How do people quantify interest rate risk in fixed income markets? Does the elasticity of bond price against market yield to maturity make sense?

The opposite of the elasticity of a bond price with respect to yield to maturity is called the modified duration of the bond.Modified duration cannot be used to quantify interest rate risk in a fixed income portfolio. One minor problem is that it doesn’t aggregate, you’re better off using the derivative of bond price with respect to yield because you can add those up. With modified duration you’d have to take the sum weighted by market value and that doesn’t work for derivative securities.One major problem is modified duration only tells you the relation of price volatility to yield volatility, and only for small yield moves. So it ignores credit, funding, liquidity, volatility, optionality and other risks; and even for price risk it only gives you a conversion factor for translating yield risk to price risk, not an absolute measure of risk.The other major problem is that you’re taking the derivative of the price of each security on its own yield. You’re answering the question, What will happen to the price of my portfolio if all yields to maturity move by the same amount? But that’s not a realistic scenario, and it can miss most of the risk.If your portfolio consists only of long position in bonds of similar credit quality and maturity, then portfolio modified duration captures most of the first order price volatility. But for general fixed-income portfolios, most of the price risk can arise from yields changing relative to one another.For example, consider a portfolio that buys one ten-year bond and shorts enough one-year bonds (say 8, but the exact number depends on interest rates) such that the net modified duration is zero. That is by no means a riskless portfolio.There are several approaches for quantifying risk in a fixed-income portfolio depending on the type of portfolio. You can model interest rate moves explicitly and include terms for other risks. One simple model is to decompose the yield curve into principle components and estimate the volatility of each component and the portfolio’s exposure to it. Or you can bootstrap a forward volatility surface.

A Data Entry Operator has been asked to fill 1000 forms. He fills 50 forms by the end of half-an hour, when he is joined by another steno who fills forms at the rate of 90 an hour. The entire work will be carried out in how many hours?

Work done by 1st person = 100 forms per hourWork done by 2nd person = 90 forms per hourSo, total work in 1 hour would be = 190 forms per hourWork done in 5hours = 190* 5 = 950Now, remaining work is only 50 formsIn 1 hour or 60minutes, 190 forms are filled and 50 forms will be filled in = 60/190 * 50 = 15.7minutes or 16minutes (approximaty)Total time = 5hours 16minutes

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Hi everyone in this video we're going to be covering the yellowest explain the reinvestment assumption implicit in calculating the yield to maturity and describe the factors that affect reinvestment risk now for this video you would need a couple of prerequisites one what are the sources of income for a bond — what is reinvestment income in a bond and three what is ATM this.l OS is extremely important I do expect to see at least one or even two questions from this in the final exam for any bond the white TM is that discount rate that equates the present value of all future cash flows to the bonds market price to explain what is the reinvestment assumption I'm going to take the help of an example consider our 20-year Treasury bond purchased at par with a face value of 100 and a 7 percent coupon rate paid semi-annually the reason that paid semi-annually is in a parenthesis because Treasury bonds have coupons paid semi-annually, and you are expected to know this in the exam every six mo

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How do people quantify interest rate risk in fixed income markets? Does the elasticity of bond price against market yield to maturity make sense?
The opposite of the elasticity of a bond price with respect to yield to maturity is called the “modified duration” of the bond.Modified duration cannot be used to quantify interest rate risk in a fixed income portfolio. One minor problem is that it doesn’t aggregate, you’re better off using the derivative of bond price with respect to yield because you can add those up. With modified duration you’d have to take the sum weighted by market value and that doesn’t work for derivative securities.One major problem is modified duration only tells you the relation of price volatility to yield volatility, and only for small yield moves. So it ignores credit, funding, liquidity, volatility, optionality and other risks; and even for price risk it only gives you a conversion factor for translating yield risk to price risk, not an absolute measure of risk.The other major problem is that you’re taking the derivative of the price of each security on its own yield. You’re answering the question, “What will happen to the price of my portfolio if all yields to maturity move by the same amount?” But that’s not a realistic scenario, and it can miss most of the risk.If your portfolio consists only of long position in bonds of similar credit quality and maturity, then portfolio modified duration captures most of the first order price volatility. But for general fixed-income portfolios, most of the price risk can arise from yields changing relative to one another.For example, consider a portfolio that buys one ten-year bond and shorts enough one-year bonds (say 8, but the exact number depends on interest rates) such that the net modified duration is zero. That is by no means a riskless portfolio.There are several approaches for quantifying risk in a fixed-income portfolio depending on the type of portfolio. You can model interest rate moves explicitly and include terms for other risks. One simple model is to decompose the yield curve into principle components and estimate the volatility of each component and the portfolio’s exposure to it. Or you can bootstrap a forward volatility surface.
A Data Entry Operator has been asked to fill 1000 forms. He fills 50 forms by the end of half-an hour, when he is joined by another steno who fills forms at the rate of 90 an hour. The entire work will be carried out in how many hours?
Work done by 1st person = 100 forms per hourWork done by 2nd person = 90 forms per hourSo, total work in 1 hour would be = 190 forms per hourWork done in 5hours = 190* 5 = 950Now, remaining work is only 50 formsIn 1 hour or 60minutes, 190 forms are filled and 50 forms will be filled in = 60/190 * 50 = 15.7minutes or 16minutes (approximaty)Total time = 5hours 16minutes

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Natwest Frb Form

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