FIN3403- CH7 (BONDS and BOND VALUATION)

The Yield Curve

(a way of forecasting what's going to happen to interest rates). (AKA the term structure of interest rates!) The Yield Curve is a plot of YTMs of comparable bonds against their maturities. So what is meant here is that all other things are the same except for maturity, ie, the risk, the coupon, etc. The yield curve or term structure of interest rates as it is also called indicates, according to one theory, the expectations of future market activity and therefore the level of interest rates. (int rates will rise over time according to theory, which happens when economic growth is looking good. bc int rate is essentially the price of money. WHEN INCOMES ARE RISING, THE DEMAND FOR MONEY WILL RISE, AND INTEREST RATES WILL RISE= healthy economy!). Normal Upward Sloped - Has been the predominant shape of yield curve for most of the past 50 years or so and indicates a growing economy. Inverted or Flat - Indicates that economic growth and interest rates will decline in the future. FIGURE 7.6 UPWARD AND DOWNWARD SLOPING YIELD CURVES: (27:52 on 3/12 lecture!) +++ HE TALKS ABOUT IT!! GO LOOK! LOO AT CHARTS SAM VERY IMPORTANT! TERMS!! Upward-slope is the predominant shape (healthy economy! good future economic activity!) Flat or downward: Indicates interest rates decline in the future. WHEN DO INT RATES DECLINE?: Interest rates decline when economic there's stagnation and the demand for money is shifting back Now, Read the book to examine more about Bond Features You should take a look at: 1) The indenture 2) Callability and Convertibility 3) Bond Ratings

Accrued Interest:

(coupon interest is prorated based on how long you hold it despite what the current price might be) Bonds are sold on an accrued interest basis and the current bond price does not reflect that interest. For example, assume a bond with a 10% semiannual coupon that is paid in June and December sells in for $935 in March. Whoever buys the bond in March will receive the 50 dollar payment in June, but the previous owner of the bond is entitled to the interest earned from January through March. Therefore, at the settlement the purchaser must pay the previous owner $25. The price of the bond just using your calculator without accrued interest is called the "clean price" (easy to get), while that including accrued interest is called the "dirty price." 10% semiannual coupon means it$50 paid twice a year! $50 because 10% of 1,000 is 100 and its semi annual?? (Settlement is when the purchase goes through!)

Treasury Securities (Bonds & Notes)

(issued by the US treasury) Notes have a maturity of 1 yr → 10 yrs, Bonds have a maturity of 10 yrs → 30 yrs. This next point pertains only to Treasuries. Each point in price is divided into 32nd's or 64th's which are multiples of 8ths. This is no different than feet being 12 inches, etc, just a way of breaking a unit into parts. This implies that a quote in the WSJ of 90:05 means 90 and five 32nds, so 90:05=90 5/32 = 90.156 on $100 of Par, but $901.56 on $1000 Par. Likewise, 85:31 = 85 31/32 = $859.69 on 1000 Par. So, prices proceed as follows: 89:31, 90:00, 90:01, 90:02, 90:03...90:29, 90:30, 90:31, 91:00, etc.

Semiannual Interest Payments

(the most prevalent/common type of bond is where the interest/coupon payments are made semiannually) (convert it to rate per period and number of periods?!+) as indicated above most bonds have semiannual coupons, so now we receive 2 payments per year which implies that the discounting & compounding twice in one year. Price=2NΣt=1 (Coupont)/2 /(1+YTM/2)^t +Par/(1+YTM/2)^2N (LONG HAND ^) Recall that the coupon payments of a bond are simply an annuity, so to find the price we find the present value of the annuity and then the present value of the lump sum Par value: Price=Coupon/2 [[1-(1+YTM/2)^-2N] /YTM/2 +Par/(1+YTM/2)^2N (SHORT HAND^) Price=50/2 [1-(1+.07/2)^-20 /0.7/2]+1000/(1+.07/2)^20 Or with the Fin. Calc.: N=20 (10x2) i=3.5 (7/2) PMT=25 (50/2) FV=1000 PV=??=-857.88

