) of an option is called thepremium. This price is determined byfactors including the stock price, strike price, time remaining until expiration (time
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value), and volatility. Because of all these factors, determining the premium of an optionis complicated and beyond the scope of this tutorial.

Why use Options?

There are two main reasons why an investor would use options: to speculate and tohedge.

SpeculationYou can think ofspeculation as betting on the movement of a security. The advantage ofoptions is that you aren't limited to making a profit only when the market goes up.Because of the versatility of options, you can also make money when the market goesdown or even sideways.

Hedging

The other function of options is hedging. Think of this as an insurance policy. Just as you

insure your house or car, options can be used to insure your investments against adownturn. Critics of options say that if you are so unsure of your stock pick that you needa hedge, you shouldn't make the investment. On the other hand, there is no doubt thathedging strategies can be useful, especially for large institutions. Even the individualinvestor can benefit. Imagine you wanted to take advantage of technology stocks andtheir upside, but say you also wanted to limit any losses. By using options, you wouldcost-effectively be able to restrict your downside while enjoying the full upside.

Types of OptionsThere are two main types of options:

American options can be exercised at any time between the date of purchase andthe expiration date. The example about Cory's Tequila Co. is an example of theuse of an American option. Most exchange-traded options are of this type.

European options are different from American options in that they can only beexercised at the end of their life.

The distinction between American and European options has nothing to do withgeographic location.

How to Read an Options Table
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Column 1: Strike Price - This is the stated price per share for which an underlying stockmay be purchased (for a call) or sold (for a put) upon the exercise of the option contract.

Option strike prices typically move by increments of $2.50 or $5.00 (even though in theabove example it moves in $2 increments).

Column 2: Expiry Date - This shows the termination date of an option contract.Remember thatU.S.-listed options expire on the third Friday of the expiry month.

Column 3: Call or Put - This column refers to whether the option is a call (C) or put (P).

Column 4: Volume - This indicates the total number of options contracts traded for the

day. The total volume of all contracts is listed at the bottom of each table.

Column 5: Bid - This indicates the price someone is willing to pay for the optionscontract.

Column 6: Ask - This indicates the price at which someone is willing to sell an optionscontract.

Column 7: Open Interest - Open interest is the number of options contracts that areopen; these are contracts that have not expired nor been exercised.

SummaryHere's recap:

An option is a contract giving the buyer the right but not the obligation to buy orsell an underlying asset at a specific price on or before a certain date.

Options are derivatives because they derive their value from an underlying asset. A call gives the holder the right to buy an asset at a certain price within a specific

period of time.
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A put gives the holder the right to sell an asset at a certain price within a specificperiod of time.

There are four types of participants in options markets: buyers of calls, sellers ofcalls, buyers of puts, and sellers of puts.

Buyers are often referred to as holders and sellers are also referred to as writers.

The price at which an underlying stock can be purchased or sold is called thestrike price. The total cost of an option is called the premium, which is determined by factors

including the stock price, strike price, and time remaining until expiration. A stock option contract represents 100 shares of the underlying stock. Investors use options both to speculate and hedge risk. Employee stock options are different from listed options because they are a

contract between the company and the holder. (Employee stock options do notinvolve any third parties.)

The two main classifications of options are American and European. Long term options are known as LEAPS.

Futures Fundamentals: A futures contract is a type of derivative instrument, or financialcontract, in which two parties agree to transact a set of financial instruments or physicalcommodities for future delivery at a particular price. If you buy a futures contract, youare basically agreeing to buy something, for a set price, that a seller has not yet produced.But participating in the futures market does not necessarily mean that you will beresponsible for receiving or delivering large inventories of physical commoditiesremember, buyers and sellers in the futures market primarily enter into futures contractsto hedge risk or speculate rather than exchange physical goods (which is the primaryactivity of the cash/spot market). That is why futures are used as financial instruments bynot only producers and consumers but also speculators.

What Exactly Is a Futures Contract?

Let's say, for example, that you decide to subscribe to cable TV. As the buyer, you enterinto an agreement with the cable company to receive a specific number of cable channelsat a certain price every month for the next year. This contract made with the cablecompany is similar to a futures contract, in that you have agreed to receive a product at afuture date, with the price and terms for delivery already set. You have secured your pricefor now and the next year--even if the price of cable rises during that time. By enteringinto this agreement with the cable company, you have reduced your risk of higher prices.

