Notes for Session 5
Econ 201
How are savings turned into investment? In chapter 2, we derived the identity S
= I. Embedded in this identity is the mechanism of some kind of institutional structure that helps take savings and turn them into investment. The more advanced such an institutional structure, the smoother the process of turning savings into productive investment and the better will be chances for improved standard of living in the future. In fact, you can take a very poor economy with very little savings and if you consider (assume!) it to have a working set of financial intermediaries that take savings and turn them into productive investment. In a few years, this economy will show improved standard of living. In a few decades, it will no longer be a poor country. In this session, we discuss the role of financial intermediaries and begin the study of financial instruments, specifically bonds. [Readings are in chapter 3]. Questions that you need to think about include the following: 1. What are financial intermediaries and why do we need them? A related question to the one asked above is: Which of the following would best explain the long run (i.e., year after year) stagnation of some low income developing countries? a. The low level of savings in these economies b. Lack of development of institutions (including financial institutions) and nonexistence of a well functioning financial market. 2. Which different types of intermediaries exist? Why do we have to have so many different types of financial institutions? 3. What are financial instruments? What are "debt" and "equity" instruments? 4. Since purchase and sale of (government) bonds are an important tool of monetary policy--which constitutes a good part of our discussion in this course-- we discuss the world of bonds in detail: a. What is a bond and what are the characteristics of a bond? A bond is an IOU (I owe you!) issued by an institution or a person who would like to borrow funds from the public. The person who buys the bond is promised the full return of the loaned out funds plus some fixed interest payment at the end of a period when the bond “matures”. Bonds are also termed “fixed income” assets where the lender receives a nominally fixed (interest) income from the bond. As such, bonds have three identifying features: fixed “coupon” payment, fixed maturity, and a par (face) value in $100 1
denominations. Essentially, the $100 is the principal of the loan and the coupon rate is the fixed interest rate the borrower agrees to pay on the date the bond matures. For example, a one-year bond with a “coupon rate” of 5% that is purchased on January 1, 2008 will pay $105 to the lender on January 1, 2009. Of course, bonds do not necessarily come in $100 denominations in reality, there are bonds with face value $500, $1000, or even tens of thousands of dollars in the market. However, for simplicity, we consider the par value at $100 where the fixed interest rate paid by the borrower of funds will be in percentage (e.g., 6% or $6 per $100 borrowed). The purchase and sale of (government) bonds by the central bank is an important tool of monetary policy and constitutes a good part of our discussion in this course. We therefore discuss the world of bonds in some detail [Readings are in chapter 3 of the text online]. The basic story of the bond! When a corporation, say Corporation A, wants to borrow from the public, it goes to a credit rating agency with its income statement, asset statement and other necessary “documents”. The credit rating agency determines that for example, another corporation, say Corporation B, is paying today $6 for every $100 borrowed. That is, the interest rate in the market for this type of loan is 6% today. The Corporation A is then asked to issue its bonds and sell them at the “coupon rate” of 6%. This rate is fixed for the life of the loan, no matter what happens to the interest rates in the future. If the corporation is borrowing for one year, then the bond is a one-year bond (the bond ceases to exist at the end of one year) and at the end of the year, the lender will receive $100 (principal) plus $6 in fixed interest (coupon) payment. The $100 is called the par value or the face value of the bond. So the bond has three characteristics: 1. Fixed maturity, 2. Fixed “coupon” rate, 3. Face value or par value (in $100 denomination).
Questions that you need to think about include the following: 1. Once a bond is issued, would you expect its price to stay $100 during the period up to its maturity? 2
Bonds, once issued and sold to the public, are highly marketable assets. There are billions of dollars of transactions in existing (i.e., previously issued) bonds everyday. If a bond is held by the bond purchaser till maturity, then this person receives the par value ($100) plus the fixed interest –called coupon rate--on the bond when the bond reaches maturity. However, the purchaser of a bond does not have to hold on to the bond, they can sell it on any day as there is a large and active market in existing bonds. Since the interest rate on loans changes frequently and for various reasons (we’ll discuss some of these reasons in our lecture session) and the process of “arbitrage” (discussed below) forces all bonds to pay the same effective interest, it implies that the market value—also called the price-- of an existing bond will change after its issue! The price changes so that the effective interest rate or “yield” paid by an existing bond is equal to the current market interest rate. 2. How do you determine the %gain (yield) on a one-year bond on the date you purchase it? On any given day, you can check out the table of Treasury Quotes, consisting of Treasury Notes and Bonds, in the Wall Street Journal (WSJ). For example on Friday October 5, 2007, the table of Treasury Quotes—Notes and Bonds-- in the WSJ shows the following one-year bond: Maturity 2008 Oct 15
Coupon 3.125
Bid 98:27
Asked 98:28
Chg -3
Asked Yield 4.24
As of October 2007, there is one year left of the life of the bond, so it is indeed a one year bond as of Oct. 2007. At the time the bond was issued, the market interest rate for this type of loan was 3.125% or $3.125 per $100 of principal (par value). This becomes the coupon on the bond. The price offered by the bond broker for this bond on Oct. 5, 2007 is 98:27 or $98.844. The number after the colon in 98:27 needs to be divided by 32 to translate the amount into fraction of dollar. That is, 98:27 is 98 dollars and 27/32 cents. The price at which the bond sells is the price “Asked” by the bond broker is 98:28 or $98.875. The “Chg” column shows that the price dropped 3/32 of a dollar since yesterday (a change of 3 basis points). Finally, the Asked Yield is the market interest rate for this type of loan on Oct. 5, 2007! On Oct. 5 2007, this bond which one year from now will pay $100 principal plus a fixed interest of $3.125 has an effective yield of 4.24% today! In other words, today, someone who wants to borrow $100 for one year will have to agree to pay $4.24 interest. Since the existing bond in the above table has an already fixed interest rate (coupon rate) that is only 3.125% and so the bond pays only $3.125 at the end of one year, would this bond be worth—to the buyer-- $100 (would the price of the bond be $100)? Would it be worth more or less than $100? 3
As the table shows, its Asked price is only 98:28 or $98.875. This means that the price of the bond today is not $100 but less than $100 at $98.875. It implies that if someone buys this bond for $98.875, they will get a yield (interest rate) of 4.24% ($4.24 per $100) on it! So even though this bond was purchased for $100—purchased at par—on the day it was issued, today, its price is only $98.875. Purchasing the bond at this price ensures that the buyer of this existing bond gets the same interest for $100 loan as anyone else would –today--on any other one year bond of this type: 4.24%. So how do we go from the fixed information on the bond and today’s price of the bond to determine the yield? Yield = percentage gain Or, Yield = {[what you get for the bond – what you pay for it] / [what you pay for it]}*100 Therefore, Yield = [(Par Value + Coupon – Price)/Price]*100 Yield = [($100 + $3.125 – $98.875) / ($98.875)]*100 = 4.3% From our calculation, we are deriving the number in the last column of the WSJ: that of Asked Yield. In the table, this number is 4.24% and our derived number is 4.3%. While the two numbers are not identical, our derivation is a simple but close approximation to the actual, more complex calculation by bond brokers. This technical difference is partly due to the fact that the $3.125 coupon is paid in two 6 month intervals rather than all at once and so the calculation in our formula above is a little different from the actual number calculated by the bond brokers. It is close enough for our purposes. Our derivations show that for an existing bond that promises to pay $100 and $2.37 in one year, its price has fallen to $98.438 in order to effectively pay 3.95% (or $3.99 by our calculation) per $100!
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