The following answer to the question (below) seems wrong to me. I think they should have used 0.01 (100bp) as the change in yield as supposed to 0.005 Please can somone help? The question is from Topic One Factor Measures of Price Sessitivity. part of the Q_Bank questions. (Valauations and Risk Models). Thank you
A bond with an 8% semi-annual coupon and 10 year maturity is currently priced at $904.52 to yield 9.5%. if the yield declines to 9%, the bond price will increase to $934.96, and if the yield increases to 10%, the bond’s price will decrease to $875.38. Estimate the percentage price chage for a 100 basis point change in rates.
The formula for the percentage price change is: (price when yield fall - price when yield rise)/2 x (nitial price) x 0.005 = ($934.96 - $875.38)/2($904.52)(0.005) = $59.58/$9.05 = $6.58. Note that this formula is also referred to as the bond’s effective duration.
QuantBoy - the typical convention is to see the price changes from 100bps swings in the numerator, but mathematically, you should be prepared to calculate duration for any bps swing that they provide you. Realize that any +/- interest rate swing they give you results in a tangent line to the bond’s price/yield curve, with the current price as the point of tangency. It is still a calculation of duration in any case.
that doesn’t answer my questions. I’m asking if they made a type error or not?
In case the last response wasn’t clear enough, let me be more specific about it and see if that helps you - notice in the question how you start out at 9.5% as the current yield? Then they talk about going to 10% or 9%? Well, you see, each of those swings is 50 bps - which is represented as 0.005 in the answer calculation. They did not make a typo. Even more specifically - 100 bps would be represented in DECIMAL PERCENT form in the solution, i.e., 0.01, 75 bps as 0.0075, etc. Make sense?
yes it does now. thank you sorry for my short message earlier. I was really frustrasted having spent so long on it.
No sweat, good luck in your studies.