Stocks, Bonds, T-bills and Inflation Hedging

Transcription

1 Stocks, Bonds, T-bills and Inflation Hedging Laura Spierdijk Zaghum Umar August 31, 2011 Abstract This paper analyzes the inflation hedging capacity of stocks, bonds and T-bills. We employ four different methods of measuring the inflation hedging capacity. We utilize total return indices for the aggregate and various niche market segments of these assets. The overall sample period for this study is We analyze the hedging potential for investment horizons ranging from 1-month up to 10-year. We document positive inflation hedging characteristics of various stock and T-bill total return indices for both short and long term investment horizons. We do not find any evidence of positive hedging capacity of bonds. Keywords: inflation hedging, investment horizon, Fisher effect, stocks, bonds, bills JEL classification: G11, G14, E44 Laura Spierdijk is affiliated to University of Groningen and Netspar. Address: University of Groningen, Faculty of Economics & Business, Department of Economics, Econometrics, & Business, P.O. Box 800, NL-9700 AV Groningen, The Netherlands. Zaghum Umar (corresponding author) is affiliated to University of Groningen and Netspar. Address: University of Groningen, Faculty of Economics & Business, Department of Economics, Econometrics, P.O. Box 800, NL-9700 AV Groningen, The Netherlands.

2 1 Introduction One of the main functions of money is its role as a stable store of value. This function is adversely affected by an increase in general price levels (decrease in purchasing power) or inflation. From a rational investor s perspective, an investment should not only yield the highest possible return but should also act as a stable store of value. For instance, for institutional investors such as pension funds, a steady stream of returns matching their long term liabilities is of utmost importance. These liabilities are often indexed to inflation and thus having their portfolio returns immunized against the risk of inflation is one of the investment objectives. Traditional asset classes such as stocks, bonds and T-bills have always allured investors in realizing diverse investment objectives, such as, risk free nominal returns (government bonds and bills), higher yields (stocks), portfolio diversification and hedging. Another attractive attribute of the traditional asset classes is the availability of an extensive list of investment alternatives, for instance, an investor can invest in bonds of various maturities, risk ratings and market segments. Equally important is the ease of trading, due to high trading volume, thereby making them more liquid as compared to other investments such as real estate, physical commodities etc. These attractive properties of the traditional assets make them an important ingredient of any investor s portfolio, whether it s an individual investor or an institutional investor. In view of the foregoing, this study is focused on investigating the inflation hedging capacity of traditional asset classes; stocks, government and corporate bonds, and T-bills. Inflation hedging capacity of stocks has been widely documented. In fact, much of the earlier research on the topic of inflation hedging focuses on the hedging capacity of stocks. See e.g. Johnson et al., 1971; Oudet, 1973; Bodie, 1976; Jaffe & Madelker, 1976; Fama & Schwert, 1977; Fama,1981, Gultekin, Traditionally, stocks are considered as a good hedge against inflation because they represent claims on real assets. These claims represent entitlement to the future earnings generated by the firm in the form of dividends and capital gains. According to this view, it is expected that an increase in the general price level will result in a proportionate increase in the future earnings of the firm, thereby compensating for the increase in price levels or inflation. However, most of the existing empirical research reports stocks as a perverse hedge or having some hedging capacity in the long run. See e.g. Johnson et al., 1971; Oudet, 1973; Bodie, 1976; 1

3 Jaffe & Madelker, 1976; Fama & Schwert, 1977; Fama,1981. Irving Fisher (1930) in his seminal work The theory of Interest, often cited as the Fisher hypothesis, postulated a direct link between nominal interest rates and inflation. The Fisher hypothesis delineates that an increase in inflation will be compensated by a corresponding increase in the interest rates, thereby, rendering bonds and T-bills as good hedges against the risk of inflation. An alternative view describes that an increase in inflation results in deterioration in the purchasing power of money lent by the lenders to the borrowers. This deterioration will force the borrowers to demand higher interest rates to compensate for the decrease in purchasing power. The rise in interest rates leads to a decline in the bonds prices, thereby making them less attractive to investors. The empirical evidence documented by different authors show incongruous results on the hedging capacity of bonds and T-bills. See e.g. Fama & Schwert, 1977; Hoevenaars et al., 2008; Attie & Roaches, Therefore, the role of fixed income securities as an inflation hedge is ambiguous. An important aspect of exploring the inflation hedging capacity of an asset is to assess the dynamics of the hedging capacity relative to the varying investment horizons, i.e. the time span over which the hedging capacity is analyzed. Patel and Zeckehauser (1987) estimate that an unexpected inflation of 1% in a particular year results in an increase of expected inflation of 0.43% in the following year and of 1% in later years. In addition, an asset might be a bad hedge in short-term but a relatively better hedge in the long-term or vice versa. For instance, various studies document perverse hedging capacity of stocks in the short run while positive hedging capacity in the long run. See e.g. Hoevenaars et al., 2008; Schotman and Schweizer, 2000; Campbell and Voulteenaho, Therefore, an asset with short term hedging capacity can be employed for short term or tactical asset allocation, while an asset exhibiting long term hedging capacity can be employed for long term or strategic asset allocation. An important question in assessing the inflation hedging properties of an asset is the choice of the econometric method to be employed for gauging the hedging capacity. As mentioned above, the inflation hedging capacity of traditional assets has been analyzed by various authors. However, different authors have used different methods for measuring the inflation hedging capacity. Spierdijk and Umar (2011) provide a detailed review and comparison of the commonly used methods of measuring the inflation hedging capacity of an asset. They document that primarily there 2

