Unit 13
To compute the future value of the cash flow from a bond, you would have to know the:
- principal amount; - coupon rate; and -number of interest payments.
Convexity
1. Convexity is the measurement of the curve that results when plotting a bond's price movements in response to changes in interest rates. 2. It is a more accurate representation than the duration of what will happen to a bond's price as interest rates change, especially when the changes are great. 3. Duration is a linear (straight-line) measurement, while convexity follows a curve. 4. Comparing two bonds, the one with the higher convexity will show a greater price increase when yields fall and a smaller decrease when yields rise (that is a good thing). 5. If we find two bonds with the same duration, the one with the higher convexity offers greater interest rate risk protection. **If you should be asked, "Which of the following is the most useful in determining the price volatility of a bond to a significant change in interest rates?" the correct choice is convexity.**
Advantages of convertible bonds to investors
1. Downside protection 2. Upside potential
Discounted Cash Flow (DCF)
1. In its simplest iteration, this is nothing more than taking all the money you are scheduled to receive over a given future period and adjusting that for the time value of money. 2. It is commonly used to value debt securities. 3. The bond's price will always reflect a yield equal to current market interest rates for comparable risk. a. Take the income payments scheduled to be received over a given future period and adjust that for the time value of money. (Discount rate based on current market interest rates) b. Take the future principal repayment - use the discount rate to compute the present value. 4. The value of the bond is the present value of its cash flow stream. a. The higher the discounted cash flow, (the sum of the present value of the income and principal) the higher the value of the bond. b. Cash flow analysis on mortgage-back debt (GNMA pass-through securities) uses average maturities. c. When used with equities, it is the dividend discount model. (Only dividends, no maturity date.)
Duration
1. Measures volatility of bond prices by weighting the time the bond interest takes to pay for the bond. a. The longer it takes to get your money back affects the volatility of bond prices. 2. Longer duration means higher bond volatility. a. Interest rates up, bond price down; interest rates down, price up based on duration. b. The zero-coupon bond's duration is maturity—most volatile. 3. If maturities are about the same, the lowest coupon has the longest duration and highest coupon has the shortest duration (least sensitive) 4. If coupons are about the same, the latest maturity has the longest duration and soonest maturity has the shortest duration (least sensitive) 5. Convexity is a more sophisticated measurement of sensitivity to interest rate changes
Nominal yield, Coupon rate, or Stated yield
1. The interest rate stated on the coupon 2. This amount is fixed at issuance
Yield to Call (YTC)
A bond with a call feature may be redeemed before maturity at the issuer's option. Unless the bond was bought at par, and is callable at par, yield to call (YTC) calculations reflect the early redemption date and consequent acceleration of the premium loss from the purchase price. A bond's YTC, similar to YTM, is the rate of return the bond provides from the purchase date to the call date and price. This calculation generates a lower return than does the YTM and should be considered by investors when evaluating a callable bond trading at a premium. The reason why we've only referred to a bond selling at a premium being called for redemption is because it is highly unlikely that an issuer would call in a bond that was available in the marketplace at a discount
A bond's duration measures...
A bond's duration measures its sensitivity (volatility) to changes in market interest rates. The longer the duration, the greater the sensitivity (bigger the price swings).
Standard & Poor's Bond Ratings
AAA Bonds of highest quality AA High-quality debt obligations A Bonds that have a strong capacity to pay interest and principal but may be susceptible to adverse effects BBB Bonds that have an adequate capacity to pay interest and principal but are more vulnerable to adverse economic conditions or changing circumstances BB B CCC C D **Plus (+) and minus (−) are used to show relative strength within a rating category.**
Yield to Maturity (YTM)
AKA Basis. Yield that also takes into account the discount or premium spread out over the years to maturity. Yield if held to maturity. YTM is also called the market-driven yield because it reflects the internal rate of return from the bond investment.
Moody's Ratings
Aaa Aa A Baa Ba B Caa Ca C **For ratings Aa through B, 1 indicates the high, 2 indicates the middle, and 3 indicates the low end of the rating class.**
Complications of projecting your client's cash flow on a portfolio of mortgage-backed securities.
Although they do have default risk (other than GNMAs), as do other debt securities, the specific risk due to the possible (some would say, likely) prepayments, complicates the computation. When doing cash flow analysis on a mortgage-backed pass-through security, you would want to know the average maturities.
Current Yield
Annual coupon ÷ current market price
A bond selling for $20 above par would be quoted
Bonds are quoted in percentages of $1,000 (par) (1% of $1,000 = $10). The proper quote would be 102; 1 02 is 102% of $1,000.
Quotes of corporate and municipal bonds
Corporate and municipal bonds are quoted as a percentage of par where 100% = $1,000. Each bond point represents $10, and the fractions are in eighths: each 1/8 = $1.25. - A bond quoted at 90 1⁄4 = $902.50. - A bond quoted at 101 3⁄4 = $1,017.50.
A bond analyst who determines the value of a debt security by adding the present value of the future coupons to the present value of the maturity value is using which of the valuation methods?
Discounted cash flow In this example, a case could be made for present value, but the better choice is discounted cash flow; it is more correct.
Quotes of government bonds
Government bonds are quoted as a percentage of par. Each point is $10, and each .1 represents 1/32 of $10 ($0.3125). - A government bond quoted at 90.8 (or 90.08) = $902.50. - A government bond quoted at 101.24 = $1,017.50. **In recent years, some quote systems have added a 0 for prices between .1 and .9 to avoid confusion (similar to the way you enter the expiration date for your credit card as 01/2020 instead of 1/2020). That is why, in the previous example, we show you both 90.8 and 90.08—they both mean 90 8/32.**
Investment-Grade Debt
In the industry, bonds rated in the top four categories (BBB or Baa and higher) are referred to as investment grade. Investment-grade bonds are generally the only quality eligible for purchase by the institutions (e.g., banks or insurance companies) and by fiduciaries and, therefore, have greater liquidity than lower-grade instruments.