Example of Equations

*(IF A QUESTION DOESNT SAY WHAT THE PAR VALUE IS YOU NEED TO ASSUME IT IS $1,000!! IF IT DOESN'T SAY SEMI-ANNUAL COUPON, YOU NEED TO ASSUME THAT IT IS ANNUAL!!)* *(ALSO! REMEMBER THAT INTEREST RATES ARE QUOTED ON AN ANNUAL BASIS!! SO IF THE QUESTION SAYS WITH A 5% COUPON PAID SEMI-ANNUALLY, THAT MEANS 5% IS THE ANNUAL RATE AND PAID SEMI-ANNUALLY MEANS HALF OF THAT 5% IS GOING TO BE PAID EVERY 6 MONTHS!! AND THE $50 IS SPREAD OVER THE YEAR! NOT 2 PAYMENTS OF $50!)* We have a 10 year bond with 5% coupon and 7% ytm, what is the price? Price=50[1-(1+.07)^-10 /.07]+1000/(1+.07)^10 So you can do this using the equation and/or the Fin. Calc.: N=10 i=7 PMT=50 (bc 5% of 1000) FV=1000 PV=??=-859.53

18. Bond Yields Martin Software has 9.2 percent coupon bonds on the market with 18 years to maturity. The bonds make semiannual payments and currently sell for 106.8 percent of par. What is the current yield on the bonds? The YTM/. The effective annual yield?

*Assume the par value is 1000!!!* since it doesn't say what it is. It sells for 106.8% of par; 106.8% of 1,000 = 1068 The coupon is quoted as a percent of par; 9.2% of 1,000= $92 paid in a year and that's gonna be 46 every 6 months Price is quoted as a percent of par as well, (they told us) Current Yield is the same thing as dividend yield for stock CY= Cash paid in a year/Current Price = 92/1068 CY= .0861= 8.61% Now to find YTM we need to solve for the yield, so n= 18x2= 36 (bc semiannual) pv= -1068 pmt= 92/2= 46 (bc semiannual) fv= 1000 i=??= 4.2289 *SO THIS IS r/m AND m IS 2 AND MULTIPLY BY m SO BASICALLY YOU'RE JUST MULTIPLYING THE ANSWER YOU GOT FOR i BY 2!* i=??= 4.2289 x2 YTM= 8.46 EAY= (1+r/m)^m -1 *r= quoted rate! which is 8.46 here!* =(1+*.0846*/2)2 -1 =.086328 EAY= 8.645

16. Interest Rate Risk Both Bond Sam and Bond Dave have 7 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has 3 years to maturity, whereas Bond Dave has 20 years to maturity. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Bond Sam'? Of Bond Dave? If rates were to suddenly fall by 2 percent instead, what would the percentage change in the price of Bond Sam be then? Of Bond Dave? Illustrate your answers by graphing bond prices versus YTM. What does this problem tell you about the interest rate risk of longer-term bonds?

*long maturity low coupon bonds are much riskier than short maturity high coupon bonds!* *"PRICED AT PAR" MEANS THAT THE YTM HAS TO BE EQUAL TO COUPON!!!! AND THAT THE PRICES ARE 1000 SO PRICE IS EQUAL TO PAR!! WHEN COUPON=YTM, PRICE=PAR!!! AND VICE VERSA! WHEN PAR=PRICE, YTM=COUPON!!* (+IN NOTES) If interest rates rise by 2%... S: Coupon= 7% semi YTM= 7% (rise by 2%)= 9% Price= 1000 Par= 1000 Maturity= 3years D: Coupon= 7% semi YTM= 7% (rise by 2%)= 9% Price= 1000 Par= 1000 Maturity= 20 years What is the percentage change in price? S: n= 3x2= 6 i= 9/2= 4.5% pmt= 7% of 1000 is $70/2= 35 fv= 1000 pv= ??= 948.43 (new price) △PriceSam= 948.43-1000 /1000 = -0.05157 △PriceSam= -5.16% D: n= 20x2= 40 i= 9/2= 4.5% pmt= 7% of 1000 is $70/2= 35 fv= 1000 pv= ??= 815.98 △PriceDave= 815.98-1000 /1000 = -0.1840 △PriceDave= -18.40% If interest rates fall by 2%... S: Coupon= 7% semi YTM= 7% (fall by 2%)=5% Price= 1000 Par= 1000 Maturity= 3years D: Coupon= 7% semi YTM= 7% (fall by 2%)= 5% Price= 1000 Par= 1000 Maturity= 20 years What is the percentage change in price? S: n= 3x2= 6 i= 5/2= 2.5% pmt= 7% of 1000 is $70/2= 35 fv= 1000 pv= ??= 1055.08 (new price) △PriceSam= 1055.08-1000 /1000 = .0551 △PriceSam= 5.51% D: n= 20x2= 40 i= 5/2= 2.5% pmt= 7% of 1000 is $70/2= 35 fv= 1000 pv= ??= 1251.03 △PriceDave= 1251.03-1000 /1000 = .251 △PriceDave= 25.10%

