- whats is the effect of prepayment option on duration of the bond? 2)The CFA text has duration formula as (V- - V+ ) Duration = ----------------- 2 * V0 *( y1-y0) Do we consider prepayment option in this?
duration is to find interest rate sensitivity to price.
Those formulas might say something about prepayment risk and their effect on bond duration but you are barking up the wrong tree. As puppy says, it’s about interest rate sensitivity of the price of bond. So if you are holding a bond at 7% and interest rates on similar bond drop to 5%, you ought to be feeling pretty good without thinking at all about formulas. The longer term the bond the better you ought to be feeling. Collecting an extra 2%/year over 30 years is better than over three months. On the other hand if the bond can be prepaid, you probably won’t get that extra 2% over 30 years. So prepayment risk certainly affects the duration of the bond when interest rates drop…
The effect of prepayment options on the duration of the bond: Bond duration goes down as interest rates go down. If you hold a mortgage at 10% and rates drop to 5%, you are going to re-finance your mortgage to 5%. This means your 10% mortgage gets paid-off. If I held your mortgage, that means I get my principal back much sooner than expected. Hence my duration has dropped.
There are 3 main types of duration, the one that is mentioned most in the text book is effective duration, hence your formula. Others are Macaulay duration and modified duration which is Macaulay duration/(1+y). Effective duration does account for the effect of embedded option. The question will provide you the exactly price changes so don’t worry about that. However, this is the most difficult part which might be greatly varied between valuation models.
Is this right? When interest rates drop the probability of prepayment increases which decreases the bonds upside potential similar to a call option on the bond. Since the upside potential is limited, the bond’s price will increase less than a bond without prepayment, and therefore the bond with the prepayment option is less sensitive to interest rate changes ie lower duration. Can someone tell me if I’m on track or not?
There is a trade off between interest rate risk and reinvestment/prepayment risk. If the reinvestment risk increases, hence the interest rate risk decreases. To calculate effective duration which is the formula used in the text book, the input price changes are estimated using binomial model and Monte Carlo simulation. I think we are not required to do such a complex valuation in level 1.