Consider the following MBS pass through with principal $300 million. The original mortgage pool has a WAM = 6 months and a WAC = 7.00%. The pass through security pays a coupon equal to 6.5%. Assume a flat term structure of interest rates of 5% (continuously compounded).

(a) What is the price of the pass through? Assume a constant PSA = 150%.

(b) Compute the duration of this security assuming that the PSA remains constant at 150%.

(c) Compute the effective duration of this security assuming that the PSA increases to 300% if the term structure shifts down by 50 basis points, while it decreases to 100% if the term structure shifts up by 50 basis points. Comment on any difference compared to your result in part (b).

(d) Compute the effective convexity of this security under the same PSA assumptions as in part (c). Interpret your results.