Bond price volatility and the price value of a basis point
1. Bond price volatility and the price value of a basis point
In earlier chapters, we learned that yields and prices have an inverse relationship.2. Bond price volatility
However, the magnitude of the effect on price depends on many factors. We now discuss three of those factors: size of yield change, coupon rate, and time to maturity.3. Small change, symmetric effect
The size of yield change has an effect on how large the bond price changes. For small increases or decreases in yield, the percentage price change is similar. What do I mean by that? Consider a bond with $100 par value, 10% coupon rate, 20 years to maturity, and an initial yield of 10%. If yields go up by 0-point-1%, the bond value goes down by 0-point-85%. If yields go down, the bond value goes up by 0-point-86%. So when yields go up or down by 1%, the percentage changes are similar. Note that we can calculate price change easily using the bondprc() function.4. Large change, asymmetric effect
Now, let's look at larger changes in yield. In general, the percentage change in bond value is larger when there is a large decrease in yield, compared to a large increase. Let's look at an example. Suppose yields changed by 4%. Once again we can calculate price change using the bondprc() function. A 4% increase (in this case, from 0-point-10 to 0-point-14), lowers the bond price by 26 and a half percent. On the other hand, a 4% decrease results in a price increase of 45-point-9%. That's a huge difference!5. Lower coupon, more volatile
Another factor that affects bond price volatility is coupon rates. In general, the lower the coupon rate, the more the bond is affected by a change in yield. Consider three bonds that all have a $100 par value, 20 years to maturity, a 10% initial yield, and an 8% new yield. Once again, we can calculate price change using bondprc(). The first bond has a 10% coupon. That bond's price increases by 19-point-6%. The second bond has a 5% coupon and that bond's price goes up by 22-point-8%.6. Lower coupon, more volatile
The third bond, which has zero coupons, goes up by a whopping 44-point-3%!7. Longer maturity, more volatile
Finally, time to maturity also affects bond price volatility. In general, the longer the time to maturity, the more the bond's price is affected by a change in yield. Consider three bonds that all have a $100 par value, 10% coupon, 10% initial yield, and a new yield of 8%. The first is a 20-year bond. As you can see, this bond's price goes up by 19-point-6%. The second is a 10-year bond and it's price increases by 13-point-4%,8. Shorter maturity, more volatile
while the third is a 5-year bond which only goes up by 8%. Looking at these examples, if you want to be able to implement hedging and investment strategies, you need a way to measure the bond price volatility that takes into account at least some of these features.9. Price value of a basis point
One way to do this is to calculate what's called the "price value of a basis point" or PV01, which is sometimes called the "dollar value of an 01." This is the estimated change in the price of the bond if the required yield changes by 1 basis point or point-01%. To understand this, it helps to go through an example. Consider a bond with a $100 par value, 5% coupon rate, 20 years to maturity, and an initial yield of 5%. The price of that bond is $100. Now, if yields go up to 5-point-01%. The price of that bond falls to 99 88.10. Price value of a basis point
The PV01 calculation is then the difference between the new and original bond price, in this case 0-point-12. So if you were told that a bond has PV01 of 0-point-12, then you can expect a $0-point-12 price increase when yields go down by 1 basis point and a $0-point-12 price decrease when yields go up by 1 basis point. The PV01 is typically expressed as a positive number. To calculate this, you have to add the abs() command for absolute value as seen in the code. PV01 is a precursor to the more advanced concept of duration, which we will discuss next. PV01 is the estimated price change for a 1 basis point change in yield, while, in its most basic sense, duration is the estimated price change for a 100 basis point change in yield.11. Let's practice!
Now, let's practice the calculation of PV01 in the next exercises.Create Your Free Account
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