2. MEASUREMENT OF INTEREST RATE RISK Pertemuan 6 -mupo- MEASUREMENT OF INTEREST RATE RISK Pertemuan 6 -mupo- Mata kuliah: F0922 - Pengantar Analisis Pendapatan Tetap Dan Ekuitas Tahun: 2010

3. Bina Nusantara University 3 MEASUREMENT OF INTEREST RATE RISK Materi: 1. Full valuation approach 2. Price volatility character 3. Duration 4. Convexity

4. 1. Full valuation approach The most obvious way to measure the interest rate risk exposure The most obvious way to measure the interest rate risk exposure of bond position or a portfolio is to re-value it when interest of bond position or a portfolio is to re-value it when interest rates changes. rates changes. Example : a manager may want to measure the interest rate Example : a manager may want to measure the interest rate exposure to a 50 basis point, 100 basis point, and 200 basis exposure to a 50 basis point, 100 basis point, and 200 basis point instantaneous change in interest rates. This approach point instantaneous change in interest rates. This approach requires the re-valuations of bond or bond portofolio for given requires the re-valuations of bond or bond portofolio for given interest rate change scenario and is reffered to as the full interest rate change scenario and is reffered to as the full valuation approach. It is sometimes reffered to as scenario valuation approach. It is sometimes reffered to as scenario analysis because it involves assessing the exposure to interest analysis because it involves assessing the exposure to interest rate change scenarios. rate change scenarios. 2. Price volatility characteristic of bonds Price of volatility Bonds: Price of volatility Bonds: 2.1 Price volatility characteristics of Option free Bonds 2.1 Price volatility characteristics of Option free Bonds A fundamental characteristic of an option free bond is that the A fundamental characteristic of an option free bond is that the price of the bond change in the opposite direction to a change price of the bond change in the opposite direction to a change in the Bond yield. in the Bond yield.

5. Price volatility characteristic of bonds (cont’) The shape of the price/yield relationship reflects for any The shape of the price/yield relationship reflects for any option option free bond is referred to as convex. This option option free bond is referred to as convex. This price/yield relationship reflects an instantaneous change in the price/yield relationship reflects an instantaneous change in the required yield. required yield. The price sensitivity of a bond to changes in the yield can be The price sensitivity of a bond to changes in the yield can be measured in terms of the dollar price or the precentage price measured in terms of the dollar price or the precentage price change. change. 2.2 Price volatility of bonds with embedded options 2.2 Price volatility of bonds with embedded options The most common types of embedded options are call ( or The most common types of embedded options are call ( or prepay) options and put option. prepay) options and put option. As interest rates in the market decline, the issuer may call or As interest rates in the market decline, the issuer may call or prepay the debt obligation prior to the scheduled principal prepay the debt obligation prior to the scheduled principal payment date. Put option gives the investor the right to payment date. Put option gives the investor the right to require the issuer to puchase the bond at a specified price require the issuer to puchase the bond at a specified price 2.2.1 Bonds with Call and prepay Options 2.2.1 Bonds with Call and prepay Options When the prevailing market yield for comparable bonds When the prevailing market yield for comparable bonds is higher than the coupon rate on callable bond, it is is higher than the coupon rate on callable bond, it is unlikely that the issuer will call the issue. unlikely that the issuer will call the issue.

6. Bonds with Call and prepay Options (cont’) If yields in the market decline, the concern is that If yields in the market decline, the concern is that the issuer will call the bond. The issuer won’t the issuer will call the bond. The issuer won’t necessarily exercise the call option as soon as the necessarily exercise the call option as soon as the market yield drops below the coupon rate. Yet, the market yield drops below the coupon rate. Yet, the value of embedded call option increases as yields value of embedded call option increases as yields approach the coupon rate from higher yield levels. approach the coupon rate from higher yield levels. The very important charcteristic of callable The very important charcteristic of callable bond,- that its price appretiation is less than its bond,- that its price appretiation is less than its price decline when rates change by a large number price decline when rates change by a large number of basic points- is referred to as negative of basic points- is referred to as negative convexity. convexity. When yield are high (relative to the issue’s coupon When yield are high (relative to the issue’s coupon rate) the Bond exihibits the same price/yield rate) the Bond exihibits the same price/yield relationship as an option-free bond; there for at relationship as an option-free bond; there for at high yield level it also has the characteristic that high yield level it also has the characteristic that the gain is greater than the loss. Because market the gain is greater than the loss. Because market have referred to shape the price/yield relationship have referred to shape the price/yield relationship