4 are five different methods for measuring inflation hedging of an asset. This study will extend the empirical application of Spierdijk and Umar (2011) and will focus on the traditional asset classes. To the best of our knowledge, this study is unique in the sense that it documents a comparative analysis of the inflation hedging capacity of traditional assets measured by different methods. Most of the existing literature on the inflation hedging capacity of traditional asset classes employs data indices representing the aggregate market. Boudoukh et al. (1994), one notable exception, analyze the hedging capacity of stocks at the industry level and report positive hedging capacity for non-cyclical industries. The main motivation for using the sectorial indices is to explore the hedging characteristics of individual sectors (stocks) that are obscured in the aggregate indices due to diversification and cross correlations among various fragments of the aggregate market. This study is different from Boudoukh et al. (1994) in a number of ways. First, as mentioned above, we use various inflation hedging measures instead of relying on a single inflation hedging measure. Second, in addition to stocks, our study explores the hedging capacity of various indices of bonds and T-bills also. Third, we document inflation hedging capacity for a wide range of investment horizons ranging from a short-term horizon of a 1-month to a long-term investment horizon of 10-year. We utilize total return indices data for USA from Thomson Reuters Datastream global equity indices database. The results are calculated for two sample periods each starting from Jan and running until Aug and Aug (the collapse of Lehman Brothers), respectively. Our results show positive hedging capacity of stocks (aggregate index and various sub-indices) for the full sample period, ending Aug. 2010, and perverse hedging capacity (except three sub-indices) for the sub-sample period, ending Aug In order to perform a robustness check, we employ the rolling window and expanding window techniques. We use a rolling window of 10 years for the rolling window technique. For the expanding window, we start with the initial sample period of Jan Jan and expand the sample period by adding an additional month till the end of the sample period in Aug Our results show that a change from negative hedging capacity to positive hedging capacity of stocks was triggered by the collapse of Lehman Brothers in Aug. 2008, which led to negative inflation rates in subsequent three months. Similarly, we employ the same methodology to investigate the hedging capacity of bonds and T-bills for the same sample period. We use Citigroup bond total return indices data with various 3

5 maturities, sectors and ratings. In general, bonds have perverse or statistically insignificant hedging capacity for both sample periods. The deterioration in hedging capacity increases with the maturity of the bond. We utilize the Merrill Lynch 6-month T-bill total returns index and Citigroup 1-year benchmark treasury total return index to asses the hedging capacity of T-bills. We document positive hedging capacity for both T-bill indices. The structure of the paper is as follows. In Section 2 a brief review of the relevant literature is presented. Section 3 describes the methodology followed by the empirical implementation and discussion of results in section 4. In the end, section 5 concludes the paper. 2 Literature review This section gives an overview of the existing academic literature on the topic of inflation hedging for the traditional asset classes. The overview is not exhaustive in nature but is an attempt to cover some of the main research findings in this strand of literature. For the purpose of this section we classify the existing literature into three (overlapping) segments. The first class of literature is focused on studies formulating new methods for measuring the hedging capacity of an asset. Spierdijk and Umar (2011) present a detailed review of the existing methods of measuring the inflation hedging capacity of an asset. The second class refers to the literature that present an empirical implementation of the various methods of inflation hedging. Tables B.6 - B.8 exhibit a list of such studies with details of assets, data utilized and hedging capacity. Our third classification refers to literature documenting a theoretical explanation of the perverse hedging capacity of stocks. We will report these explanations in the remainder of this section. Oudet and Furstenberg (1973) propose that stocks would be a perfect hedge against both transitory and permanent inflation given that they are held upto a suitable investment horizon. The length of the investment horizon depends on the expected stock prices, nominal earnings forecast and the interest rate adjustment mechanism. In a related study, Oudet (1973) revisits the notion of stocks being a good hedge against inflation. In the theoretical part of his study, he elaborates the factors that may render stocks as a good hedge against inflation. He explains that a rise in inflation 4

