The sixth property was demonstrated by Homer and Liebowitz Firstly, firms and especially financial intermediaries have tied up huge amounts of capital in fixed income instruments.

The next part will discuss strengths and weaknesses of duration analysis. Fooladi describes that banks may take modest bets by setting a duration gap or set the duration gap close to zero.

Hence, OAS is model dependent and incorporates volatility like variable interest rates or prepayment rates. Furthermore, the term "partial durations" or "key rate durations" is a vector of durations, where each duration is only valid for a limited maturity range.

Nevertheless, his proof is generally acknowledged. However, the shape of the yield curve fluctuates over the business cycle and consequently this expected slope change has to be considered. A main function of banks is to provide maturity transformation.

Moreover, it Duration and essay immunization, hedging and Duration Gap Analysis as practical applications. However, duration analysis is an adaptable framework and used carefully, a tool to get a first impression of interest-rate risk.

The proof that duration is an elasticity was provided by Hicks in The change in an asset price due to change in interest rates can be calculated by: When the portfolio duration equals the length of the planning period, the portfolio is immunized and the realized return will not fall below the promised rate of return.

Hence, proper hedging of these instruments becomes important. Secondly, the key figure duration provides an intuitive approach to educate potential customers.

The next paragraph considers two applications of duration in risk management: Bierwag and Fooladi specify that banks use off-balance-sheet securities like interest rate futures, options and swaps to reduce adjustment time and to save costs.

It is calculated by regressing price movements of the asset versus some market benchmark. These include bonds partly with optional characteristics or recent financial innovations like swaps, interest rate options or floaters. As one can see in Figure Further problems involve uncertainty over the proportion of assets and liabilities.

Fourthly, interest rate risk, which is measured by the sensitivity of bond prices to changes in yields, is less than proportional to bond maturity. Hence, banks usually have short-term liabilities and long-term assets. The standard definition according to Macaulay is: Ho states that practitioners tie duration and vega measures which specify the sensitivities to the shift in the swap curve and the volatility surface, respectively.

To put it in a nutshell, with increasing complexity of securities, myriad extensions have been added to the former duration analysis founded by Macaulay to handle the occurring risks.

To overcome these weaknesses, Mishkin and Eakins mentions more sophisticated approaches such as scenario analysis and value-at-risk analysis and convexity which is a second-order Taylor series approximation and can be used as a correction measure.

Ingersoll, Skelton, Weil, stated that the key figure Duration can be interpreted as an attempt to quantify this qualitative observations through a single and numerical measure.

This leads to a better understanding of financial instruments in general and how they behave when interest rates change. Fooladi describes that the realized rate of return encompass interest accumulated from reinvestment of coupon income and the capital gain or loss at the end of the planning period when the portfolio is sold.

Furthermore, different duration measures face different assumptions about slope and shape of the yield curve or the stochastic process driving interest rates.

The weights are the current market value of each security. Hedging and immunization for a portfolio and Duration Gap Analysis. In his approach volatility risk is measured by the value sensitivity of an option to the change in the implied volatility function at the key rate points on the curve.

The second equation shows how banks can adjust their duration gap by shifting weights on assets or liabilities. Paroush and Prisman strengthen this assumption and show that convexity second-order can be more important than the duration first order. Redington derived the duration independently and used it for portfolio immunization.

It is based on the additivity of single durations. Bodie, Kane, Marcus Empirical studies and Figure The Duration and essay "Modified duration" is calculated by the formula: The duration concepts has its origins in the work of MacaulaySamuelsonHicks and Redington The second described application is Duration Gap Analysis which is an extension to the immunization approach, because it includes liabilities.

Occurring large shocks to interest rates, riskless arbitrage became possible, but on the practical side the riskless-arbitrage argument seemed hypothetical.The strengths and limitations of duration analysis Published: November 27, As stated by the US Federal Reserve, interest rate risk impacts on a various range of stakeholders, and hence financial actors are interested in quantifying its impact.

Free duration papers, essays, and research papers. Definitions of Words Relating to the Sea - Definitions of Words Relating to the Sea The Wave Machine The wave machine is a simulator that will allow you to create an ocean wave and determine its height.

Graduate School of Business Administration University of Virginia UVA-F Duration and Convexity The price of a bond is a function of the promised payments and the market required rate of return. The Duration is one of the most popular assignments among students' documents.

If you are stuck with writing or missing ideas, scroll down and find inspiration in the best samples. Duration is quite a rare and popular topic for writing an essay, but it certainly is in our database.

The modified duration of a bond portfolio is equal to the weighted average modified duration of the individual bonds, the weights being the present values of the bonds. Therefore, the modified duration of this bond portfolio is. Free Essay: California Debt and Investment Advisory Commission Duration Basics Introduction Duration is a term used by fixed-income investors, financial.

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