# Session 4 Te - S4 The Term Structure of Interest Rates Background Reading 1 The Term Structure of Interest Rates Objectives Use the term structure

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S4: The Term Structure of Interest Rates – Background Reading 1 The Term Structure of Interest Rates Objectives: Use the term structure of interest rates to i) infer risk free interest rates and ii) forward interest rates Learning Outcomes appreciate the demand for risk free assets by the retail investors and how this demand is met by the income stripping exercise carried out by the financial institutions appreciate the need to estimate market expectations of future interest rates for the purpose of investment decisions learn from the expectation and liquidity premium hypotheses (i) the relationship between forward interest rates and market expectations of future interest rates (ii) the choice of bonds with different maturities appreciate the arguments for the demand for liquidity premium by retail investors and the willingness of corporations to offer additional returns beyond market expectations

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S4: The Term Structure of Interest Rates – Background Reading 2 Are Fixed Coupon Bonds Risk Free Assets? Let’s refer to the 5.75% May 2021 CGS that we priced before on Thu, 11/11/10 using a YTM of 5.530% and a settlement date on Mon, 15/11/10 . 2.875x(1+ ? ) 20 2.875x(1+ ? ) 19 2.875x(1+ ? ) 18 2.875x(1+ ? ) 17 ……. 2.875 x(1+ ? ) 1 (\$ 101.735 ) \$2.875 \$2.875 \$2.875 \$2.875 ….. \$2.875 \$ 2.875+\$100 15/11/10 15/05/11 15/11/11 15/05/12 15/11/12 ….. 15/11/20 15/05/21 holding period Since the YTM is 5.5.30% p.a. compounded semi-annually, investors would expect their investment of \$101.735 to grow to \$180.393 when the bond matures on 15/05/21. 21 ) 2 % 530 . 5 1 ( 735 . 101 180.393 To achieve this, all the coupon interests have to be reinvested at the same initial yield of 5.530% in the future, i.e., CI 15/05/21 = 2.875 x(1+ 5.530 /2) 20 + 2.875 x(1+ 5.530 /2) 19 + … + 2.875 x(1+ 5.530 /2) 1 + 2.875 = 80.393 FV 15/05/21 = 100.000 In summary, fixed coupon bonds are not risk free - the yield is only an expected return for holding the bond to maturity as investors may not be able to reinvest all the coupon interests at the same rate as the initial yield. there is an implicit (though unrealistic) assumption about the YTM that that investors can reinvest all the future coupon interest at the same rate as the initial yield.
S4: The Term Structure of Interest Rates – Background Reading 3 How do we measure expected return if we don’t hold the bond to maturity? We know what to expect if we were to hold a bond to maturity, but what if our investment horizon doesn’t match the bond’s maturity? For example, if we have a 2-year investment horizon, which of the following choices should we choose? 0 1 2 3 4 . . . n roll over two 1-year bonds buy and hold a two-year bond to maturity, or buy a n-year bond and sell it after two years, where n > 2. We should first compare the “expected” return, rather than the YTM, of these alternatives

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## This note was uploaded on 06/12/2011 for the course ASB 1001,2522, taught by Professor Nicole during the One '09 term at University of New South Wales.

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Session 4 Te - S4 The Term Structure of Interest Rates Background Reading 1 The Term Structure of Interest Rates Objectives Use the term structure

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