Price change estimation

Given the initial full price of 104.5673, the euro price change estimated using duration is... 

Consequently, the convexity measure (or just simply convexity as it is referred to by some market participants) that could be reported for this UK strip are 165.35, 330.68, 1.6535, or 3.3068. All of these values are correct, but they mean nothing in isolation. To use them to obtain the convexity adjustment to the price change estimated by duration requires knowing how they are computed so that the correct convexity adjustment formula is used. It is the convexity adjustment that is important—not the convexity measure in isolation. 

YIELD CHANGE PRICE CHANGE ESTIMATE USING PRICE DURATION... 

And the price change estimate based on modified duration is... 

The modified duration of the bond at the initial yield, as seen above, is 7.64498. So the price change estimate using modified duration is... 

The method of correcting for price changes that have occurred in the past when estimating costs for design purposes has been discussed in Chap. 6 (Cost Estimation). As this discussion showed, the history of cost changes in the United States in the recent past has been strongly inflationary. For example, the Marshall and Swift All-Industry Installed-Equipment Cost Index doubled from 273 in 1968 to 545 in 1978. In the ten-year period from 1978 to 1988, the index... 

An effective interest rate of 7.18 percent will cause a doubling of value when compounded for 10 years while a 5 percent rate will give a 63 percent increase in 10 years and a 4 percent rate will give a 48 percent increase in 10 years. Consequently, past history of price changes in the United States would indicate that a rate of inflation of at least 3 percent and perhaps as high as 7 percent can be expected for at least the near future, and this factor should be taken into account in presenting design estimates of cost. 

The sensitivity estimates for the effect of changes in cost factor values on leve lized H2 production and PV electricity prices are estimated by the least squares, linear regression method. The regression results provide an estimate of the effect of unit changes in cost factor values on H2 production and PV electricity prices. The sensitivity results are presented in Table 5, Fig. 4, and Fig. 5. 

The economic analysis of investment alternatives generally entails the estimation of cash flows and the application of some measure of worth, such as net present value or the internal rate of return, in order to make a decision. The estimation of these cash flows requires the estimation of prices, whether they be the price of goods sold to forecast revenues or the estimation of wages to forecast labor costs. Over time these prices change. An increase in price is known as inflation, while a decrease in price is termed deflation. These concepts and their measurement are explained in this chapter. Cash flow analysis methods are revisited under the assumption of price changes, as their effects can be significant (Fleischer 1994). This is especially true when one considers after-tax cash flow analysis, as the effects of depreciation and taxes represent one of the most important aspects of investment analysis (Park and Sharp-Bette 1990). 

Now let ns examine how well duration does in estimating the percentage price change when the yield increases by 200 basis points rather than a 10 basis points. In this case. Ay is eqnal to +0.02. Substitnting into equation (4.2) we have... 

Graphical Depiction of Using Duration to Estimate Price Changes... 

Earlier we used the graph of the price/yield relationship to demonstrate the price volatility properties of bonds. We can use graphs to illustrate what we observed in our examples about how duration estimates the percentage price change, as well as some other noteworthy points. 

We demonstrated this property earlier using a UK gilt principal strip priced to yield 4.435% with a duration of 17.631. For a 10 basis point change in yield, the estimate was accurate for both an increase and decrease in yield. However, for a 200 basis point change in yield the approximate percentage price change was off considerably. 

Mathematically, any function can be estimated by a series of approximations referred to a Taylor series expansion. Each approximation or term of the Taylor series is based on a corresponding derivative. For a bond, duration is the first-term approximation of the price change and is related to the first derivative of the bond s price with respect to a change in the required yield. The convexity measure is the second approximation and related to the second derivative of the bond s price. 

The approximate percentage price change based on duration and the convexity adjustment is found by summing the two estimates. So, for example, if yields change from 4.435% to 5.435%, the estimated percentage price change would be... 

The BPV for other bonds can be found following a similar procedure. If, for example, AF in equation (16.10) is replaced by AP(3i g (i.e., price changes in a cash market bond) the resulting estimate of P will provide an estimate of the BPV of the CMB. 

It should be pointed out that (19.14) clarifies the components that are normally used in estimating the OHR. However, if the specific investor has certain pertinent information that would indicate a price change in a given direction, then it would result in more precision if certain components of (19.14) are used and not all parts. As an example, assume that a price increase is expected at the maturity date. Based on this information we can conclude that the following conditions are fulfilled ... 

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