TOPIC 44: TIME-INFLUENCED SECURITY VALUATION CONCEPTS in .NET framework

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TOPIC 44: TIME-INFLUENCED SECURITY VALUATION CONCEPTS
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Note: For present value, future value, and internal rate of return (IRR), see Topic 14 1 Bond duration A Duration is the average time it takes to capture interest and principal repayments It seeks to compare bonds with different coupons and maturities by determining how sensitive the price of each bond is to interest rate changes B Bonds exhibit more price volatility the longer the term to maturity If two bonds have the same coupon, the bond with the greater maturity will have the longer duration Low coupon bonds are generally more volatile than high coupon bonds If two bonds have the same maturity, the bond with the lower coupon will have the longer duration C The process gets a little more complex for a bond with a shorter (longer) maturity and smaller (larger) coupon For bonds with different maturities and coupon rates, using duration is an excellent technique for determining which bond is more volatile to changes in interest rates D The bond with the longer duration will decline more in price with an increase in interest rates; the bond with the longer duration will increase more in price with a decrease in interest rates E To illustrate how duration is determined, consider a 10 percent semiannual three-year bond The current interest rate on similar bonds is 12 percent The bond is currently selling for $95082 The cash ows are as follows: Year 05 10 15 20 25 30 Payment $50 $50 $50 $50 $50 $1,050
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F The duration of a bond is the sum of the present value of cash ows weighted by a time period (t) in which the payment is received All individual present values are summed and then divided by the current price of the bond The following demonstrates this relationship: Solve Present Value (PV) $4717 $4450 $4198 $3960 $3736 $74021
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Period (t) 1 2 3 4 5 6 Sum =
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Interest 6% 6% 6% 6% 6% 6%
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Cash Flow $50 $50 $50 $50 $50 $1,050
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PV t $4717 $9000 $12594 $15840 $18681 $4,44125 $5,04857
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Duration
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$5,04857 $95082
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265 years
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148 - Investment Planning G Because of semiannual compounding: Annual payment and interest rate are divided by 2, the number of payments is multiplied by 2, and duration of 530 is divided by 2 H The duration of 265 years means that the investor collects on average all interest and principal repayment within 265 years Keep in mind that not all payments are received at 265 years Duration represents the weighted average of all payments Therefore, duration is not the sum of all present values (which is the price of the bond) The longer the term to maturity, the more weight put on the calculation I Duration can be precisely de ned as the approximate percentage change in the price of a bond to a small change in interest rates More speci cally, duration is the approximate percentage change in price with a 100 basis point change in interest rates Therefore, duration of 265 means that the price of a bond will change approximately 265 percent with a 100 basis point change in interest rates J For large changes in yield (50 or more basis points), duration tends to underestimate the increase in price that occurs with a decrease in yield, and overestimate the decrease in price that comes with an increase in yield 2 Bond convexity A The price-yield relationship can be represented by a tangent line The tangent line shows the rate of change in price to changes in yield The slope of the tangent line is one basis point The tangent line is strongly related to duration In fact, duration is used interchangeably with a tangent line because both estimate the rate of change in price There is more duration the steeper the tangent line and less duration the atter the tangent line
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B There is an interesting relationship between duration (tangent line) and the approximate change in price The actual price change is greater than the estimated price change when yields decrease; the actual price change is less than the estimated price change when yields increase C Duration becomes less exact with greater changes in yields because the price-yield relationship is not linear, but curved How curved the path actually is depends on the degree of convexity The distance between the tangent line (estimated price) and the curvature of the actual path (actual price) is the error in estimating price based on duration If the degree of convexity is measured, the price of a bond can be estimated with more accuracy D Duration is used to approximate the rst percentage change in price Convexity is used to approximate the second and is added to duration
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Topic 45: Bond and Stock Valuation Methods - 149
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