6 may result in growth in the real earnings due to the lead-lag proposition, i.e. the cost of the production do not increase as fast as the price of the final products, resulting in higher profits. Another reason cited for the positive effect of inflation on firms equity is the debtor-creditor proposition i.e. business firms are net debtors and an increase in inflation results in deterioration of the real value of their obligations. However, the empirical results of his study did not find any evidence of positive inflation hedging capacity of stocks. Modigliani and Cohn (1979) attribute the perverse hedging capacity of stocks to the mispricing of stock markets due to inflation illusion. They argue that the mispricing of stock markets result in undervaluation of stocks during periods of high (positive) inflation. They elaborate that this mispricing is the outcome of two inflation induced errors committed in the valuation of stocks. Firstly, the accounting profits ignore the gains resulting from the decrease in the real value of nominal debt. This implies that the firm could employ more debt to resort to the pre-inflation real capital structure. The additional funds obtained through the acquisition of new debt would allow the firm to repay the interest expense on existing loans while maintaining the same dividend and reinvestment policies. Secondly, the equity earnings should be capitalized using real rather than nominal rates. The discounting of the earnings at the nominal interest rate results in undervaluation of stocks. Fama (1981) documents an alternative hypothesis, known as the proxy hypothesis, and elaborates the underlying role of real activity in the relation between stock returns and inflation. The proxy hypothesis postulates that the negative relation between stock returns and inflation is spurious and owes to the fact that inflation is negatively related to real activity while stock returns have a positive relation with real activity. Geske and Roll (1983) supplement and extend Fama s proxy hypothesis by adding another piece to the puzzle by elaborating the role of fiscal sector in explaining the spurious relation between stock returns and inflation. They argue that corporate and personal taxes are a major source of the government s revenue. A decrease in corporate earnings, and thus in stock prices, adversely affects the fiscal sector in the form of reduced taxes, resulting in fiscal deficit. In order to finance the deficit, the government will either resort to borrowing or printing money, thus triggering inflation. This increase in inflation will induce rational investors to increase the nominal interest rates. The main point of their explanation is a reverse causality between inflation and stock returns i.e. 5

7 stock returns trigger changes in nominal interest rates and expected inflation. Boudoukh et al. (1994) test the Fisher hypothesis for US stocks at the industry level. They group the entire market of stocks into 22 industries and analyze the relation between inflation and stock returns. They document that the hedging capacity of stocks depends upon the cyclical tendency of a particular industry. Their conclude that non-cyclical industries, in general, have better hedging capacity. Campbell and Voulteenaho (2004) analyze the relation between stock prices and inflation by employing the dividend-price ratio model of Campbell and Shiller (1988). They test three alternative explanations of the effect of inflation on the stock s yield or the dividend-price ratio. Firstly, if stocks were claims on real assets, an increase in expected inflation would result in an increase in future earnings of the stocks, thereby rendering no effect on the dividend price ratio, implying positive relation between inflation and stocks. Secondly, the long run growth rate of dividends may be affected by inflation resulting in an increase in the nominal dividend-price ratio. The risk of inflation in turn, could induce investors to increase the equity risk premium and the real discount rate. As per this explanation, inflation is positively related to stock prices. Lastly, they test the Modiglani and Cohn (1979) hypothesis of mispricing driven by inflation illusion. Their findings validate only the Modigliani-Cohn hypothesis that the negative relation between stock prices and inflation is due to mispricing driven by inflation illusion. They document that the mispricing effect tends to diminish with an increase in the investment horizon. 3 Theoretical background and methodology Spierdijk and Umar (2011) report five widely used measures for gauging the inflation hedging capacity of an asset. 1 In order to measure the hedging capacity of traditional asset classes, we adopt the methodology employed in Spierdijk and Umar (2011). In this section, we will give only a summary of the salient features of the aforementioned methodology. The first measure for assessing the hedging capacity of an asset is the Pearson correlation coefficient (denoted by ρ) between inflation and nominal returns on an asset, as shown by Bodie (1982). The hedging capacity increases with the absolute value of the correlation coefficient. A 1 For a detailed review please refer to Spierdijk and Umar (2011). 6

8 positive (negative) value of correlation coefficient implies a long (short) position in that asset. A value of 1 < ρ < 0, ρ = 0 or 0 < ρ < +1 implies that an asset is a perverse hedge, non-hedge or a positive hedge against inflation, respectively. A correlation coefficient of +1(-1) implies an asset is a perfect positive (negative) hedge against inflation. Bodie (1976) documents an alternative method of measuring the hedging capacity of an asset by formulating a hedge ratio (denoted by S) and the associated cost of hedging (denoted by C). Bodie s hedge ratio measures the reduction in the variance of the real return of a risk free nominal bond by adding a risky asset to the portfolio consisting of a nominally risk free bond only. The portfolio with the minimum variance of the real returns is referred to as the global minimum variance (GMV) portfolio. The lower the value of the hedge ratio, the better the hedging capacity of the risky asset. Bodie s hedge ratio can be written in terms of the correlation coefficient as S = 1 - ρ 2. The cost of hedging measures the reduction in the expected real return of the risk free nominal bond by adding the inflation hedging risky asset. The lower the reduction in expected return, the better the hedging capacity of an asset. The third method for gauging the hedging capacity of an asset is the empirical testing of Fisher hypothesis as employed by Fama and Schwert (1977). The Fisher coefficient (denoted by β) is the coefficient of inflation in a regression of nominal asset returns on inflation. A value of β < 0, β = 1 or β > 1 implies that an asset is a perverse, complete or a more than complete hedge against inflation, respectively. For a value of 0 < β < 1, an asset is a partial hedge against inflation. The Fisher coefficient is a scaled version of the correlation coefficient and the scaling factor is the ratio of the volatility of asset return to the volatility of inflation. (Spierdijk and Umar, 2011) The fourth method of inflation hedging is the hedge ratio (denoted by ) introduced by Schotman and Schweizer (2000). Similar to the Fisher coefficient, the Schotman and Schweitzer s hedge ratio is also a scaled version of the correlation coefficient. However, the scaling factor is the reciprocal of the scaling factor of Fisher coefficient. Schotman and Schweitzer s hedge ratio is the coefficient of nominal asset returns in a regression of inflation on nominal asset returns and shows the optimal proportion of risky asset in a portfolio. Spierdijk and Umar (2011) document that the portfolio arising from Schotman and Schweitzer s hedge ratio is the same as the inflation tracking portfolio of Lamont (2001). Spierdijk and Umar (2011) document that choice of a particular measure depends on the con- 7