Long-term Debt
It is important to understand that debt capital refers to long-term debt financing. Long-term debt is money borrowed for a minimum of five years, although more frequently the length of time is 20-30 years.
High-Yield Bonds
Lower-grade bonds, known in the industry as junk bonds, are now more commonly called high-yield bonds. Because of their lower ratings (BB or Ba or lower) and additional risk of default, high-yield bonds may be subject to substantial price erosion during slow economic times or when a bond issuer's creditworthiness is questioned.
Can governments or municipalities issue convertible bonds?
No
Ranking Yields from Lowest to Highest: Discounts
Nominal CY YTM YTC
Convertible Bonds: Anti-Dilutive Protection
One of the concerns of any holder of a convertible security (bond or preferred stock) is protection against the potential dilution resulting from a stock split or a stock dividend. For example, if you owned a bond convertible into 20 shares and the issuer declared a 2-for-1 stock split, in order for you to have the same conversion powers, you would need to be able to convert into 40 shares. If the conversion privilege were expressed as a conversion price, the new price would now be half the former one allowing you to convert into twice as many new shares.
How often do bonds pay interest?
Semi-annually
DEF 5s35 @106 What does this mean?
The DEF is the issuer, the 5 is the nominal or coupon rate, the 35 is the maturity date of 2035 and the 106 is the price ($1,060). So, what is the "s"? It is nothing but a separation between the coupon and the maturity date.
Factors you need to know to find YTC
The YTC computation involves knowing: - the amount of interest payments to be received, - the length of time to the call, - the current price, and - the call price.
How do you find the approximate average duration of bonds in a bond mutual fund?
The approximate average duration of bonds in a bond mutual fund can be estimated by finding the mean (average) of the individual bonds. Keep in mind, you may have to take each bond and figure out the proportion of the portfolio its duration represents.
Discount Rate
The discount rate is just another way of stating the current interest rate in the marketplace. If the discount rate is higher than the coupon rate, the present value (the expected market price) will be below par. Conversely, if the discount rate is lower than the coupon rate, the present value will be above the par value.
An analyst would use the discounted cashflow method in an attempt to find...
The fair value of a security DCF uses the present value of future cash flows, based on a specified discount (interest) rate, to evaluate the price that a security should be selling for in the market. If the current market price of the security is less than this value, it has a positive net present value (NPV) and should be a good investment. The opposite is true if there is a negative NPV (the market price is higher than that computed under the DCF method).
Coupon Rate
The interest rate that a bond issuer will pay to a bondholder
Three main issuers of debt securities
The largest issuer of debt securities is the U.S. government. Corporations issue bonds to finance their operations and substantial sums are also borrowed by state governments and those political entities that are subdivisions of a state, such as cities, counties, towns, and so forth. These issues from state and local political entities are called municipal bonds.
Disadvantages of convertible bonds to investors
The only disadvantages to investors in convertible bonds are that they receive a lower interest rate than a nonconvertible debt and, of course, the possibility that the convertible bond may be called away before one is ready to convert.
Indenture or Deed of Trust
The terms of the loan are expressed in a document known as the bond's indenture. The indenture, sometimes also referred to as the deed of trust, states the issuer's obligation to pay back a specific amount of money on a specific date. The indenture also states the issuer's obligation to pay the investor a specific rate of interest for the use of the funds as well as any collateral pledged as security for the loan and all other pertinent details.
Treasury Inflation Protection Securities (TIPS)
Treasury Inflation Protection Securities (TIPS), helps protect investors against purchasing power risk. These notes are issued with a fixed interest rate, but the principal amount is adjusted semiannually by an amount equal to the change in the Consumer Price Index, the standard measurement of inflation. They are issued with maturities of 5, 10, and 30 years. The interest payment the investor receives every six months is equal to the fixed interest rate times the newly adjusted principal. TIPS adjust the principal value every 6 months to account for the inflation rate. Like other Treasury securities, TIPS are exempt from state and local income taxes on the interest income generated, but are subject to federal taxation. However, in any year when the principal is adjusted for inflation, that increase is considered reportable income for that year even though the increase will not be received until the note matures.
Treasury STRIPS
Treasury securities that are sold in bulk to large dealers, who then strip out the coupons from principal, repackage the cash flows, and sell them separately as zero-coupon bonds; Coupon strips are strips created from coupon payments stripped from the original security; Principal strips refer to principal payments with the coupons stripped off; Taxed on their implicit interest rate Treasury STRIPS are zero-coupon bonds and, as such, have a longer duration than those paying semiannual interest. The longer the duration, the greater the interest rate risk.
Factors that go into a bond's duration
Two factors go into the computation of a bond's duration: - the length to maturity and - the coupon rate.
Zero-coupon bond duration
With no periodic interest payments (that's why it's called zero-coupon), the duration of a zero-coupon bond will always equal its length to maturity. In other words, if we're trying to compute how long it will take for the income payments to return your principal, without any interest payments, you can't expect to get your money back until maturity date. If that is the case with a zero-coupon bond, then as we find bonds paying interest, the more they're paying every six months, the quicker the payback.
Factors that have an inverse relationship to a bond's maturity.
coupon rate yield to maturity current yield **The relationship between the time to maturity (length) and duration is a linear one.**
The (higher/lower) the discounted cash flow (DCF), the more valuable the investment.
higher
