Could some one please explain a specific part of BB example 1 below. I don’t understand how you calculate the approximate 1% return due to reinvestment income over the two year period? Many thanks.
Jesper Bloch works for Discrete Asset Management (DAM) in Zurich. Many of the firm’s more risk-averse clients invest in a currency-hedged global government bond strategy that uses cash flows to purchase new issues and seasoned bonds all along the yield curve to maintain a roughly constant maturity and duration profile. The yield to maturity of the portfolio is 3.25% (compounded annually), and the modified duration is 4.84. DAM’s chief investment officer believes global government yields are likely to rise by 200 bps over the next two years as central banks remove extraordinarily accommodative policies and inflation surges. Bloch has been asked to project approximate returns for this strategy over horizons of two, five, and seven years. What conclusions is Bloch likely to draw?
Answer: If yields were not expected to change, the return would be very close to the yield to maturity (3.25%) over each horizon. The Macaulay duration is 5.0 (= 4.84 × 1.0325), so if the yield change occurred immediately, the capital gain/loss and reinvestment impacts on return would roughly balance over five years. Ignoring convexity (which is not given), the capital loss at the end of two years will be approximately 9.68% (= 4.84 × 2%). Assuming yields rise linearly over the initial two-year period, the higher reinvestment rates will boost the cumulative return by approximately 1.0% over two years, so the annual return over two years will be approximately −1.09% [= 3.25 + (−9.68 + 1.0)/2]. Reinvesting for three more years at the 2.0% higher rate adds another 6.0% to the cumulative return, so the five-year annual return would be approximately 2.71% [= 3.25 + (−9.68 + 1.0 + 6.0)/5]. With an additional two years of reinvestment income, the seven-year annual return would be about 3.44% [= 3.25 + (−9.68 + 1.0 + 6.0 + 4.0)/7]. As expected, the capital loss dominated the return over two years, and higher reinvestment rates dominated over seven years. The gradual nature of the yield increase extended the horizon over which the capital gain/loss and reinvestment effects would balance beyond the initial five-year Macaulay duration.