BOND PRICE VOLATILITY. PRICE YIELD PRICE YIELD RELATIONSHIP CONVEX SHAPE

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Transcript of BOND PRICE VOLATILITY. PRICE YIELD PRICE YIELD RELATIONSHIP CONVEX SHAPE

  • BOND PRICE VOLATILITY

  • PRICEYIELDPRICE YIELD RELATIONSHIPCONVEX SHAPE

  • WHAT IS VOLATILITY ?Volatility, a statistic similar to standard deviation, measures the uncertainty of the annualised underlying asset return.

    More precisely, volatility is the annualized standard deviation of the natural logarithm of the underlying asset return.

  • PROPERTY 1 : THE PERCENTAGE CHANGE IN THE PRICE OF THE BOND IS NOT THE SAME FOR ALL BONDS (NOT LINEAR) PROPERTY 2 : FOR A VERY SMALL CHANGE IN THE YIELD, THE PERCENTAGE PRICE CHANGE OF THE BOND IS ROUGHLY THE SAME.PROPERTY 3: FOR A LARGE CHANGE IN THE YIELD, THE PERCENTAGE PRICE CHANGE IS NOT THE SAME FOR AN INCREASE AS IT IS FOR A DECREASE. (Handout)PROPERTY 4: FOR A GIVEN LARGE CHANGE IN BASIS POINTS, THE PERCENTAGE INCREASE IN PRICE IS GREATER THAN THE PERCENTAGE DECREASE IN PRICE.

  • COMPONENTS OF A BONDTHAT AFFECTS ITS VOLATILITYCOUPON RATETERM TO MATURITY

  • MEASURES OF BONDPRICE VOLATILITYINTEREST RATE SENSITIVITY OF A BOND

  • MONEY MANAGERS, ARBITRAGEURS AND TRADERS NEED TO HAVE A WAY TO MEASURE A BONDS PRICE VOLATILITY TO IMPLEMENTHEDGING AND TRADING STRATEGIES.PRICE VALUEOF A BASIS POINTYIELD VALUEOF A PRICE CHANGEDURATION3 techniques

  • PRICE VALUE OF BASIS POINTCHANGE IN PRICE OF THE BONDIF YIELD BY 1BP(DOLLAR PRICE CHANGE NOT %)FROM THE HANDOUT (#3), YOU CAN NOTICE THERE IS NO GREAT CHANGE FOR ANY BOND WITH SUCH AN INCREMENTAL MOVE IN RATES.(1BP = 0.01 %)P63 OF OBLI

  • YIELD VALUE OF A PRICE CHANGECALCULATE THE YTM OF THE BOND IF THE BOND DECREASES BY X DOLLARS.YIELD VALUE = NEW YIELD - THE OLD YIELDYIELD VALUE OF THE PRICE CHANGE

  • STOCKSBETABONDSDURATIONOPTIONSDELTASensitivity analysis

  • DURATIONDURATION IS A MEASURE OF SENSITIVITY OF A BONDS MARKETPRICE TAKING INTO CONSIDERATION ITS COUPON AND TERM TOMATURITY.

    (A ZERO-COUPON BOND THAT MATURES IN n YEARS HAS A DURATION OF n YEARS)MACAULEY DURATIONMODIFIED DURATION

  • WEIGHTED PRESENT VALUE OF CASH FLOWSDURATION mac= ----------------------------------------------------------------- PRESENT VALUE OF CASH FLOWSMACAULEY DURATIONBond Price

  • IIIII1010101010 coupon + principalConsider this 7-year bond 10% coupon priced at 95 with a YTM of 11.06%I10Approx. (10+(5/7)/0.951 year1 year1 year1 year1 year1 year1 year110 WEIGHTED PRESENT VALUE OF CASH FLOWSDURATION = ----------------------------------------------------------------- PRESENT VALUE OF CASH FLOWS (9x1) + (8.11x2) + (7.30x3).(52.77x7)DURATION = ----------------------------------------------------------------- 95Macc. Duration = 5.31

  • What is the Macauley duration of a 20 year zero coupon bond ?20 years !!

  • MODIFIED DURATION = Sensitivity MACAULEY DURATION 1 + yY = required yieldAPPROXIMATE PERCENTAGE CHANGE IN PRICEFOR A GIVEN CHANGE IN YIELD

  • SENSITIVITY Mc CauleyDURATIONSENSITIVITY = - ---------------------1 + y

    See page 78 for an approximate calculation of duration

  • DurationS = - ------------ ( 1 + y )Measure of Sensitivity(modified duration)For every i increase in rate, the sensitivity of the bond willdecrease by S

  • Consider our 7-year bond 10% coupon priced at 95 with a YTM of Macc. Duration = 5.3111.06%Modified duration or Duration = 5.31 / (1 + 0.1106) = 4.78For each 100BP change in rates, the bond will vary by 4.78%

  • WHAT IS THE Modified DURATION OF A ZERO COUPON BOND ?ITS MATURITY---------------------- 1 + y

  • Duration of a Bond PortfolioPortfolio duration = 0.10 x 4 + 0.4 x 7 + 0.3 x 6 + 0.2 x 2 = 5.4

    BONDMKT VALUEWEIGHTMODIFIEDDURATIONA$10 mil.0.104B$40 mil.0.47C$30 mil.0.36D$20 mil.0.22total100 mil.1

  • What if rates increase by 50BP?Portfolio decreases by 0.5 x 5.40 = 2.70% using duration 5.40

    BONDMKT VALUEWEIGHTMODIFIEDDURATIONA$10 mil.0.104B$40 mil.0.47C$30 mil.0.36D$20 mil.0.22total100 mil.1

  • CONVEXITYPRICEYIELDCONVEX SHAPEDURATION (linear)YPPD+CYXXD+CPDXD

  • CONVEXITY ContdConvexity is a measure of the curvature of the price/yield relationship.

    Mathematically, convexity is the second derivative of price with respect to yield divided by price. (duration is first)

  • Consider our 7-year bond 10% coupon priced at 95 with a YTM of 11.06%Modified duration or Duration = 5.31 / (1 + 0.1106) = 4.78Its convexity is at 31.08 Using duration and convexity by what % would this bond change byIf rates decreased by 200BP?4.78 x 2 + ( (31.08) (0.02)2) x 100) = 10.18%

  • APPROXIMATING PERCENTAGE PRICE CHANGE USING DUARTION AND CONVEXITYConsider a 25-year 6% bond selling to yield 9%.The modified duration for this bond is 10.62 and its convexity 183 What is the approximate percentage price change if yield rise by 200 basis points ?DurationDown 10.62 x 2 = - 21.24%Convexity( (convexity)(r)2) x 100)= +3.66%Estimated % price change due to duration and convexity = -17.58%

  • You always ADD convexity to duration , never subtract it. Consider a 25-year 6% bond selling to yield 9%.The modified duration for this bond is 10.62 and its convexity 183 What is the approximate percentage price change if yield decreaseby 200 basis points ?Durationup 10.62 x 2 = + 21.24%Convexity (convexity)(r)2 = +3.66%Estimated % price change due to duration and convexity = +24.90%

  • THANK YOU AND HAVE A GOOD WEEK

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