Question

Question 3. Suppose the yield on a one year bond is 8%, the yield on a two year bond is 9%, and the yield on a three year bond is 10%. The liquidity premium is constant at 3%. What is the expected return on the (three-year) investment strategy of rolling over three consecutive one year bonds (i.e., buying a one year bond, then buying a new one year bond with the payoff next year, etc.)?

Answer 1

Sol :

To determine expected return on Investment over 3 consecutive one year bonds is as follows,

Number of years (n) = 3 years

liquidity premium = 3%

Return on year 1 inclusive of liquidity premium (R1)= 8% + 3% = 11%

Return on year 2 inclusive of liquidity premium (R2)= 9% + 3% = 12%

Return on year 3 inclusive of liquidity premium (R3)= 10% + 3% = 13%

Expected return on Investment = [(1+R1) x (1+ R2) x (1+R3)]^(1/n) - 1

Expected return on Investment = [(1+11%) x (1+12%) x (1+13%)]^(1/3) - 1

Expected return on Investment = (1.11 x 1.12 x 1.13)^(1/3) - 1

Expected return on Investment = 11.9970 or 12.00%

Therefore expected return on Investment over 3 consecutive one year bonds is 12%