9 text in which inflation hedging capacity of an asset is assessed. Therefore, the choice of a particular measure varies depending upon the objectives of an inflation hedging investor. To obtain multi-period hedge ratios, an econometric model is a good alternative to the use of overlapping returns (Hodrick, 1992). Spierdijk and Umar (2011) employ a Vector Autoregressive (VAR) model to capture the relation between inflation and asset returns. They use a reduced-form VAR(p, q) model to specify the dynamics between nominal one-period asset returns (r t ) and oneperiod inflation rates (π t ): π t = α 1 + r t = α 2 + p q β 1i r t i + γ 1j π t j + ε 1t ; i=1 p β 2i r t i + j=1 i=1 j=1 q γ 2j π t j + ε 2t. (1) Here (ε 1t ) and (ε 2t ) are mutually and serially uncorrelated error terms, with IE[ε 1t ] = IE[ε 2t ] = 0 and contemporaneous covariance matrix IE[ε 1t ε 2t ] = Σ. Spierdijk and Umar (2011) use standard properties of VAR models to calculate the various hedging measures for investment horizons of 1-month to 10-year. To assess the overall uncertainty of the hedging measures arising due to estimation risk and residual risk, they calculate confidence intervals using the wild bootstrap. 4 Empirical results This section starts with a brief description of the data of asset returns and inflation. Thereafter, we report the values of the different hedging measures for various investment horizons. 4.1 Data We use monthly data for the years and utilize the total return indices for asset returns and inflation, available from the Thomson Reuters Datastream database. Total return indices incorporate factors such as capital gains, dividends and coupon payments into the overall return of an asset. We utilize monthly inflation rates based on the seasonally corrected US all urban consumer price index (CPI) 2 and use the 1-month compounded rate on a 3-month T-bill as the nominal 2 The CPI series has been downloaded from Thomson Reuters Datastream, where it is named USCONPRCE. 8

10 interest rate. As discussed in the literature review, stocks are the most widely researched asset class in the field of inflation hedging. The stocks returns used in most of the existing studies are calculated from an index representing the aggregate market, for instance, the S&P500 or Dow Jones Industrial Average index. However, in addition to the aggregate market index, there are sub-indices representing certain niche segments of the whole market. An aggregate equity index is a diversified portfolio of almost all the sectors of an economy and is quite heterogeneous in composition. This heterogeneity results in suppression of certain industry specific trends which are otherwise evident in a relatively homogeneous portfolio of an industry specific index. Figure 8 in Appendix A exhibits the yearly return of the aggregate market equity index along with various industrial equity sub-indices of the Thomson Reuters Datastream database for the period The return of each of the sub-indices varies considerably from the aggregate market index in terms of magnitude, volatility and trend. For instance, the return on the aggregate market index declined in / , however, the oil and gas sector showed an increase in return for the same years. We employ various equity indices available in Thomson Reuters Datastream database and asses the inflation hedging potential for each of these sectorial indices. Please refer to Section A.1 for details of the stocks data utilized in this study. There is a wide array of investment options available for investing in fixed income securities, bonds and T-bills, that can be classified in terms of risk rating, maturities and issuer. From an inflation hedging perspective, a shorter maturity bond reflects the expectations of market participants regarding interest rate and inflation in the short run, while a longer maturity bond gives an indication of these expectations in the long run. Similar to the equity indices, there is a wide array of bond indices ranging from representing an aggregate market index to specific sectorial sub-indices. We employ various Citigroup indices to analyze the hedging capacity of bonds and T-bills. In addition, we use the total returns index of BofA Merrill Lynch U.S. 6-month T-bills because the Citigroup indices do not provide data for maturities less than 1-year. Section A.2 provide details of the various bonds and T-bills indices used in this study. The upper panel of Table 1 provides sample statistics on monthly inflation rates, nominal yields on the 3-month T-bills, nominal returns on the Datastream aggregate stock market index, Citigroup aggregate bond market index and Merrill Lynch 6-month T-bill index. The average monthly infla- 9

