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Chapter 6

# Chapter 6 - Chapter 6 Yield Measures Spot Rates and Forward...

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1 Chapter 6 Yield Measures, Spot Rates, and Forward Rates

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2 Plan of the lecture Various yield measures : current yield, yield to maturity, yield to call, yield to put, and yield to worst … Spot rates Nominal spread , zero-volatility spread , and option-adjusted spread ( OAS ) Forward rates
3 Sources of return An investor in fixed income market expects to receive dollar return from one or more of the following sources: 1) Coupons (periodic interests) 2) Face value repayment and capital gain or capital loss resulted from bond price change and 3) Reinvestment of previous coupon payments Subject to reinvestment risk Any yield measure must take into account all of the above three sources of return

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4 Yield measures Suppose there is a 3 year bond, with a 6% coupon rate, semiannual coupons, and a face value of \$1,000: If you pay \$947.58 for this bond, what is your annual return on the bond investment ?
5 Yield measures Current yield Current yield is calculated by dividing the annual coupon payments by the bond’s price: Current yield = Coupon payments Bond price Coupon payments = \$60 per year (= 6% × \$1,000) Price of \$947.58 Current yield = \$60 = 6.33% \$947.58

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6 Yield measures Current yield is an incomplete measure of the return on bonds since it only considers the coupons but ignores : 1) Any capital gain (or capital loss ) on this bond: for example, at the maturity date the face value is repaid and there will be a capital gain at that time (\$1,000 - \$947.58 = \$52.42) and 2) Any income from reinvestment of previous coupons Recall from ADMS3530 : current yield on bonds is similar to dividend yield on stocks in that both are incomplete measures of the rate of return on bond (or stock) investment
7 Yield measures Yield to maturity is defined as the interest rate which makes the present value of the bond’s cash flows equal to its current price. Yield to maturity ( YTM , or yield ) is also the internal rate of return ( IRR ) on bond investment ( Why ? )

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8 Yield measures Yield to maturity For the 3 year bond you are working with, you know the price of the bond is \$947.58 To calculate the yield to maturity, you must solve for “ r ” (the interest rate) in the following equation: 6 6 ) r 1 ( 000 , 1 \$ ] ) r 1 ( r 1 r 1 [ 30 \$ 58 . 947 \$ + + + - × = There is no closed-form solution, so you have to use a financial calculator ( see the next slide ... )
9 Yield measures Yield to maturity If you use a TI BAII Plus financial calculator, then apply the following keystrokes: 30 (PMT); 1,000(FV); 6(N); -947.58(PV); CPT (I/ Y) You will see 4%. This is the interest rate per 6 months. The yield to maturity is an APR with semiannual compounding . So the yield to maturity is 4% × 2 = 8%

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10 Yield measures Example 1 : bond price = \$1,000 = par, coupon rate = 6%, current yield = \$60 / \$1,000 = 6%, and YTM = 6% Example 2 : bond price = \$947.58 < par, coupon rate = 6% < current yield = \$60 / \$947.58 = 6.33% < YTM = 8% Example 3 : bond price = \$1,027.54 > par, coupon rate = 6% > current yield = \$60 / \$1,027.54 = 5.84% > YTM = 5% Bond selling at Relationship Par Coupon rate = current yield = YTM Discount Coupon rate < current yield < YTM Premium Coupon rate > current yield > YTM Consider the 3 year bond that we have been working with:
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Chapter 6 - Chapter 6 Yield Measures Spot Rates and Forward...

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