Bonds Features

1) Coupon Rate the annual, or almost universally, semiannual interest payment from the issuer of the Bond. The coupon rate quoted as a percent of par or face value, i.e., 5% of $1000 is $50 per year and if paid semiannually would be two $25 payments per year, every 6 months. 2) Par or Face Value- the value that is repaid at the maturity date, usually $1000 but this can vary for different bonds, i.e., some municipal bonds have face values of $25000. 3) Maturity- the length of time that the bond is outstanding, i.e., the length of time of the loan. 4) Yield to Maturity- the discount rate which equates the present values of all net cash flows to the cost or price of the bond. 5) Price or Present Value of a Bond- Note that the bond price consists of a Present Value of an Annuity and the PV of a lump sum. (fixed/constant coupon bond. It's a fixed $ payment for a fixed number of periods so it's an annuity) Therefore, for a *constant annual coupon bond* we have: Price=Coupon(PVIFAr%,nyrs)+FV(PVIFr%,nyrs) (HE SAID DONT LOOK AT THIS ONE, LOOK AT THE ONE RIGHT BELOW) In terms of the pricing equation, we have: Pricet=NΣt=1CashFlowt/(1+YTM)^t = NΣt=1 Coupont/(1+YTM)^t+Par/(1+YTM)^N = (THIS IS THE PVA FORMULA? ENDING WITH ] AND THE PAR SECTION OF IT IS THE PV OF LUMP SUM FORMULA!!:) Coupon [1-(1+YTM)^-N /YTM]+Par/(1+YTM)^N So this is a PVA and PV of a Lump Sum. For a Zero Coupon Bond: (all that's left is the PV of a lump sum portion of the formula) Pricet= Par/(1+YTM)^N A ZERO COUPON BOND IS THE MOST VARIABLE TYPE OF BOND! Bc you don't have any cash flow and only the par value at the end so any YTM changes will cause it to increase or decrease a lot THE SOONER YOU GET YOUR MONEY FROM A BOND, THE LESS RISKY/VOLATILE IT IS. *A short maturity high coupon bond is less risky than a longer-term lower coupon bond!!!!*

The Yield to Maturity assumes the following:

1) The Investor will hold the bond until maturity. 2) All intermediate cash flows will be reinvested at the same rate as the YTM. (YTM is always changing so it's not true) Note: YTM's are market rates of interest determined by the supply and demand for loanable funds.

Basis Point:

1/100 of 1% interest, i.e., One percentage point = 100 Basis points

23. Using Bond Quotes Suppose the following bond quotes for IOU Corporation appear in the financial page of today's newspaper. Assume the bond has a face value fo $1,000 and the current date is April 19, 2012. What is the yield to maturity of the bond? What is the current yield? Company (Ticker): IOU (IOU) Coupon: 6.2 Maturity: April 19, 2028 Last Price: 108.96 Last Yield: ?? EST Vol (000s): 1827