11 tion rate is 0.24%, with standard deviation 0.27%. The average monthly nominal return on the 3-month T-bill equals 0.40%, with volatility 0.22%. The average monthly nominal return on the stocks, bonds and T-bill index during this period is 0.90%, 0.73% and 0.46%, respectively. The corresponding volatilities are 4.57%, 1.36% and 0.29%. The monthly inflation rate is characterized by a high excess kurtosis, reflecting strong departures from normality. The negative skewness indicates that the majority of the inflation rates lie to the right of the mean. The return on the stock, bonds and T-bills index has a much lower excess kurtosis, but still the departure from normality is substantial. The skewness of stock returns is negative, reflecting a relatively fat left tail. The skewness for bonds and T-bills index is positive, implying a relatively fat right tail. The small excess kurtosis of the monthly yield on the T-bills illustrates a much stronger resemblance to the normal distribution. The positive skewness indicates that the bulk of yields lie to the left of the mean. We also consider the sub-period that ends before the fall of Lehman Brothers and does not contain the last two turbulent years of the recent financial crisis. The lower panel of Table 1 provides sample statistics for the sub-sample period, from which we notice considerable differences in kurtosis and skewness for inflation rate implying that the inflation process has changed significantly due to the financial crisis. Figure 7 exhibits the changing dynamics of the inflation process and stocks over the period Jan Aug VAR model We estimate the VAR model of Equation (1) by means of OLS per equation. We use a lag length of 2 as indicated by Akaike information criterion for all assets. Tables 2, 3 and 4 display the estimation results for aggregate stocks, bonds and T-bill total return indices, respectively. We estimate the VAR model for the full sample period, running from Jan until Aug and for the sub-period spanning the period from Jan until Aug The adjusted R 2 is very low for the stocks and bonds return equation, whereas it is higher for the inflation and T-bill equation. Spierdijk and Umar (2011) document the importance of the divergent time series properties of asset returns and inflation. They explain the impact of asset/inflation volatility on various hedging measures. This result is evident if we examine the contemporaneous covariance matrix Σ corresponding to the model innovations in Equation (1). Table 5 exhibits the variance of various asset 10

12 returns and inflation innovations along with their contemporaneous correlations. The value of the innovation variance of inflation is substantially lower than that for the asset return indices. The value of the innovation variance for stocks returns is substantially higher than for bonds and T- bills returns. The persistence parameter for the T-bill index is highest, whereas it is substantially lower for the stocks index. Overall, Table 5 shows that the stock index, and to a certain extent also the bond index, are highly volatile as compared to the inflation process. 4.3 Estimated hedging measures We calculate the hedging measures for various investment horizons ranging from 1-month to 10- year by implementing the approach described in Section 3. Table 6 exhibits the VAR-based hedging measures along with the corresponding bootstrapped confidence intervals for aggregate stocks, bonds and T-bill total return indices, respectively Stocks The first panel of Table 6 shows that the aggregate stock index exhibits a positive correlation with inflation for all investment horizons. However, the 1-month correlation coefficient is small and statistically insignificant. The 6-month correlation is significantly positive with a value of The value of the correlation coefficient is positive and statistically significant for investment horizons of 6-month and beyond. The patterns exhibited by the Fisher coefficient are similar to the correlation coefficient for all investment horizons. The estimated Fisher coefficient is less than unity and is statistically insignificant for a 1-month investment horizon. The Fisher coefficient is statistically significant and greater than unity for investment horizons of 6-month and beyond. The lower bound of the confidence interval is positive but less than unity for all investment horizons, implying that stocks are a complete hedge against inflation (β =1). 4 According to Bodie s hedge ratio, the aggregate stock index reduces a small part of the real return variance of the risk free asset (3-month T-bills) for investment horizon of 6-month and 3 To calculate the cost of hedging, we take the average k-period T-bills rate in the expression for the cost of hedging. Here we make the simplifying assumption that the k-period T-bill rate is equal to k times the monthly T-bill rate (Spierdijk and Umar, 2010). 4 The lower bounds of confidence intervals should be greater than unity to infer that stocks are more than a complete hedge against inflation (β > 1). 11

