An investor holds a portfolio of mortage backed securities valued at $100m.

For fixed income portfolios where standard cash flow discounting models are not available, duration calculations are based upon estimated price moves in response to a change in rates. Recall that we define duration as the percentage change in price expected for a 1% change in yield. In this case, we have three price points known to us:

Line | Price | Yield

a | $102 | r - 45bps

b | $100 | r

c | $ 97 | r + 45bps

(where r is the current yield)

The change in price from line a to line c is $102m - $97m = $5m. We use the middle point, ie $100m, to calculate the percentage change. Therefore the percentage change in price is $5m/$100m = 5%.

The change in yield between lines a and c is 90 basis points [=(r+45bps) - (r-45bps)]. In other words, the change in price is 5% for a 90 bps change in yield. So the duration can be calculated as 5/(90/100) = 5.56. The other answers are incorrect.