6.2% of 1000= $62 CY= 62/1089.6 *(WHY?)* CY= 5.69% YTM: n= 16 (2028-2012= 16 years (maturity)) pv= -1089.6 pmt= 62 fv= 1000 i= ??= 5.35% YTM= 5.35%

Calculating YTM's and other Variables in Bond Problems

As in the pricing of bonds, YTM's are found in the same three ways, formula, financial calculator and from the tables. However, unlike finding the bond's price where we had a unique solution for the price, we cannot solve uniquely for the YTM. This implies that we must solve for it by trial and error by plugging different values for the YTM in the bond pricing equation and calculating to see if the present value of the coupon payments and the par are equal to the given price. For example, assume a 10 year maturity bond has an 10% annual coupon and a price of $749.06, what is the yield to maturity? For this particular example, we know if we try a YTM of 10%, the same as the coupon, we will get a value of $1,000, which means that we have tried a discount rate that is too low. That is, we have not discounted the coupons and the par enough to get the price of $749.06, so we have to increase the discount rate that we try. Let's now up the rate to 20% and see what we get: 749.06??=??100[[1-(1.20)^-10] /.20]+1000/(1.20)^10 (need something greater than 10% to get to 749+?) What we get from this trial is $580.75. So, now we have gone too high on the rate, i.e., we have discounted the cash flows too much to get the price of $749.06. So we now reduce the rate and try 15%, which gives us the desired price. *(WON'T BE ON SHORT ANSWER PART OF TEST! BUT IT WILL DEFINITELY BE ON SHOFT ANSWER PART!)* The financial calculator uses the same iterative process, trial and error, but does it much faster than we did: N = 10 PV = -749.06 PMT = 100 FV=1000 i= ?? 15% Now let's look at the same bond but now it has a semiannual coupon payment. In this case the number of payments are doubled, the price will be different, and the rate we find will have to be doubled. The following would be put into the calculator: N = 20 (10x2) PV = -745.14 PMT = 50 (100/2) FV=1000 i= ?? 7.5% times 2 = 15% (WHEN YOU SOLVE FOR ANYTHING THAT HAS A DIFFERENT COMPOUNDING INTERVAL THAN ANNUAL, YOU ARE SOLVING FOR r/m WHICH IS R OVER THE COMPOUNDING INTERVAL, WHIC IS 2 IN THIS CASE)

Bond Pricing Examples

Assume a bond has a $1,000 par value, a 10% annual coupon rate, 10 years to maturity, and an 8% yield to maturity. We want to find the price. From the discussion above, we know that since the YTM is less than the coupon rate, the bond will sell at a premium, i.e., Price > Par. We can calculate this price using one of three methods: 1)The formula 2)The financial calculator (the coupon is greater than the YTM so it's giving us more cash so we will pay more for than, so the price will be above par). The Formula: Price=100[[1-(1.08)^-10] /.08]+1000/(1.08)^10 =$1,134.20 Par = 1000 Price = ? Coupon = 10% annually Maturity = 10 years YTM = 8% so, The Calculator: N=10 i = 8 FV = 1000 PMT = 100 PV = ? = -$1,134.20 (price is greater than par?) Assume that we have the same bond, however now the coupon is semiannual instead of annual. Let's see how that will change the bond's price: Price=50[[1-(1.04)^-20] /.04]+1000/(1.04)^20 =$1,135.9 With the Calculator: N=20 i = 4 FV = 1000 PMT = 50 PV = ? = $1,135.90 Note that in this case the semiannual coupon bond price is greater than the annual price, but this is not always the case even though it seems like it should be because the payments start sooner. In general though, the rule is the following: For semiannual coupon bonds, when the rate in the numerator of the bond pricing equation is greater than that in the denominator of the equation, the price will be greater than when the opposite is true. In essence, when the coupon rate is greater than the yield to maturity, the numerator of the equation is growing at a more rapid rate than it is being discounted and the price will be greater. In other words, if we calculated the price for a bond that had an annual coupon of 8% and a YTM of 10% and then calculated the semiannual coupon bond price, the semiannual price would be lower than the annual price.