13 longer. Similarly, Bodie s cost of hedging measure is negative, implying that the expected real return of the optimal portfolio containing both the 3-month T-bills and the stock index is higher than the real yield on the 3-month T-bills only. However, the values for both the hedge ratio and the cost of hedging are statistically insignificant. Similarly, Schotman and Schweitzer s hedge ratio is positive but the values are statistically insignificant. The small value of the hedge ratio implies little weight for stocks in the inflation hedging portfolio. The small magnitude of the hedge ratio owes to the large volatility of stocks relative to the volatility of inflation. The above analysis reflects that the aggregate stock market index does exhibit some positive inflation hedging capacity. However, the statistical significance of the hedging capacity is very low. Another important implication is a remarkable improvement in the hedging capacity, for an increase in the investment horizon from 1-month to 6-month. However, for longer investment horizons there is no substantial improvement in hedging capacity Bonds After analyzing the hedging capacity of the aggregate stock index, we proceed with analyzing the inflation hedging capacity of the aggregate bond index. We utilize the total return index data of the Citigroup overall broad investment grade index. The second panel of Table 6 exhibits the hedging measures for the full sample period ranging from Jan Aug All the hedging measures show perverse hedging capacity of bonds. The 1-month correlation is -0.07, implying perverse hedging capacity of the bonds total return index. The confidence interval shows that the correlation coefficient is significantly negative. For longer investment horizon the correlation coefficient increases in magnitude but is still negative. The confidence intervals imply that the values of the correlation coefficient are not significantly different from zero. Similar to the correlation coefficient, the Fisher coefficient is negative for all investment horizons. The Fisher coefficient has a significantly negative value of for a 1-month investment horizon, thus implying perverse hedging capacity. The Fisher coefficient, although still negative, exhibits an increase for longer investment horizons. The values for longer investment horizons are not significantly different from zero. 12

14 Bodie s hedge ratio also exhibits perverse hedging capacity, with no reduction in the real return variance of the portfolio, for all investment horizons. Bodie s cost of hedging has positive values for all investment horizons, implying that adding the bond index to the portfolio consisting of a nominally risk-free asset only, results in a lower expected return than obtained by the nominally risk free asset alone. The values of Bodie s measures are statistically insignificant for all investment horizons. Similarly, Schotman and Schweitzer s hedge ratio suggests no weight for the aggregate bond index in the portfolio and the values are not significantly different from zero. To conclude, the result of the hedging measures show that the aggregate bond index has perverse inflation hedging capacity for all investment horizons. Most of the values of the hedging measures are statistically insignificant month T-bills To test the hedging capacity of 6-month T-bills, we utilize the BofA Merrill Lynch U.S. 6-month T-bill total return Index. 5 The third panel of Table 6 exhibits the values of the hedging measures along with the corresponding confidence intervals. The correlation coefficient is significantly positive for all investment horizons implying positive inflation hedging capacity. The 1-month correlation coefficient is 0.25, reflecting positive hedging capacity. The 6-month correlation coefficient is 0.48, exhibiting a substantial increase relative to the 1-month correlation. Although the value of the correlation coefficient increases from 6-month to 1-year and from 1-year to 2-year investment horizons, however, the relative increase in the value of the correlation coefficient is not as remarkable as that from 1-month to a 6-month investment horizon. For investment horizons of 3-year and beyond, the relative increase in the value of correlation coefficient is almost negligible. The Fisher coefficient also has significantly positive values for all investment horizons. The value of the Fisher coefficient is less than unity for 1-month and 6-month investment horizons. The confidence bounds for the 6-month investment horizon reflect that we cannot reject the hypothesis of a complete hedge against inflation (β = 1). For investment horizons of 1-year and beyond the Fisher coefficient is greater than unity. However, the confidence bounds reflect that the 6-5 The data for 3-month T-bill index was also available, however, since we use the nominal yield on 3-month T-bills in calculating the Bodie s hedging measures, therefore, we employ the 6-month T-bills total return index. 13

15 month T-bill index is a complete hedge against inflation for these investment horizons. The Fisher coefficient increases with the length of the investment horizon. The highest relative increase in the Fisher coefficient is from an investment horizon of 1-month to 6-month. The values of the Fisher coefficient for the T-bill index are lower than the corresponding values for the stock index, whereas the values of the correlation coefficient are higher. The reason for this phenomenon owes to the low variance of T-bill index compared to the stocks index. Bodie s hedge ratio also exhibits positive hedging capacity and has statistically significant values for all investment horizons. The 6-month T-bill index reduces the real return variance of the nominal 3-month T-bill upto 6% for a 1-month investment horizon. The reduction in real return variance increases substantially for 6-month, 1-year and 2-year investment horizons to 23%, 32% and 39%, respectively. The reduction in the real return variance increases with the investment horizon and has a maximum reduction of 45% for a 10-year investment horizon. Bodie s cost of hedging measure exhibit negative but statistically insignificant values. Schotman and Schweitzer s hedge ratio exhibits statistically significant inflation hedging capacity for the 6-month T-bill index for all investment horizons. The hedge ratio for a 1-month investment horizon exhibits a weight of 19%, for the 6-month T-bill index in the inflation hedging portfolio. The weight of 6-month T-bill index in the inflation hedging portfolio increases to 25% for 6-month and 1-year investment horizons. The value of the hedge ratio for longer investment horizons is slightly higher at 26% year T-bills In this section, we report the results for the hedging capacity of T-bills with a maturity of 1-year. We use the Citigroup USBIG Treasury benchmark 1-year total return index. The fourth panel of Table 6 exhibits the hedging measures for various investment horizons. In general, all the hedging measures depict positive inflation hedging capacity and the hedging capacity improves with an increase in the investment horizon. The correlation coefficient is significantly positive for all investment horizons. The 1-month correlation is 0.14 and increases substantially to 0.33 and 0.38 for 6-month and 1-year investment horizons, respectively. For longer investment horizons, the relative increase in the correlation coefficient is negligible. 14

