Q3: Suppose that we have three key rates given i.e 2 years, 16 years and 30 years. The duration of the zero coupon security is approximately the number of years to maturity. Thus the three key rate durations are 2, 16 and 30. Consider the following two portfolios of $100. Portfolio 1 2 2-year issue $50 16-year issue SO 30-year issue $50 SO SO $100 The key rate durations for the three issues and the duration are as follows. Issue 2-years 16-years 30-years D(1) 2 0 0 D(2) 0 16 0 D(3) 0 0 Crash Duration 2 16 30 30 D (1) = Key rate duration for the 2 year part of the curve. D (2) = Key rate duration for the 16 year part of the curve. D (3)= Key rate duration for the 30 year part of the curve. Required: a) Calculate key rate duration and effective duration for each portfolio. b) Assume the following 2 different scenarios and calculate the change in the value of both the portfolios. Scenario 1: The 2-year key rate shifts up 10 basis points, and the 30-year key rate shifts down 10 basis points. Scenario 2: The 2-year key rate shifts down 10 basis points, and the 30-year key rate shifts up 10 basis points. Q3: Suppose that we have three key rates given i.e 2 years, 16 years and 30 years. The duration of the zero coupon security is approximately the number of years to maturity. Thus the three key rate durations are 2, 16 and 30. Consider the following two portfolios of $100. Portfolio 1 2 2-year issue $50 16-year issue SO 30-year issue $50 SO SO $100 The key rate durations for the three issues and the duration are as follows. Issue 2-years 16-years 30-years D(1) 2 0 0 D(2) 0 16 0 D(3) 0 0 Crash Duration 2 16 30 30 D (1) = Key rate duration for the 2 year part of the curve. D (2) = Key rate duration for the 16 year part of the curve. D (3)= Key rate duration for the 30 year part of the curve. Required: a) Calculate key rate duration and effective duration for each portfolio. b) Assume the following 2 different scenarios and calculate the change in the value of both the portfolios. Scenario 1: The 2-year key rate shifts up 10 basis points, and the 30-year key rate shifts down 10 basis points. Scenario 2: The 2-year key rate shifts down 10 basis points, and the 30-year key rate shifts up 10 basis points