Bond estimate

Duration
What It Is:
Duration is a measure of a bond's sensitivity to interest rate changes. The higher the bond's duration, the greater its sensitivity to the change (also know as volatility) and vice versa.

How It Works/Example:
There is more than one way to calculate duration, depending on one's compounding assumptions, but the Macaulay duration (named after Frederick Macaulay, an economist who developed the concept in 1938) is the most common. The formula is:



where:

t = period in which the coupon is received
C = periodic (usually semiannual) coupon payment
y = the periodic yield to maturity or required yield
n = number periods
M = maturity value (in $)
P = market price of bond

The formula is complicated, but what it boils down to is: Duration = Present value of a bond's cash flows, weighted by length of time to receipt and divided by the bond's current market value. For example, let's calculate the duration of a three-year, $1,000 Company XYZ bond with a semiannual 10% coupon.

Period	Cash Flow	Period x Cash Flow	PV of $1 at 5%	Present Value of the Cash Flow
1	$50	$50	0.952	$47.62
2	$50	$100	0.907	$90.70
3	$50	$150	0.863	$129.58
4	$50	$200	0.822	$164.54
5	$50	$250	0.783	$195.88
6	$1,050	$6,300	0.746	$4,701.16
Total				$5,329.48

Notice in the table above that we first weighted the cash flows by the periods in which the occurred and then calculated the present value of each of these weighted cash flows (also, a measure of 5% is used instead of 10% because payments are semiannual).

To calculate the Macaulay duration, we then divide the sum of the present values of these cash flows by the current bond price (which we are assuming is $1,000):

Company XYZ Macaulay duration = $5,329.48 / $1,000 = 5.33

As mentioned earlier, duration can help investors understand how sensitive a bond is to changes in prevailing interest rates. By multiplying a bond's duration by the change, the investor can estimate the percentage price change for the bond. For example, consider the Company XYZ bonds with a duration of 5.53 years. If for whatever reason market yields increased by 20 basis points (0.20%), the approximate percentage change in the XYZ bond's price would be:

-5.53 x .002 = -0.01106 or -1.106%

Note that this is an approximation. The formula assumes a linear relationship between bond prices and yields even though the relationship is actually convex. Thus, the formula is less reliable when there is a large change in yield.

In general, six things affect a bond's duration:

Bond's Price
Note that if the bond in the above example were trading at $900 today, then the duration would be $5,329.48 / $900 = 5.92. If the bond were trading at $1,200 today, then the duration would be $5,329.48 / $1,200 = 4.44.

Coupon
The higher a bond's coupon, the more income it produces early on and thus the shorter its duration. The lower the coupon, the longer the duration (and volatility). Zero-coupon bonds, which have only one cash flow, have durations equal to their maturities.

Maturity
The longer a bond's maturity, the greater its duration (and volatility). Duration changes every time a bond makes a coupon payment. Over time, it shortens as the bond nears maturity.

Yield to Maturity
The higher a bond's yield to maturity, the shorter its duration because the present value of the distant cash flows (which have the heaviest weighting) become overshadowed by the value of the nearer payments.

Sinking Fund
The presence of a sinking fund lowers a bond's duration because the extra cash flows in the early years are greater than those of a bond without a sinking fund.

Call Provision
Bonds with call provisions also have shorter durations because the principal is repaid earlier than a similar non-callable bond.

Why It Matters:
Understanding the duration formula is not nearly as important as understanding that duration is a measure of risk because it has a direct relationship with price volatility. The greater duration of the bond, the greater its percentage price volatility.

By providing a way to estimate the affect of certain market changes on a bond's price, duration the investor can choose investments that will better meet his future cash needs. Duration also helps income investors who want to take on minimal interest rate risk (that is, they believe interest rates might fall) understand why they should consider bonds with high coupon payments and shorter maturities.

What is stock and bond?

What does it mean to own stock? Basically it means that a stock holder has a share in the company it holds stock in. In a sense the stockholders own a piece of the company that it has stock in. Stock shares are traded, bought and sold at a stock exchange such as the New York Stock Exchange which is the best known, but by no means the only stock exchange. Stocks are a type of security, Securities are instruments giving to their legal holders rights to money or other property. Securities include stocks, bonds, notes, mortgages,

How does one get to own stock? Usually stock is obtained through a stock broker. Let's say you wish to own a piece of Toys R Us or Coca-Cola. You would call a stock broker and he would tell you how much a share in the company would be. He would then place an order for the stock for you. When the stock is purchased, the broker would keep a stock certificate that shows that you are the legal owner of the stock until you choose to sell it.

What are the advantages of owning stock? One is that it allows the stock owner to share in the profits of a company. These profits come in the form of dividends, which are allocated according to how much stock one holds in the company. Of course one of the disadvantages is that one can lose money if a stock's price goes down.

What makes stock prices go up and down? There are many reasons: how much profit or loss a company has, the time of year, good or bad publicity about the company, how the economy is doing in general, etc..

There are several different kinds of stock. Preferred stock is a type of stock in which the stockholder gets a certain percentage of dividends each year based on the profits of the company. Common stockholders get dividends based on the remainder of the profits after preferred stockholders have been paid their dividends.

Another way to purchase stocks is through mutual funds. A mutual fund is an investment company that continually offers new shares and buys existing shares back at the request of the shareholder and uses its capital to invest in diversified securities of other companies. An investor puts money into a mutual fund and then the company invests the money on behalf of the investors.

What are bonds and how do they differ from stocks? A bond is a certificate of debt issued by a government or corporation guaranteeing payment of the original investment plus interest by a specified future date. Basically one is making a loan to the government or corporation and gets paid a sum of money in the future for letting the government or corporation borrow the money. Bonds are one way the government raises money besides taxes.