16 The 1-month, 6-month and 1-year Fisher coefficients are less than unity. However, the upper confidence bounds for 6-month and 1-year investment horizons reflect complete hedging capacity. The 1-year T-bill index is also a complete hedge for longer investment horizons. Bodie s hedge ratio reflects positive hedging capacity for all investment horizons. However, the hedge ratio is significant for investment horizons of 1-year and beyond. The 1-year T-bill index reduces the real return variance of the risk free asset by 14% and 16% for 1-year and 2-year investment horizons, respectively. For longer investment horizon, the reduction in real return variance is upto 17%. Bodie s cost of hedging measure, although negative in magnitude, is statistically insignificant. Schotman and Schweitzer s hedge ratio reflects positive inflation hedging capacity for all investment horizons with statistically significant values. The hedge ratio for a 1-month investment horizon exhibits a weight of 0.08% in the inflation hedging portfolio, which increase to 14%, 15% and 16% for 6-month, 1-year and longer investment horizons, respectively Parameter stability The above sections discussed the hedging capacity of stocks, bonds and T-bills for the full sample period ranging from Jan Aug However, before drawing any meaningful conclusions about the hedging capacity of these assets it is necessary to deal with the issue of parameter stability. We utilized both the rolling window approach and the expanding window approach to analyze the parameter stability over the various fragments of the total sample period. We start with the rolling window approach with a window size of 10 years. In order to select an optimal rolling window, we resort to the technique of eyeballing. Figures 1, 2 and 3 exhibit the rolling window graphs for stocks, bonds and T-bill indices, respectively. The most striking patterns are exhibited by the T-bill index, shown in figure 3. For instance, a closer look at the rolling window graph of the correlation coefficient shows a gradual improvement in the hedging capacity of T-bills during the 90 s till the financial crises of This period is characterized by a healthy growth in US economy and moderate values for inflation and interest rate. An improvement in hedging capacity is exhibited from However, in 2005 an increase in the volatility of the rate of inflation lead to perverse hedging capacity during Subsequently, the decrease in T-bill rates and inflation lead to a positive hedging capacity in 2008 and beyond. 15

17 Next, we continue our analysis by using an expanding window approach. We start with an initial sample of 5 years, ranging from Jan till Jan. 1987, and then progressively increasing our sample size by adding a data point till Aug. 2010, the end of the full sample period. It is pertinent to mention here that the notorious Black Monday also occurred in 1987, therefore this period represent the occurrence of first major financial crisis in our full sample period. Figures 4, 5 and 6 exhibit the expanded window graphs for stocks, bonds and 6-month T-bill indices, respectively. The Datastream aggregate stocks index is the only index that exhibits a significant sign change of the hedging measures, with negative hedging capacity changing into positive hedging capacity in As shown in Figure 7, the collapse of Lehman Brothers led to a substantial decrease in stocks return and inflation rate. The reduction in the inflation rate and stock returns led to the inversion of the sign of hedging measures in The above analysis shows that the collapse of the Lehman Brothers in 2008 has a significant impact on the hedging capacity of aggregate stocks index. Therefore, we extend our analysis and examine the hedging capacity of aggregate stocks index for the sub-period Jan Aug in detail. Table 7 reports the hedging measures for the sub-sample that runs from Jan Aug. 2008, just before the fall of Lehman Brothers. The first and second panel of Table 7 exhibit the hedging measures for the aggregate stocks total return index and aggregate bond total return index, respectively. All the hedging measures based on the subperiod exhibit perverse hedging capacity. In addition, the hedging capacity deteriorates for longer investment horizon, thus negating the hypothesis of improvement in hedging capacity for longer investment horizons. Next, we analyze the parameter stability of the 6-month and 1-year T-bill total return indices. The third and fourth panel of Table 7 exhibit the hedging measures for 6-month and 1-year T- bill total return indices, for the period Jan Aug Qualitatively, the hedging capacity exhibit similar pattern to the full sample period, however, there is a decrease in the numerical values of hedging measures. The results for the subsample period are quite similar to the results for the full sample period with all measures showing positive hedging capacity. Also, the hedging capacity either improves or remains constant with an increase in the length of investment horizon. In absolute terms, the value 6 The Citigroup aggregate bond index exhibit a small and insignificant sign change of the hedging measures during

