Inflation-linked bonds

From market observation we know that index-linked bonds can experience considerable volatility in prices, similar to conventional bonds, and therefore, there is an element of volatility in the real yield return of these bonds. Traditional economic theory states that the level of real interest rates is cmistant however, in practice they do vary over time. In addition, there are liquidity and supply and demand factors that affect the market prices of index-linked bonds. In this chapter, we present analytical techniques that can be applied to index-linked bonds, the duration and volatility of index-linked bonds and the concept of the real interest rate term structure. Moreover, we show the valuation of inflation-linked bonds with different cash flow structures and embedded options. 

Therefore, the inflation expectation could be assumed comparing the yield of a conventional bond to the yield of an inflation-linked bond with similar maturity. This average inflation expectation is known as break-even inflation rate and is given by Fisher s equation (6.1) ... 

Therefore, the break-even analysis allows to determine the spread that equals the price of a conventional bond to the one of an inflation-linked bond. This approach assumes a risk-neutral pricing by which an investor treats conventional and inflation-linked bonds the same. Under break-even hypothesis, both bonds have the same nominal yield. Note if the inflation breakeven is greater than expected inflation, for an investor is favorable to buy a conventional bond. Conversely, the inflation-linked bond is more attractive. If inflation breakeven and expectations are equal, the investor bond s choice will be then indifferent. Figure 6.2 shows the trend of UKGGBEIO and UKGGBE20 Index... 

Also the simple difference between the yield of conventional and inflation-linked bonds or yield spread is an indicator for expected inflation. For example, on 18 September 2014 the 10-year UK 0 1/8% inflation-linked 2024 had a money yield of 2.125% and a real yield of -0.410%, assuming an inflation of 2.571%. Differently, the 10-year benchmark, the UK T A% 2023 had a gross... 

To obtain the price of an inflation-linked bond, it is necessary to determine the value of coupon payments and principal repayment. Inflation-linked bonds can be structured with a different cash flow indexation. As noted above, duration, tax treatment and reinvestment risk, are the main factors that affect the instrument design. For instance, index-aimuity bmids that give to the investor a fixed annuity payment and a variable element to compensate the inflation have the shortest duration and the highest reinvestment risk of aU inflation-linked bonds. Conversely, inflation-linked zero-coupon bonds have the highest duration of all inflation-linked bonds and do not have reinvestment risk. In addition, also the tax treatment affects the cash flow structure. In some bond markets, the inflation adjustment on the principal is treated as current income for tax purpose, while in other markets it is not. 

The first step for estimating future streams is to know the expected inflation. To do this, the procedure needs the future trend of index in which the inflation expectation is built. The inflation expectation determined by countries is based on a different basket of products and services. For instance, inflation-linked bonds issued in the United Kingdom or UK index-linked gilts, are linked to the Retail Price Index (RPI) inflation-linked bonds issued in the United States or TIPS are linked to the Consumer Price Index (CPI). Table 6.1 summarizes the key global inflation indices used by the major issuers of inflation-linked bonds. 

Inflation-Linked Bonds with Zero-Coupon Indexation Zero-coupon bonds linked to the inflation do not pay coupons. Therefore, the unique adjustment is made to the principal. These types of bonds offer no... 

Table 6.2 illustrates the cash flow structure of an inflation-linked bond with zero-coupon indexation. 

Inflation-Linked Bonds with Coupon Indexation... 

As noted above for inflation-linked bonds with zero-coupon indexation, the coupon can be adjusted in a similar way ... 

Another structure for inflation-linked bonds is when both, coupons and principal, are linked to the inflation. The value is given by (6.12) ... 

Consider the example in which a hypothetical conventional bond and inflation-linked bond pay an annual coupon of 2%, with a discount rate of 3%. The second one pays coupons and principal linked to the inflation. To understand the effect of the inflation, Figure 6.6 shows the loss of value of a conventional bond compared to an inflation-linked bond. The evidence is that maintaining a flat discount rate, a change of the inflation rate affects only to an inflation-linked bond, increasing its value, while the value of a conventional bond remains unchanged. In reality, over the bond s life, the value of the first one remains unchanged while the value of second one depreciates as the inflation increases. 