Bond Prices & Interest Rates

Bond prices rarely sell at their Par or Face Value, and do so usually only at issue. They sell at a Premium or Discount depending on market interest rates and the relationship between the coupon, the YTM, the par and the price. In general the YTM is approximately equal to the coupon rate plus the bond's capital gain or capital loss: YTM ≈ Coupon + Capital Gain or Capital Loss Capital Gain: Price < Par when the bond is bought so the owner gets a gain when held to maturity. (When you buy for less than par and get back par at the end) Capital Loss: Price > Par when the bond is bought so the owner incurs a loss when held to maturity. (When you buy for more than par and get back par at the end) Why would someone buy a bond knowing that they will incur a capital loss? Because the coupon will be higher that prevailing rates offsetting the loss. (lower coupon bonds have lower prices relative to higher coupon bonds. That difference explains whether a bond price is above or below par. Adjustment process. Slowly over time) To understand the equation above and how it represents a constant adjustment process, consider a bond in the market that sells at Par and has a fixed coupon of 10% when the Market Rate, i.e., the YTM is 8%. This would imply the following relationship: 8% ≈ 10% + 0 Clearly investors will find this bond attractive considering they can only make 8% in the market. Therefore, investors will bid the price of this bond up such that it will now sell for a premium to the Par. After the price has been bid up, subsequent buyers of this bond will incur a capital loss if the bond is held to maturity of approximately 2%, i.e., 8% ≈ 10% + -2% (the 8% is the market rate of interest. the 10% is a bond we're considering buying that sells at par and pays 10%? the coupon rate? yet the market is paying 8% for bonds comparable to this. Selling for par so no capital gain or loss. We like the 10%) (MIMICKING THE YTM FORMULA UP THERE^) Thus the price has been bid up to a level such that the combined return from the coupon and the capital loss just equal market rate YTM of 8%. Next consider the opposite situation where the bond has a YTM is 8%, but now the coupon is 6%, again selling at Par. In this case investors will not want to hold this bond because rates in the market are higher. Therefore, investors will sell this bond until its price has adjusted to the point where the combined coupon rate plus the capital gain will just equal the market YTM of 8%. That is we have: 8% ≈ 6% + 2%. Given the discussion above we have the following general relationships between Par, Price, Coupon and YTM If YTM > Coupon ⇒ Par > Price: The bond will sell at a discount and a capital gain will augment the lower coupon rate. If YTM < Coupon ⇒ Par < Price: The bond will sell at a premium and a capital loss will reduce the higher than market rate coupon. If YTM = Coupon ⇒ Par = Price: The bond will sell at Par. * WILL BE ON TEST ^^^^^* When issuing bonds, most firms set the coupon rate they will pay equal to the current YTM for comparable bonds in the market place. This way they will get the full price for the bonds because price=par. However, at times when interest rates are high, firms cannot pay a high coupon and they might set the coupon rate lower than the currently quoted YTM, therefore, they will get a lower price than par.

Bonds

Bonds- Coupon Bonds are simply loans from a government or corporation to a lender or buyer of the bond (individuals, mutual funds, governments, etc) in which the issuer sells the bond and in return for receiving the price of the bond they pay to the buyer an annual or semiannual coupon interest payment until maturity and at maturity they pay back the Par or Face Value, which is typically $1,000.