That's how the futures market works. Except instead of a cable TV provider, a producerof wheat may be trying to secure a selling price for next season's crop, while a breadmaker may be trying to secure a buying price to determine how much bread can be madeand at what profit. So the farmer and the bread maker may enter into a futures contractrequiring the delivery of 5,000 bushels of grain to the buyer in June at a price of $4 perbushel. By entering into this futures contract, the farmer and the bread maker secure aprice that both parties believe will be a fair price in June. It is this contract-and not thegrain per se--that can then be bought and sold in the futures market.
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So, a futures contract is an agreement between two parties: a short position, the party whoagrees to deliver a commodity, and a long position, the party who agrees to receive acommodity. In the above scenario, the farmer would be the holder of the short position(agreeing to sell) while the bread maker would be the holder of the long (agreeing tobuy). (We will talk more about the outlooks of the long and short positions in the section

on strategies, but for now it's important to know that every contract involves bothpositions.)

In every futures contract, everything is specified: the quantity and quality of thecommodity, the specific price per unit, and the date and method of delivery. The priceof a futures contract is represented by the agreed-upon price of the underlying commodityor financial instrument that will be delivered in the future. For example, in the abovescenario, the price of the contract is 5,000 bushels of grain at a price of $4 per bushel.

Summary on Futures:

The futures market is a global marketplace, initially created as a place for farmersand merchants to buy and sell commodities for either spot or future delivery. Thiswas done to lessen the risk of both waste and scarcity.

Rather than trade in physical commodities, futures markets buy and sell futurescontracts, which state the price per unit, type, value, quality and quantity of thecommodity in question, as well as the month the contract expires.

The players in the futures market are hedgers and speculators. A hedger tries tominimize risk by buying or selling now in an effort to avoid rising or decliningprices. Conversely, the speculator will try to profit from the risks by buying orselling now in anticipation of rising or declining prices.

The CFTC and the NFA are the regulatory bodies governing and monitoring

futures markets in the U.S. It is important to know your rights. Futures accounts are credited or debited daily depending on profits or losses

incurred. The futures market is also characterized as being highly leveraged dueto its margins; although leverage works as a double-edged sword. It's important tounderstand the arithmetic of leverage when calculating profit and loss, as well asthe minimum price movements and daily price limits at which contracts can trade.

Going long, going short, and spreads are the most common strategies usedwhen trading on the futures market.

Once you make the decision to trade in commodities, there are several ways to participatein the futures market. All of them involve risk, some more than others. You can tradeyour own account, have a managed account or join a commodity pool.

Risk and Diversification:

What is Risk?

Whether it is investing, driving, or just walking down the street, everyone exposesthemselves to risk. Your personality and lifestyle play a big deal on how much risk you
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are comfortably able to take on. If you invest in stocks and have trouble sleeping at nightsbecause of your investments you are probably taking on too much risk.

The Different Types of Risk

Lets take a look at the two basic types of risk:

Systematic Risk- A risk that influences a large number of assets. An example ispolitical events. It is virtually impossible to protect yourself against this type ofrisk.

Unsystematic Risk- Sometimes referred to as "specific risk". It's risk that affectsa very small number of assets. An example is news that affects a specific stocksuch as a sudden strike by employees.

Diversification is the only way to protect yourself from unsystematic risk. (We willdiscuss diversification later in this tutorial).

Now that we've determined the fundamental types of risk lets look at more specific typesof risk, particularly when we talk about stocks and bonds:

Credit or Default Risk - This is the risk that a company or individual will be

unable to pay the contractual interest or principal on its debt obligations. Thistype of risk is of particular concern to investors who hold bond's within their

portfolio. Government bonds, especially those issued by the Federalgovernment, have the least amount of default risk and least amount of

returns while corporate bonds tend to have the highest amount of default riskbut also the higher interest rates. Bonds with lower chances of default are

considered to be investment grade, and bonds with higher chances areconsidered to be junk bonds. Bond rating services, such as Moody's, allows

investors to determine which bonds are investment-grade, and which bondsare junk.

