![]() ![]() The yield computed at the time of purchase (i.e., YTM) considers all three sources of return, including, coupon payments, capital gain/loss, and reinvestment income. The bond cannot be held to maturity, and may have to be sold for less than the purchase price because the interest rate required by the market is higher than the YTM.Future interest rates may be less than the YTM.However, in reality the YTM of a bond may not be realized because: YTM measures an investor's return from the bond correctly only if these assumptions are true. YTM can be viewed as a weighted average of the spot rates applying to the bond's cash flows. By trial and error or using a financial calculator, YTM is found to be 8%. The cash flows for this bond are (1) 4 payments every six months of $50, and (2) a payment 2 years from now of $1,000. The coupon reinvestment rate is the same as the YTM.įor example, consider a 10%, 2-year bond selling for $1,036.30 (selling at premium).The issuer does not default: All coupon and principal payments are made in full when due. The yield-to-maturity measures an investor's return from the bond correctly only if these assumptions are true: If the spot curve is downward sloping, the forward curve will lie below the spot curve. If the spot rate is increasing, so spot rate n is greater than spot rate n - 1, then forward rate must be above spot curve. You can think of the spot rate for a given maturity as a sort of average of the forward rates for all maturities up to and including the spot rate's maturity. The spot rate is the geometric mean of the forward rates. Similarly, we can calculate spot rates from forward rates. What is the forward rate starting 10 years from now, for 2 years? The spot rate is 5% for 10 years, and 6% for 12 years. (T*+T)= T* TĮd is considering a bond purchase but cannot decide if he wants to hold the bond for 10 years or 12 years. Given spot rates for maturities of T* and T* + T, we can compute the forward rate starting at T* for T: The value of the second choice after 2 years should be 1,000 x (1 + 0.08) x (1 + F(1,1)) = 1,210 soį(1,1) is the 1-year forward rate starting 1 year from now. The returns from the 2 choices should be the same. Invest in the 1-year bond, and again invest the proceeds after 1 year in a 1-year bond.The value of his investment after 2 years will be $1,000 x (1 + 0.1) 2 = $1,210 ![]() Let's say an investor wants to invest $1,000 for 2 years. In our example, P(1) = 0.92593, and P(2) = 0.82645Ī forward rate, f(T*, T), is the interest rate beginning some time in the future, T*, for a period of time T. P(T) = 1/(1+r(T) ) T is called the discount factor. Bond A is a 1-year bond and bond B is a 2-year bond. A spot rate, r(T), is the interest rate today for a specified period of time T.Ĭonsider two zero coupon bonds. ![]()
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