Value of a Conventional Bond ------Value of an Inflation-Linked Bond... 

If the price of an inflation-linked bond is 104.95 and the price of a conventional bond is 95.42, the difference of value represents the inflation premium, or 9.53. 

Bond valuation with real cash flows and yields We currently illustrate the pricing of inflation-linked bonds adopting real cash flows. As noted earlier, according to Fisher s theory, the real yield is given by the following equation ... 

In a deflationary environment a conventional bond performs very well, while an inflation-linked bond gives negative returns. Some of inflation-linked bonds include deflation protection.In practice, in the event of deflation, the bondholder will receive at maturity the par value although the redemption value is less than 100. Therefore, the bondholder will obtain at least the par value. Note that the deflation floor applies to the redemption value only leaving coupon payments exposed to the deflation risk. 

Therefore, we propose an example in which we price an inflation-linked bond by using a binomial tree. Conventionally, this type of pricing model is not implemented in the reality, but it allows to understand the impact of the embedded option on bond s value. 

For example, inflation-linked bonds issue in the United States, Italy, France, Sweden and Germany. Note that inflation-linked bonds issue in the United Kingdom does not include deflation protection. 

Therefore, without considering the deflation floor, the value of an inflation-linked bond is equal to 4.83+93.02 = 97.85. 

In other words, the option is valuable when the principal is lower than 100. When the inflation rate drops and the economy is in a hypothetical deflation scenario, the option is in the money. This increases the value of an inflation-linked bond. Note that the probability of a deflation scenario depends on the market sentiment and implied inflation rate between conventional and... 

As described above, inflation-linked bonds allow to save investors from changes in the general level of prices. However, the indexation is not perfect creating a lag between the index prices and the adjustment to the bond cash flows. According to Deacon and Derry (2004) at the end of a bond s life there is no inflation protection, matched with an equal period before the issue in which the inflation compensation is paid. Figure 6.11 shows an example of indexation lag according to Deacon and Derry (2004). 

The Web site associated with this book contains an Excel spreadsheet demonstrating the valuation of inflation-linked bonds, as described in this chapter. The reader may use the spreadsheet to value such bonds using his or her own parameter inputs. 

Considering the example shown in Table A1 of a hypothetical bond with coupons and principal linked to the inflation. We assume a 5-year inflation-linked bond with a 2% annual coupon payment. The expected cash flows, coupons and principal, are discounted with a discount rate of 3%. The valuation is performed by the following steps. 

Diedrich, S., 2011. Inflation-linked bonds not always the best answer to inflation. PAAMCO Research Paper. 

Huber, S., 2014. Inflation-linked bonds - Preserving real purchasing power and diversifying risk. Credit Suisse. 

Kramer, W., 2013. An introduction to inflation-linked bonds. Lazard Asset Management. McCulloch, L, 1971. Measuring the term structure of interest rates. 1. Bus. XLIV, 19-31. McCulloch, L, 1975. The tax-adjusted yield curve. 1. Financ. 30 (3), 811-830. 

Standard Life Investments, Guide to inflation-linked bonds , June 2013. 

What is worthy then of a further investment of cash to purchase this second edition Hopefully the new chapters on asset swap spread relative value, convertible bonds, callable/putable bonds and floating-rate notes will be sufficient justification additionally we have updated the previous chapters on inflation-linked bonds and risky corporate bonds valuation. We have also included Excel spreadsheets that enable the reader to apply the analysis described in the chapters right away to bonds that he or she selects. 

Last, but not least, one sector that is increasingly gaining importance, not only in terms of amounts issued but also in investors interest, is the inflation-linked bond market. Up to this moment the French Tre-sor has been the main issuer of these bonds, although some other treasuries have already issued small amounts in these type of bonds (Greece) or have expressed their desire to do it in the future (Italy). 

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