Country Risk This refers to the risk that a country won't be able to honor

its financial commitments. When a country defaults it can harm theperformance of all other financial instruments in that country as well as other

countries it has relations with. Country risk applies to stocks, bonds, mutualfunds, options and futures that are issued within a particular country. This

type of risk is most often seen in emerging markets or countries that have asevere deficit.

Foreign Exchange Risk When investing in foreign countries you must

consider the fact that currency exchange rates can change the price of theasset as well. Foreign exchange risk applies to all financial instruments that

are in a currency other than your domestic currency. As an example, if youare a resident of America and invest in some Canadian stock in Canadian

dollars, even if the share value appreciates, you may lose money if theCanadian dollar depreciates in relation to the American dollar.

Interest Rate Risk - A rise in interest rates during the term of your debt

securities hurts the performance of stocks and bonds.


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Political Risk - This represents the financial risk that a country's government

will suddenly change its policies. This is a major reason that second and thirdworld countries lack foreign investment.

Market Risk - This is the most familiar of all risks. It's the day to day

fluctuations in a stocks price. Also referred to as volatility.Market risk appliesmainly to stocks and options. As a whole, stocks tend to perform well during a

bull market and poorly during a bear marketvolatility is not so much acause but an effect of certain market forces. Volatility is a measure of risk

because it refers to the behavior, or temperament, of your investmentrather than the reason for this behavior. Because market movement is the

reason why people can make money from stocks, volatility is essential forreturns, and the more unstable the investment the more chance it can go

dramatically either way.

Diversification

With the stock markets bouncing up and down 5% every week there needs to be asafety net for individual investors. Diversification is the answer.

Diversifying your portfolio may not be the sexiest of investment topics. Still, most

investment professionals agree that while it does not guarantee against a loss,diversification is the most important component to helping you reach your long-

range financial goals while minimizing your risk. But, remember that no matter howmuch diversification you do, it can never reduce risk down to zero.

What do you need to have a well diversified portfolio? There are 3 main aspects you

should have to ensure the best diversification:

1. Your portfolio should be spread among many different investment vehiclessuch as cash, stocks, bonds, mutual funds, and perhaps even some realestate.

2. Your securities vary in risk. You're not restricted to picking only blue chipstocks. In fact, the opposite is true. Picking different investments with

different rates of return will ensure that large gains offset losses in otherareas. Keep in mind that this doesn't mean invest in penny stocks!

Your securities should vary by industry, minimizing unsystematic risk to small groupsof companies.

Another question people always ask is how many stocks they should buy to reducethe risk of their portfolio. The portfolio theory tells us that after 10-12 diversified

stocks you are very close to optimal diversification. This doesn't mean buying 12

internet or tech stocks will give you optimal diversification, instead you need to buystocks of different sizes and from various industries.
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Advanced Bond Concepts: Duration(http://www.investopedia.com/university/advancedbond/advancedbond6.asp )

The term duration, having a special meaning in the context of bonds, is a

measurement of how long in years it takes for the price of a bond to be repaid by its

internal cash flows. It is an important measure for investors to consider, as bondswith higher durations are more risky and have higher price volatility than bonds withlower durations.

For each of the two basic types of bonds the duration is the following:

1. Zero-coupon bond Duration is equal to its time to maturity.

2. Vanilla bond - Duration will always be less than its time tomaturity.

Let's first work through some visual models that demonstrate the properties of

duration for a zero-coupon bond and a vanilla bond.

Duration of a Zero Coupon Bond

The red lever above represents the four-year time period it takes for a zero couponto mature. The money bag balancing on the far right represents the future value of

the bond, the amount that will be paid to the bondholder at maturity. The fulcrum, orthe point holding the lever, represents duration, which must be positioned where the

red lever is balanced. The fulcrum balances the red lever at the point on the time linewhen the amount paid for the bond and the cash flow received from the bond are

equal. Since the entire cash flow of a zero-coupon bond occurs at maturity, the

fulcrum is located directly below this one payment.

