CHAPTER 4

DEBT MARKETS AND LENDING RATES

Let’s suppose that a new employee is hired and has negotiated a salary of X. The employee thinks X is very good and is proud of his negotiating skills. On the first day on the job, the employee discovers that another new employee doing the same job and having the same skill set is earning more. Suddenly the employee isn’t happy. On the other hand, if he finds that another new employee doing the same job and having the same skill set is earning less, the employee is happier.

The same concept can be applied to interest rates on debt instruments. An issuer negotiates an interest rate for a bond offering that the issuer thinks is a good rate. The bonds are offered. Awhile later another corporation with the same finances et cetera issues a similar bond and pays a lower rate of interest. The issuer of the first bond isn’t happy but if the opposite had occurred they would be very happy. The investor who acquired the bonds is on the opposite side of the emotional roller coster. In the middle is the market.

The market accommodates the disparity in the bonds’ interest rates by the prices the bonds trade at. Other factors, such as the degree of risk, longevity of the debt, and so on all affect the interest rates the debt has to pay. With all the factors involved, there must be a base rate from which all other rates emanate. Some of these key rates are universal, others are domestic in origin. But they set the lending rates that are used.

• DEBT PRICING •

The pricing of bonds is quite an interesting process; it comprises the present value of all cash flows. Let’s assume, for instance, that the reader tells a friend about a $10,000 bonus due in one year’s time, which he or she would like right now. Since the bonus is guaranteed, the friend offers to buy it. If the friend was to pay $10,000 for the $10,000 bonus a year from now, that friend would be without the use of the money during that year. The reader would have a big advantage, having been paid one year earlier. Instead, the friend and the reader negotiate a price that is fair to both of them, settling on $9,500. Therefore, that $500 discount represents payment to the friend for doing without the money for a year as well as a penalty to the reader for obtaining the funds one year early. The present value of $10,000 receivable a year from now, in this particular case, is $9,500. Similarly, each payment in a bond’s life has to be discounted to its present value and these present values added up to get to today’s price.

The formula for Present Value = Pay Out times 1/[1 + Rate] times the number of times it happened, or PV = PO × [1/1 + R] × t. If a bond was to pay 7 percent on $1,000, it will be paying $70 a year or $35 every six months. The tricky part of the formula is the rate. It’s not the interest rate of the bond; it’s the current interest rate that the bond is trading at in the marketplace. In other words, for a 7 percent bond priced to yield 8 percent, the R would be 8 percent. If the 7 percent bond was priced to yield 6 percent, the R would be 6 percent. A 7 percent bond paying interest six months from now, priced to yield 8 percent, would be PV = PO $35/1/[1 + 4%] × 1 (the number of times this event happened; the next payment, it would be 2).

Present Value at Work

The following are two examples of the present value calculations of a ten-year 7 percent bond that pays its interest twice a year. One bond is priced at a discount priced to yield approximately 8 percent, the other is priced at a premium to yield approximately 6 percent. In addition: both examples are followed by the quick “Rule of Thumb” method, which is used to estimate the yield.

(The calculation using this method, in the first example, is to take the bond’s discounted price of $932.13 and subtract it from the bond’s maturity value of $1,000.00, which leaves a gain of $67.87. Amortizing this gain over ten years comes to $6.79 per year. While the bond is paying $70.00 per interest per year, its value is theoretically increasing at a rate of $6.79 for a net of $76.79. To determine an average theoretical value of the bond over its life, add the current market value and the value at maturity together and divide by 2 to arrive at the average theoretical value of $966.06. Divide 76.79 by 966.06 = 0.0794878 or 7.95 percent. The calculation for the premium bond is different only in that the rate of depletion is subtracted from the interest payment.)

$1,000 7 PERCENT SEMIANNUAL INTEREST-PAYING 10-YEAR BOND, PRICED AT A DISCOUNT

Payment Number	Payout × Factor	Present Value Amount
1	35 × .961538	$33.76
2	35 × .924556	32.36
3	35 × .888996	31.11
4	35 × .854804	29.92
5	35 × .821927	28.77
6	35 × .790314	27.66
7	35 × .759918	26.60
8	35 × .730690	25.57
9	35 × .702506	24.59
10	35 × .676564	23.64
11	35 × .649508	22.73
12	35 × .624597	21.86
13	35 × .600574	21.02
14	35 × .577475	20.21
15	35 × .555264	19.43
16	35 × .533908	18.68
17	35 × .513373	17.97
18	35 × .493628	17.28
19	35 × .474642	16.61
20	1,035 × .456386	472.36
	Total:	$ 932.13

$1,000.00 − $932.13 = $67.87

$67.87/10 = $6.79

$6.79 + $70 = $76.79

($1,000.00 + $932.13)/2 = $966.06

$76.79/10 = 7.679 or 6.78 percent

$1,000 7 PERCENT SEMIANNUAL INTEREST-PAYING 10-YEAR BOND, PRICED AT A PREMIUM

Payment Number	Payout × Factor	Present Value Amount
1	35 × .970874	$33.98
2	35 × .942596	32.99
3	35 × .915141	32.03
4	35 × .888486	31.10
5	35 × .862608	30.19
6	35 × .837483	29.31
7	35 × .813091	28.46
8	35 × .789409	27.63
9	35 × .766416	26.82
10	35 × .744093	26.04
11	35 × .722420	25.28
12	35 × .701739	24.55
13	35 × .680950	23.83
14	35 × .661116	23.14
15	35 × .641861	22.47
16	35 × .623661	21.83
17	35 × .605015	21.17
18	35 × .587393	20.59
19	35 × .570285	19.96
20	1,035 × .553674	573.05
	Total:	$1,074.42

$1,074.42 − $1,000.00 =$74.42

$74.42/10 = $7.44

$70 − $7.44 = $62.56

($1,074.42 + $1,000)/2 = $1,037.21

$62.56/$1,037.21 = .0603156 or 6.03 percent

Duration and Convexity

Duration predicts a change in the bond’s value caused by a change in interest rate. It is an abstract figure that tests the sensitivity to a change in interest rates. Bond convexity measures the sensitivity to a change in interest rates. It tracks where a bond price deviates from the expected move predicted by duration.