Bond Quotes

CHART!!!+ In the above Corporate Bond Most Active quotes you see first the name and symbol, then the coupon. Looking at Bank of America we see that the coupon is 3.125% which most is $31.25 per year or $15.625 per 6 months. It is due in June of 2012, has ratings of triple A, which is the highest, then we see the high, low, last and change from yesterday. The last means that the price is $1035.90 and the change was down $1.05. The yield is the YTM, which is 2.037%. Finally, what is not listed but we can calculate is the coupon yield which is cash in a year divided by price, which equals $31.25/$1035.9=3.02%. Looking at the first bond maturing in 2018 we see that the coupon is 3.5% or $35 per year and $17.5 per six months. Next we see the bid and asked, the dealer buys at the bid and sells to you at the ask, which is your purchase price. Recall these are in 32nds, so the ask price at 108.24 is 108 24/32 which equals 108.75 or $1087.5. Finally, we see the YTM of 2.42%. (Current yield/coupon yield is the same as dividend yield! It's the same definition for stocks and bonds. It's the cash paid in a year divided by current price. Higher is better!) (dividend yield is next chapter) Next let's look at Treasury Bond Quotes: U.S. Treasury Quotes TREASURY NOTES & BONDS Treasury note and bond data are representative over-the-counter quotations as of 3pm Eastern time. Figures after colons in bid and ask quotes represent 32nds; 101:26 means 101 26/32, or 101.8125% of face value; 99:01 means 99 1/32, or 99.03125% of face value. For notes and bonds callable prior to maturity, yields are computed to the earliest call date for issues quoted above par and to the maturity date for issues below par. CHART+!!! (remember the bid and asked are in 32nd so you have to take whatever the number is to the right of the colon and divide by 32 and add that on!?)

Chapter 7 Interest Rates and Bond Valuation Questions 4. Bond Yields A Japanese company has a bond outstanding that sells for 87 percent of its Yen 100,000 par value. The bonds has a coupon rate of 4.3% paid annually and matures in 18 years. What is its YTM of this bond?

For the formula we would have to do trial and error so we are just gonna use the calculator Financial Calc: n= 18 pv= -87,000 (.87x100,000) pmt= 4,300 (.043x100,000) *(REMEMBER COUPON IS STATED AS A PERCENT OF PAR, SO 4.3% OF PAR)* fv= 100,000 i= ??= 5.45

Graphical Relationship Between Price and Yield-to-matuirty

GRAPH PV declines as the interest rate/yield to maturity increases This is a longer-term bond so a shorter-term one wouldn't be such a downward slope, more flat.

A Typical Bond (TREASURY!!) Quote

IN NOTES Don't see any Bid or Asked prices going above 32 so that's how you know it's treasury!! Rate is the coupon rate, meaning each one of those bonds is paying a coupon rate according to this number. The coupon rate is quoted as a percent of par, par on these is $1000 so ex.,: rate 2: that's 2% of par, so $20 Maturity here is the maturity of the note meanings its less than a 10 yr maturity The dealer sells this bond to us for 99:31 but the dealer bought it for 99:30, which means they made 1 32nd which is (1/32)= 0.03125x1000= $31.25 The change here is the change from yesterday? Asked yield is yield to maturity (THE LARGER THE COUPON, THE YTM WILL EVENTUALLY GET HIGHER.? IF THE BOND IS PAYING A LARGER OUPON, IT MEANS YORUE GETTING MORE CASH DURING THE YEAR AND PEOPLE PAY FOR THAT. IN THE 6 7/8 ONE YOU CAN SEE ITS SELLING FOR ABOVE BAR (IN ASKED COLUMN) BECAUSE THE COUPON RATE IS GREATER THAN THE YIELD TO MATURITY

Corporate Bonds:

Prices are quoted in fractions of a point in 1000th's of a point eg. 98.203, 105.685, etc. and are based on a par of 1000, so these would be priced at $982.03 and $1056.85.

*Features of a Microsoft Bond*

SCREENSHOT 11:60 on lecture-3:00!! Sinking fund- An account managed by the bond trustee for the purpose for repaying the bonds/for early bond redemption. The company makes annual payments to the trustee, who then uses the funds to retire a portion of the debt. The trustee does this by either buying up some of the bonds in the market or calling in. a fraction of the outstanding bonds. + Call provisions- Registered vs Bear a bonds (drug dealers Terms of a bond call premium deferred call provision bond ratings call protected bond Indenture- The written agreement between the corporation (the borrower) and its creditors. It is sometimes referred to as the deed of trust. Usually, a trustee ( abnk, perhaps) is appointed by the corporation to represent the bondholders. The trust company must (1) make sure the terms of the indenture are obeyed, (2) manage the sining fund), and (3) represent the bondholders in default- that is, of the company defaults on its payments to them. The Bond indenture is a legal document. It can run several hundred pages and generally makes for tedious reading. It generally includes the following provisions: 1. The basic terms of the bonds 2. The total amount of bonds issued 3. A description of property used as security 4. The repayment arrangements 5. The call provisions 6. Details of the protective covenants DEFINE!! *KNOW!!!* *ON TEST!!!* RANDOMIZED FROM BOOK!!* *PAGES 207-209 IN BOOK!!!!*