Duration of a Vanilla or Straight BondConsider a vanilla bond that pays coupons annually and matures in five years. Its

cash flows consist of five annual coupon payments and the last payment includes theface value of the bond.
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The moneybags represent the cash flows you will receive over the five-year period.To balance the red lever (at the point where total cash flows equal the amount paid

for the bond), the fulcrum must be further to the left, at a point before maturity.Unlike the zero-coupon bond, the straight bond pays coupon payments throughout

its life and therefore repays the full amount paid for the bond sooner.

Factors Affecting Duration

It is important to note, however, that duration changes as the coupons are paid tothe bondholder. As the bondholder receives a coupon payment, the amount of the

cash flow is no longer on the timeline, which means it is no longer counted as afuture cash flow that goes towards repaying the bondholder. Our model of the

fulcrum demonstrates this: as the first coupon payment is removed from the redlever (paid to the bondholder), the lever is no longer in balance (because the coupon

payment is no longer counted as a future cash flow).

The fulcrum must now move to the right in order to balance the lever again:


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Duration increases immediately on the day a coupon is paid, but throughout the lifeof the bond, the duration is continually decreasing as time to the bond's maturity

decreases. The movement of time is represented above as the shortening of the red

lever: notice how the first diagram had five payment periods and the above diagramhas only four. This shortening of the timeline, however, occurs gradually, and as it

does, duration continually decreases. So, in summary, duration is decreasing as timemoves closer to maturity, but duration also increases momentarily on the day a

coupon is paid and removed from the series of future cash flowsall this occurs until

duration, as it does for a zero-coupon bond, eventually converges with the bond'smaturity.

Duration: Other factorsBesides the movement of time and the payment of coupons, there are other factors

that affect a bond's duration: the coupon rate and its yield. Bonds with high couponrates and in turn high yields will tend to have lower durations than bonds that pay

low coupon rates, or offer a low yield. This makes empirical sense, since when abond pays a higher coupon rate, or has a high yield, the holder of the security

receives repayment for the security at a faster rate. The diagram below summarizeshow duration changes with coupon rate and yield.

Types of DurationThere are four main types of duration calculations, each of which differ in the way

they account for factors such as interest rate changes and the bond's embedded

options or redemption features. The four types of durations are Macaulay duration,modified duration, effective duration, and key-rate duration.

Macaulay DurationThe formula usually used to calculate a bond's basic duration is the Macaulay
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duration, which was created by Frederick Macaulay in 1938 but not commonly useduntil the 1970s.

Macaulay duration is calculated by adding the results of multiplying the present valueof each cash flow by the time it is received, and dividing by the total price of the

security. The formula for Macaulay duration is as follows:

n = number of cash flows

t = time to maturityC = cash flow

i = required yieldM = maturity (par) value

P = bond price

Remember that bond price equals .

So the following is an expanded version of Macaulay duration:

Let's go through an example:

Betty holds a five-year bond with a par value of $1000 and coupon rate of 5%. For

simplicity, let's assume that the coupon is paid annually and that interest rates are5%. What is the Macaulay duration of the bond?
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= 4.55 years

Fortunately, if you are seeking the Macaulay duration of a zero-coupon bond, the

duration would be equal to the bond's maturity, so there is no calculation required.

Modified DurationModified duration is a modified version of the Macaulay model that accounts for

changing interest rates. Because they affect yield, fluctuating interest rates will

affect duration, so this modified formula shows how much the duration changes foreach percentage change in yield. For bonds without any embedded features, bondprice and interest rate move in opposite directions, so there is an inverse relationship

between modified duration and an approximate one-percentage change in yield.Because the modified duration formula shows how a bond's duration changes in

relation to interest rate movements, the formula is appropriate for investors wishingto measure the volatility of a particular bond. Modified duration is calculated as the

following:

OR

Let's continue analyzing Betty's bond and run through the calculation of her modifiedduration. Currently her bond is selling at $1000, or par, which translates to a yield to

maturity of 5%. Remember that we calculated a Macaulay duration of 4.55.


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= 4.33 years

Our example shows that if the bond's yield changed from 5% to 6%, the duration ofthe bond will have declined to 4.33 years. Because it calculates how duration will

change when interest increases by 100 basis points, the modified duration will

always be lesser than Macaulay duration.