Macaulay Duration and Modified Duration

There are two forms of duration used to measure the effect of interest rate changes on process of yields. One is Macaulay duration, which measures the weighted average time until all the cash flows are received measured in years, and the other is modified duration, which measures price sensitivity. Both of these, but especially Macaulay, will tell how long it will take the investor to be repaid by the bond itself.

Here’s an example of Macaulay duration:

A five-year zero-coupon bond will take five years to pay back its investor.

Bond Issue 5 Yrs Payment

As it took five years before the bond paid back its investment, the duration is five years.

Here’s an example of modified duration:

Let’s suppose a twenty-year bond that pays $35 interest semiannually. It is trading at 70 percent or $700, and the duration on the bond would be ten years ($70 per year × 10 yrs = $700).

Yr #1	Yr #2	Yr #3	Yr #4	Yr #5
$70	$70	$70	$70	$70
Yr #6	Yr #7	Yr #8	Yr #9	Yr #10
$70	$70	$70	$70	$70
Yr #11	Yr #12	Yr #13	Yr #14	Yr #15
$70	$70	$70	$70	$70
Yr #16	Yr #17	Yr #18	Yr #19	Yr #20
$70	$70	$70	$70	$1,070

Note: The last payment includes face amount of the bond plus the interest payment.

If the bond was acquired at a price of 77 percent of its face value or $770, the duration would be eleven years ($70 × 11 yrs = $770) without compounding the annual interest payments. A 10 percent rise in the bond’s price would result in a one-year extension of its duration.

As interest rates rise, bond prices fall, and as interest rates fall, bond prices rise. Therefore as interest rates changed, the duration of the bond would change also. If interest rates in the market fell so that the market price of the aforementioned bond was par, or 100 percent of its face value, a buyer at that price would have to wait approximately 14½ years ($70 × 14.5 = $1,015) to get his or her money back.

• INTEREST ONLY/PRINCIPAL ONLY BONDS •

Earlier, we discussed the fact that issuers try to alter debt products from the basic bond structure to offer something slightly different that will attract investors. The basic bond structure in the United States is: Principal, name of issuer or issue, coupon rate, payment dates, and maturity date.

$10,000 ZAPPO (issuing company) 8% (interest rate)

Cl (Callable) 20XX (First year call feature is alive)

FA (February/August) 20ZZ (Maturity year).

A bond issued for twenty years that pays interest twice a year can be altered to become at least two other products. One is a twenty-year zero-coupon bond and the other is a semiannual interest-paying instrument. The forty interest payments (twenty years x two) can then be broken down into near-term and long-term payments, if a market exists for it. The zero-coupon bond is known as the principal only portion, the interest payment vehicle as the interest only portion.

• U.S. TREASURY BONDS •

United States Treasury bonds lend themselves to this special treatment. Bond dealers or other financial institutions would buy the bonds, put them in escrow, and strip the interest payments away from the principal. The principal became a zero-coupon bond (which the U.S. Treasury didn’t offer) and the interest payment would be sold apart from the core bonds. The principal and each slice of the interest payments—now a zero coupon which maintains its original maturity date and with shorter maturities for the interest payments—each receive their own CUSIP numbers.

These products were originally sold under the names LIONs, TIGERs, CATs, etc. Now, the government issues OID (original issue discount) zero-discount bonds. As a result, a twenty-year U.S. Treasury bond that pays interest every six months can, theoretically, be converted into as many as forty coupon payment bonds and one twenty-year zero-coupon bond. Usually a buyer of the interest payments will buy a “strip” of payments.

Dominant Lending Rates

In the United States, U.S. Treasury bills, notes, and bonds are the benchmark instruments that longer-term and other debt instruments’ interest is based on. For short-term debt, as in overnight loans, the base rates used are LIBOR, the federal funds rate, the U.S. Treasury rate, and Euribor.

LIBOR (London Interbank Offered Rate)

The LIBOR rate is set by London banks and is an average rate these banks charge one another. The rate is used to set mortgage rates and many of the derivative products discussed in this book.

Federal Funds Rate

This is similar to the LIBOR but is used as a basis for U.S. banks to charge one another for borrowing funds. It is sometimes referred to as the “overnight rate,” but that term is generic to any rate used for lending purposes.

U.S. Treasury Rate

The U.S. Treasury rate is the base rate used to set the interest rate of U.S. Treasury instruments of different tenors; that is, the durations of the instrument. Many domestic debt instruments, corporate bonds, notes, etc., are priced off the Treasury rates.

Euribor (Euro Interbank Offered Rate)

Euribor is the rate set by a panel of European banks and represents the rate of interest charged by European Union banks for interbank borrowing. When it was determined that the LIBOR rates were being manipulated and that scandal broke, Euribor was one of the rates put forward to replace LIBOR as the primary source for funding.

These cash rates have many applications in both the derivative and nonderivative worlds. Besides being used to set interest rates or the resulting yields, these base rates play an integral part in many of the derivatives discussed in this book. A product user trying to get a better loan position may enter into a fixed or floating LIBOR rate swap. An owner of a collateralized mortgage obligation securitized instrument may want to hedge against interest rate changes that would negatively affect the value of the fixed-rate mortgage pools he or she owns. To do this, he or she would want to exchange that cash flow for one that is floating.

Now, let’s turn our attention to the various forms of mutual funds.