There are three sources of return an investor can expect to receive by investing in bonds:

1. The coupon payment made by the issuer.
2. Any capital gain or loss (negative dollar return) when the bond matures, is called or is sold. This is the difference between the purchase price and the price when the bond is no longer owned by you.
3.
Income from the reinvestment of interim cash flows such as interest payments and any prepayments of principal prior to the final or stated maturity date. You take the interim payment and invest it in another fixed income security to earn additional returns. This is also known as interest on interest.

This section is all about formulas and bond math; some of the questions you see on your CFA Level 1 exam will almost certainly come out of this section.

1. Current Yield
Current yield relates the annual dollar coupon interest to the bond's market price:

Formula 14.10

Current Yield = annual dollar coupon interest / price



Example: Current Yield
IBM ten-year bond with a rate of 5% and market price of 98.

Answer:
Step1 - Figure out the annual dollar coupon interest= .05 x $100 = 5$

Current Yield = $5 / 98 = .05102= 5.1%

Current yield is greater when bond is selling at a discount. The opposite is true for a premium bond. If a bond is selling at par, the current yield will equal the coupon rate.

The drawback using current yield is that it only considers the coupon interest and nothing else.

2. Yield to Maturity (YTM)
Yield to maturity is the most popular measure of yield in the market. It isthe rate that will make the present value of a bond's cash flows equal toits market price plus accrued interest. To find YTM, one has to develop the cash flows and then, through trial and error, find the interest rate thatmakes the present value of cash flow equal to the market price plus accrued interest.

This is basically a special type of internal rate of return (IRR).

Example: Yield to Maturity
An example using the above IBM bond the cash flows will consist of 20 payments of $2.50 every six months and a payment, twenty six-month periods from now, of $100. The present values, using various semi-annual discounts, are as follows:

Semi-annual interest Rate  Present Value
2.50% 100
2.60% 99.5
2.70% 99
2.80% 98.5
2.90% 98



When the rate of 2.9% is used the present value of the cash flows is equal to a price of $98.00. Hence the semi-annual yield to maturity is 2.9%. Now that we have found this we must make it into a market convention rate or the bond-equivalent yield. To get this yield, just double the semi-annual rate. In this example, it would be 5.8% yield to maturity.

Bond Price, Coupon Rate, Current Yield and Yield to Maturity

  • For a bond selling at par:
    Coupon Rate = Current Yield = Yield to Maturity
  • For a bond selling at a discount:
    Coupon Rate < Current Yield < Yield to Maturity
  • For a bond selling at a premium:
    Coupon Rate > Current Yield > Yield to Maturity

The limitations of the yield to maturity measure are that it assumes that thecoupon rate will be reinvested at an interest rate equal to the YTM. Besides that it does take into considerationthe coupon income and capital gains orloss as well as the timing of the cash flows.

3. Yield to First Call
Yield to first call is computed for a callable bond that is not currently callable. The actual calculation is the same as the Yield to Maturity with the only difference being that instead of using a par value and the stated maturity, the analyst will use the call price and the first call date in calculating the yield.

4. Yield to First Par Call
Again, yield to first par call is the same procedure as above, with the difference being that the maturity date that will be used instead of the stated maturity date is the first time the issuer can call the bonds at par value.

5. Yield to Refunding
Yield to refunding is used when the bonds are currently callable but there are certain restrictions on the source of funds used to buy back the debt when a call is exercised. The refunding date is the first date the bond can be called using a lower-cost debt. The calculation is the same as YTM.

6. Yield to Put
Yield to put is the yield to the first put date. It is calculated the same way as YTM but instead of the stated maturity of the bond, one uses the first put date.

7. Yield to Worst
Yield to worst is the yield occurs when one calculates every possible call and put date that has the lowest possible yield. For example if you calculate all the call dates and the yield comes out as follows 5.6%, 7.6%, 8.2% and 7.5%, the yield to worst would be 5.6%. This measure means little to the potential return; it is supposed to measures the worst possible return the investor will receive if the bond is called or put.

8. Cash Flow Yield
Cash flow yield deals with mortgage-backed and asset-backed securities. The cash flows of these securities are interest and principal payments. What makes this complicated is that the borrowers who make up the mortgage or asset pool can prepay their loans in whole or in part prior to the scheduled principal payment. Because of this, the cash flows have to be estimated and an assumption must be made as to when these principle prepayments may occur. The rate that exists when the prepayments occurs is called the prepayment rate or prepayment speed.Once this rate is estimated, a yield can be calculated. The yield is the interest rate that will make the present value of the estimated cash flows equal the price plus accrued interest.

Example: Cash Flow Yield
Because cash flows for these securities are usually monthly, a bond-equivalent yield must be developed. The math here is a little different than in the above examples:

Step 1 - the effective semi-annual yield must be computed from the monthly yield by compounding it for six months.

Effective semi-annual yield = (1 + monthly yield) to the 6th power -1

Step 2 - Double the effective semi-annual yield to get the annual cash flow on a bond equivalent basis.

Cash flow yield = 2 x {(1 + monthly yield) to the sixth power-1}

Answer:
So if the monthly yield is .8% then:

Cash flow yield = 2*{ 1.008) to the sixth power -1}
= 2 x .04897
= 9.79%

Assumptions Underlying Traditional Yield Curve Measures

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