Effective DurationAs the modified duration formula discussed above assumes that the expected cash

flows will remain constant, even if prevailing interest rates change, it is accurate foroption-free fixed-income securities. On the other hand, cash flows from securities

with embedded options or redemption features will change when interest rates

change. For calculating the duration of these types of bonds, effective duration is themost appropriate.

Effective duration requires the use of binomial trees to calculate the option-adjusted

spread (OAS). There are entire courses built around just those two topics, so thecalculations involved for effective duration is beyond the scope of this tutorial. There

are, however, many programs available to investors wishing to calculate effectiveduration.

Key-Rate DurationThe final duration calculation to learn is key-rate duration, which calculates the spotdurations of each of the 11 key maturities along a spot rate curve. (To refresh your

knowledge of this curve, see the section of this tutorial on the term structure of

interest rates.) These 11 key maturities are at the 3-month and 1, 2, 3, 5, 7, 10, 15,20, 25, and 30-year portions of the curve.

In essence, key-rate duration, while holding the yield for all other maturitiesconstant, allows the duration of a portfolio to be calculated for a one-basis-point

change in interest rates. The key-rate method is most often used for portfolios suchas the bond-ladder, which consists of fixed-income securities with differing

maturities. Here is the formula for key-rate duration:

The sum of the key-rate durations along the curve is equal to the effective duration.

Duration and Bond Price VolatilityMore than once throughout this tutorial, we have already established that when

interest rates rise, bond prices fall, and vice versa. But how does one determine thedegree of a price change when interest rates change? Generally, bonds with a high

duration will have a higher price fluctuation than bonds with a low duration. But it is
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important to know that there are also three other factors that determine howsensitive a bond's price is to changes in interest rates. These factors are term to

maturity, coupon rate, and yield to maturity. Knowing what affects a bond's volatilityis important to investors who use duration-based immunization strategies (which we

discuss below) in their portfolios.

Factors 1 and 2: Coupon rate and Term to MaturityIf term to maturity and a bond's initial price remain constant, the higher the coupon,

the lower the volatility, and the lower the coupon, the higher the volatility. If thecoupon rate and the bond's initial price are constant, the bond with a longer term to

maturity will display higher price volatility, and a bond with a shorter term to

maturity will display lower price volatility.

Therefore, if you would like to invest in a bond with minimal interest rate risk, abond with high coupon payments and a short term to maturity would be optimal. An

investor who predicts that interest rates will decline would best potentially capitalizeon a bond with low coupon payments and a long term to maturity, since these

factors would magnify a bond's price increase.

Factor 3: Yield to Maturity (YTM)

The sensitivity of a bond's price to changes in interest rates also depends on its yieldto maturity. A bond with a high yield to maturity will display lower price volatility

than a bond with a lower yield to maturity (but similar coupon rate and term tomaturity). Yield to maturity is affected by the bond's credit rating, so bonds with

poor credit ratings will have higher yields than bonds with excellent credit ratings.Therefore, bonds with poor credit ratings typically display lower price volatility than

bonds with excellent credit ratings.

All three factors affect the degree to which bond price will change in the face of achange in prevailing interest rates. These factors work together and against each

other. Consider the chart below:

So, if a bond has both a short term to maturity and a low coupon rate, its

characteristics have opposite effects on its volatility: the low coupon raises volatilityand the short term to maturity lowers volatility. The bond's volatility would then be

an average of these two opposite effects.
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ImmunizationAs we mentioned in the above section, the interrelated factors of duration, coupon

rate, term to maturity, and price volatility are important for those investorsemploying duration-based immunization strategies. These strategies aim to match

the durations of assets and liabilities within a portfolio for the purpose of minimizingthe impact of interest rates on the net worth. To create these strategies, portfolio

managers use Macaulay duration.

For example, say a bond has a two-year term with four coupons of $50 and a par

value of $1000. If the investor did not reinvest his or her proceeds at some interestrate, he or she would have received a total of $1200 at the end of two years.

However, if the investor were to reinvest each of the bond cash flows until maturity,

he or she would have more than $1200 in two years. Therefore, the extra interestaccumulated on the reinvested coupons would allow the bondholder to satisfy a

future $1200 obligation in less time than the maturity of the bond.

