# Duration and convexity relationship quizzes

### Duration & Convexity - Fixed Income Bond Basics | Raymond James

Jan 3, Find out how duration and convexity measures can help fixed-income investors manage risks such Macaulay's duration formula is as follows. View Notes - Quiz 2 p's from INB at Rollins College. (up to 10 marks) Answer Selected Answer: Duration and convexity are commonly used e Correct Answer: Relationship between spot interest rates and maturity of a bond Response. Bond Convexity. Quiz Duration is a first approximation of a bond's price or a of the price/yield relationship in order to give a more accurate estimated price.

## FRM-I “Duration” Tutorial: Master the Art of Calculating Duration & Convexity

So according to definition, any change in interest rate should reflect 1. As highlighted in the figure 1.

As evident from figures 1. This is demonstrated as duration effect and is given below. Duration effect captures both the direction and magnitude of change in bond price due to a change in yield.

Modified duration is very similar to Macaulay duration, but improvises by discounting the Macaulay duration back by one payment time period.

For example, if the bond is a semi-annual bond, the Macaulay duration should be discounted back by six months using the current yield.

Duration works only for small changes in the yield. When the change in the yield is high, say basis points, duration becomes inaccurate due to the convexity effect. Convexity Duration assumes a linear relationship between bond price and yield, which is not true especially when there is high volatility in yields.

Convexity takes off where duration stops in a sense that it gives a more accurate price of a bond based on interest rate changes than Duration.

### FRM-I “Duration” Tutorial: Master the Art of Calculating Duration & Convexity - EduPristine

The formula for measuring convexity is: T he second term in the above equation is the second derivative of the bond price and yield functions.

The first derivative measure that is duration measures how price changes with yields, while second derivative is a measure of changes in the first derivative with changes in the yields. The relationship between yields and bond prices is more of a curved line rather considering a straight line as estimated by duration.

This curvature in bond price can be best estimated when we combine Duration effect and the Convexity effect which results in a more accurate price of the bond. The exception is long-term, low coupon bonds, on which it is possible to have a lower duration than on an otherwise comparable shorter-term bond. Callable Bonds A callable bond exhibits positive convexity at high yield levels and negative convexity at low yield levels.

- Duration & Convexity: The Price/Yield Relationship

Negative convexity means that for a large change in interest rates, the amount of the price appreciation is less than the amount of the price depreciation. When the required yield for the callable bond is higher than its coupon rate, the bond is unlikely to be called.

**Bond Convexity**

When the required yield becomes lower than the coupon rate, the value of the call option increases because it is getting more and more likely that the bond may be retired at the call price. The call price will set an upper limit on the price of the callable bond. In contrast, for an option-free bond, the bond price will rise unabated as the yield falls.

If the required yield rises but not higher than the coupon ratethe price of the non-callable bond falls and the price of the call option falls. As the price of a callable bond is the difference between the price of the non-callable bond and the price of the embedded option, the price of a callable bond will not fall as much as a non-callable bond.

Therefore, a callable bond exhibits negative convexity at low yield levels. Putable Bonds The difference between the value of a putable bond and the value of an otherwise comparable option-free bond is the value of the embedded put option. When the required yield for the putable bond is low relative to the issuer's coupon rate, the price of the putable bond is basically the same as the price of the option-free bond because the value of the put option is small.