Prices

There are conventions in bond pricing quotes because people and publications do not wish to print all digits of a price when they can base it on a par of $100 and have the same meaning except we are all supposed to know that the par is really $1000. Therefore:1 point in price = $1 on $100 par value, but Par values are typically $1000.So, if the price = $90 $900 on a $1000 FV bond

Interest Rate Risk

^e)Interest rate risk is the variability of bond returns that are caused by unexpected changes in interest rates. The rule of thumb regarding interest rate risk is that the sooner you get you're your money from a bond, the less risky it is, thus this implies that shorter maturity higher coupon bonds are less risky. There are two main sources of Interest Rate risk: 1)Maturity: Prices of long-term bonds tend to be more volatile to interest rate changes than prices of short-term bonds. In the example below we have both bonds with YTM=Coupon so Par=Price, the only difference between the two is the maturity. Next, we change the YTM to 11% for both to see what happens to the prices of the bonds. e.g.: Bond A , Bond B Maturity 25 5 YTM 10% 11% 10% 11% Coupon 10% 10% Price $1000 ?? $1000 ?? Par $1000 $1000 Bond A on the Fin. Calc.: N=25, i=11, PMT=100, FV=1000, PV=??=-915.78 Bond B on the Fin. Calc.: N=5, i=11, PMT=100, FV=1000, PV=??=-963.04 So we see that the longer maturity bond has much more price variation, it is down $85 compared to just $37 for bond B. So this amounts to: Bond A , Bond B %ΔP=(915.78-1000)/1000~=-8.42% , %ΔP=(963-1000)/1000~=-3.7% Duration takes into account coupon and maturity. Right now interest rates are going up and bond prices are going down so we're looking for low duration! 2) Coupon Rates: Prices of low coupon bonds are more volatile to changes in interest rates than prices of high-coupon bonds. e.g.: Bond C , Bond D Maturity 25 25 YTM 10% 11% 10% 11% Coupon 10% 4% Price $1000 ?? $455.38 ?? Par $1000 $1000 Bond C on the Fin. Calc.: N=25, i=11, PMT=100, FV=1000, PV=??=-915.78 Bond D on the Fin. Calc.: N=25, i=11, PMT=40, FV=1000, PV=??=-410.48 So we see that the lower coupon bond has more price variation than the high coupon bond. So this amounts to: Bond C , Bond D %ΔP=(915.78-1000)/1000~=-8.42% , %ΔP=(410.48-455.38)/455.38~=-9.86% Of course we should also know that: Bond prices and yields are inversely related: as yields increase, bond prices fall. This follows directly from the bond pricing equation, it's a ratio so when the YTM in the denominator increases, the ratio which is the price decreases and vice versa. FIGURE 7.2: Talked about the other day. 30 yr bond and 1 yr bond. + Fisher Effect: The Fisher equation relates nominal interest rates to the real interest rate and the expected inflation rate in the following manner: (1+rnom)=(1+rreal)(1+π^e) Where: rnom is the nominal or quoted rate rreal is the real interest rater π^e is expected inflation

10. Inflation and Nominal Returns Suppose the real rate is 2.5 percent and the inflation rate is 4.1 percent. What rate would you expect to see on a Treasury bill?

fischer equation (1+rnom)=(1+rreal)(1+π^e) = (1.0250)(1.041) = 6.7% R=6.70%

Interest Rates or Yields

the relationship between the coupon interest that the bond pays and the yield to maturity determines whether they can sell the bond for above or below par value !!!!!! (The coupon interest payment is set by the issuer. Not the yield to maturity! That's a market rate determined by the supply and demand of loanable funds!)