7. Bonds with Call and prepay Options (cont’) as negative convexity, market participants refer for an as negative convexity, market participants refer for an option free bond as positive convexity. option free bond as positive convexity. Thus, a callable bond exhibits negative convexity at Thus, a callable bond exhibits negative convexity at low yield levels and positive convexity at high yield low yield levels and positive convexity at high yield levels levels 2.2.2 Bonds with embedded Put options 2.2.2 Bonds with embedded Put options Putable bonds may be reedemed by the bond holder Putable bonds may be reedemed by the bond holder on the dates and at put price specified in the on the dates and at put price specified in the indenture. indenture. Typicly, the put price is par value. The advantage to Typicly, the put price is par value. The advantage to investor is that if yields rice such that the bond’s value investor is that if yields rice such that the bond’s value falls below the put price, the investor will exercise the falls below the put price, the investor will exercise the put option. If the put price is par value, this means put option. If the put price is par value, this means that if market yields rise above the coupon rate, the that if market yields rise above the coupon rate, the bond’s value will fall below par and the investor will bond’s value will fall below par and the investor will exercise the put option. exercise the put option. At low yield levels (low relative to issue’s coupon At low yield levels (low relative to issue’s coupon rate), the price of the putable bond is basically the rate), the price of the putable bond is basically the same as the price of the putable is less than that for same as the price of the putable is less than that for an option free bond. an option free bond.

8. Bonds with embedded Put options (cont’) As rates rise, the price of the putable bond declines, As rates rise, the price of the putable bond declines, but the price decline is less than that for an option free but the price decline is less than that for an option free bond. bond. When yields rise to a level where the bond’s price When yields rise to a level where the bond’s price would fall below the put price, the price at levels is the would fall below the put price, the price at levels is the put price. put price. 3. Duration. Duration is a measure of the approximate price sensitivity of a bond to interest rate changes. Duration is a measure of the approximate price sensitivity of a bond to interest rate changes. Specifically, it is the approximate precentage change in price for a 100 basis point change in rate. Specifically, it is the approximate precentage change in price for a 100 basis point change in rate. To improve the approximate provided by duration, an adjusment To improve the approximate provided by duration, an adjusment for “convexity” can be made. Hence, using duration combined for “convexity” can be made. Hence, using duration combined with convexity to estimate the precentage price change of a bond with convexity to estimate the precentage price change of a bond caused by changes in interest rates is called duration/convexity caused by changes in interest rates is called duration/convexity approach. approach.

9. Duration (cont’) Dutration of a bond is estimate as follows: price if yield decline – price if yield rise price if yield decline – price if yield rise 2(initial price) (change in yield in decimal) 2(initial price) (change in yield in decimal) If we let : ∆Y = change in yield in decimal ∆Y = change in yield in decimal V o = initial price V o = initial price V―= price if yield decline by Y V―= price if yield decline by Y V+= price if yield increase by Y V+= price if yield increase by Y DURATION = V― - V+ DURATION = V― - V+ 2(V o ) (∆Y) 2(V o ) (∆Y) Example: consider a 9% coupon for 20 year option free bond selling Example: consider a 9% coupon for 20 year option free bond selling at 134.6722 to yield 6%. Let’s change the yield down and up by 20 at 134.6722 to yield 6%. Let’s change the yield down and up by 20 basis points and determine what the new prices will be for the basis points and determine what the new prices will be for the numerator. If the yield decresed by 20 basis points, the price would numerator. If the yield decresed by 20 basis points, the price would decrese to 131.8439 decrese to 131.8439

10. ∆Y = 0.002 ∆Y = 0.002 V o = 134.6722 V o = 134.6722 V―= 137.5888 V―= 137.5888 V+= 131.8439 V+= 131.8439 DURATION = 137.5888 - 131.8439 = 10.66 DURATION = 137.5888 - 131.8439 = 10.66 2x(134.6722)x(0.002) 2x(134.6722)x(0.002) It means that a duration of 10.66 the approximate change in price for this bond is 10.66% for a 100 basis point change in rates 4. Convexity adjusment The duration measure indicates that regardless of whether The duration measure indicates that regardless of whether interest rate increase or decrease, the approximate precentage is interest rate increase or decrease, the approximate precentage is the same. the same. The formula for convexity adjusment to precentage price change is The formula for convexity adjusment to precentage price change is Convexity adjusment to precentage price change = C x (∆Y) 2 x100

11. Convexity adjusment (cont’) Where Y = the change in yield for which the precentage price change is sought and C = V+ + V― - 2Vo C = V+ + V― - 2Vo 2V o ( ∆Y) 2V o ( ∆Y) Example: For our hypothetical 9% 20 year bond selling to yield 6%, for a 20 basis point change in yield (∆Y = 0.002) : C = 131.8439+137.5888-2 (134.6722) = 81.95 C = 131.8439+137.5888-2 (134.6722) = 81.95 2 (134.6722) (0.002) 2 2 (134.6722) (0.002) 2