Understanding what duration is, how it is used, and what factors affect it will helpyou determine a bond's price volatility. Volatility is an important factor in

determining your strategy for capitalizing on interest rate movements. Furthermore,duration will also help you determine how you can protect your portfolio from

interest rate risk.

For any given bond, a graph of the relationship between price and yield is convex.

This means that the graph is curved rather than a straight-line (linear). The degreeto which the graph is curved shows how much a bond's yield changes in response to

a change in price. In this section we take a look at what affects convexity and howinvestors can use it to compare bonds.

Convexity and DurationIf we graph a tangent at a particular price of the bond (touching a point on thecurved price-yield curve), the linear tangent is the bond's duration, which is shown in

red on the graph below. The exact point where the two lines touch represents

Macaulay duration. Modified duration, as we saw in the preceding section of thistutorial, must be used to measure how duration is affected by changes in interest

rates. But modified duration does not account for large changes in price. If we wereto use duration to estimate the price resulting from a significant change in yield, the

estimation would be inaccurate. The yellow portions of the graph show the ranges inwhich using duration for estimating price would be inappropriate.
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Furthermore, as yield moves further from Y*, the yellow space between the actual

bond price and the prices estimated by duration (tangent line) increases.

The convexity calculation, therefore, accounts for the inaccuracies of the linearduration line. This calculation that plots the curved line uses a Taylor series (a

calculus theory), which is very complicated and something we won't be describinghere. The main thing for you to remember about convexity is that it shows how

much a bond's yield changes in response to changes in price.

Convexity

Properties of Convexity

Convexity is useful also for comparing bonds. If two bonds offer the same duration

and yield but one exhibits greater convexity, changes in interest rates will affecteach bond differently. A bond with greater convexity is less affected byinterest rates than a bond with less convexity. Also, bonds with greater

convexity will have a higher price than a bond with lower convexity,regardless of whether interest rates rise or fall. This relationship is illustrated in

the following diagram:


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As you can see Bond A has greater convexity than Bond B, but they both have thesame price and convexity when price equals *P and yield equals *Y. If interest rates

changed from this point by a very small amount, then regardless of the convexity,both bonds would have approximately the same price. When yield increases by a

large amount, however, the prices of both Bond A and Bond B decrease, but BondB's price decreases more than Bond A's. Notice how at **Y the price of Bond A

remains higher, demonstrating that investors will have to pay more money (accept alower yield to maturity) for a bond with greater convexity.

What Factors Affect Convexity?Here is a summary of the different kinds of convexities produced by different types

of bonds:

1) The graph of the price-yield relationship for a plain vanilla bond

exhibits positive convexity. The price-yield curve will increase as yielddecreases, and vice versa. Therefore, as market yields decrease, the

duration increases (and vice versa).

2) In general, the higher the coupon rate, the lower the convexity of a

bond. Zero-coupon bonds have the highest convexity.

3)Callable bonds will exhibit negative convexity at certain price-yield

combinations. Negative convexity means that as market yieldsdecrease, duration decreases as well. See the chart below for an

example of a convexity diagram of callable bonds.
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Remember that for callable bonds, which we discuss in our section detailing types ofbonds, modified duration can be used for an accurate estimate of bond price when

there is no chance that the bond will be called. In the chart above, the callable bond

will behave like an option-free bond at any point to the right of *Y. This portion ofthe graph has positive convexity because, at yields greater than *Y, a companywould not call its bond issue: doing so would mean the company would have to

reissue new bonds at a higher interest rate. (Remember that as bond yields increase,

bond prices are decreasing and thus interest rates are increasing.) A bond issuerwould find it most optimal, or cost-effective, to call the bond when prevailing interest

rates have declined below the callable bond's interest (coupon) rate. For decreases in

yields below *Y, the graph has negative convexity as there is a higher risk that thebond issuer will call the bond. As such, at yields below *Y, the price of a callable

bond won't rise as much as the price of a plain vanilla bond.

Convexity is the final major concept (after bond pricing, yield, term structure, and

duration) you need to know for gaining insight into the more technical aspects of the

bond market. Understanding even the most basic characteristics of convexity allowsthe investor to better comprehend the way in which duration is best measured, andhow changes in interest rates affect the prices of both plain vanilla and callable

bonds.
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