18 of all hedging measures, except the Fisher coefficient, for the subsample period are lower than the corresponding values for the full sample period. The increase in the value of Fisher coefficient owes to the higher volatility of T-bill total return index in the subsample period. 4.4 Hedging capacity of Stock Sub-indices In this section we analyze the hedging capacity of various stock subindices. We present here the hedging measures and confidence intervals of a few selected indices. The hedging measures for the remaining indices are available on request. For a general overview of the hedging capacity of various indices, please refer to Tables A.1 - A.3. We start our analysis by examining the hedging capacity for the full sample period. The first panel of Table 8 displays the hedging measures for Oil & Gas ICB industry. All the hedging measures exhibit significantly positive hedging capacity. The 1-month correlation is 0.15 and reflect an increase in value to 0.55 and 0.66 for 6-month and 1-year investment horizons, respectively. The improvement in hedging capacity is marginal for 2/3/4-year investment horizons and remains constant for longer investment horizons. The Fisher coefficient for 1-month investment horizon is However, the confidence interval reflects complete hedging capacity. The Fisher coefficient also exhibits a substantial increase for 6-month and 1-year investment horizons with numerical values of and 19.02, respectively. The confidence intervals reflect more than complete hedging capacity (β > 1). The 1-month Bodie s hedge ratio exhibits an insignificant reduction in the real return variance of 2%. Similar to the other two measures, there is a significant increase in the hedging capacity for an investment horizon of 6-month, with a reduction of upto 30% in the real return variance of the risk free asset. The hedging capacity improves for 1-year investment horizon, reflecting a 36% reduction in the real return variance. However, for longer investment horizons the improvement in hedging capacity is marginal. Bodie s cost of hedging measure is negative for all investment horizons, reflecting that the expected return of the portfolio of the inflation hedging and risk free asset is better than the expected return of the risk free asset alone. The improvement in expected return increases substantially for longer investment horizons and has a maximum value of 2.17% for an investment horizon of 10-year. The combined results of Bodie s measures suggest that although the reduction in real return variance is not substantial for investment horizons longer 17

19 than 1-year, yet the improvement in expected return may entice an investor to hold a position in the Oil & Gas total return index for longer investment horizons. Schotman and Schweitzer hedge ratio is very small in magnitude, primarily due to the large volatility of stock returns. Utilities, Basic Materials and Industries are the other ICB industry sub-indices, reported in Table 8, having significantly positive inflation hedging capacity. The pattern of the inflation hedging measures is similar to that of the Oil & Gas index. The other six ICB industry indices also show similar inflation hedging patterns, however, the values of the hedging measures for these indices are statistically insignificant. For an overview of the hedging capacity of the remaining subindices, please refer to the penultimate column of Tables A.1 - A.3. Similar to the aggregate stock return index, we analyzed the hedging capacity of the subindices for the subsample period of Jan Aug At the ICB industry level Basic Materials, Finance, Industries, Health Care, Consumer services, Consumer goods, Technology and Telecommunication exhibit negative hedging capacity with statistically significant values. All the hedging measures suggest that the hedging capacity deteriorates with an increase in the investment horizon. Although, the hedging measures for Oil & Gas and Utilities suggest some inflation hedging capacity, however, the values for these industries are statistically insignificant. We extend our analysis to examine the hedging capacity of the stock sub-indices at a further niche level. We find that most of the sub-indices have negative hedging capacity or partial hedging capacity with statistically insignificant results. The correlation and Fisher coefficient for Marine Transportation; Gas, Water and Multi-Utilities; and Gas Distribution reflect significantly positive hedging capacity. Table 9 exhibits the hedging measures for these sub-indices for various investment horizons. Bodie s measures and Schotman and Schweitzer s measure reflect statistically insignificant hedging capacity. In general, the hedging capacity for these 3 sub-indices improves substantially from 1-month to 6-month investment horizon. For longer investment horizons hedging capacity does not reflect any substantial improvement. 4.5 Hedging capacity of Bonds Sub-indices Tables A.4 and A.5 report the hedging capacity of various bond subindices analyzed in this study. In general, the bond indices have either perverse hedging capacity or a partial hedging 18

20 capacity with statistically insignificant results for both the full sample and sub-sample periods. In general, the hedging capacity is inversely related to the maturity of the bond index, i.e, the hedging capacity is higher for short maturities and vice versa. The economic significance of these results is that the short maturities allow the prices of these securities to adjust more quickly to the changes in inflation dynamics, whereas the same is not possible for longer maturity bonds. 4.6 Discussion A large part of the academic literature on the topic of inflation hedging is focused on the hedging capacity of stocks. Historically, stocks are considered as good hedges against inflation because they are claims on real assets. However, the empirical results documented by various authors show perverse hedging capacity. As discussed in Section 2 and Tables B.6 - B.8, several authors have put forward various explanations for this empirical contradiction. In the following paragraphs we present a comparison of our results with the existing literature. We find evidence of positive hedging capacity of the aggregate stock market total return index for the full sample period ranging from Jan Aug. 2010, for investment horizons of 6-month to 10-year. As mentioned above, most of the existing literature report stocks as a perverse hedge against inflation, except a few studies documenting positive hedging characteristics in the long run. 7 We find positive hedging capacity of the aggregate stock index for both short-term and medium to long-term investment horizons. A striking pattern in our result is the improvement in hedging capacity from 1-month to 6-month investment horizon and a relatively constant hedging capacity for investment horizons of 2-year and beyond. The reason for perverse hedging capacity at 1-month investment horizon may be attributed to the fact that the level of inflation (CPI) is generally announced after a lag of 15 days. Therefore, the true impact of inflation may not be reflected in stock returns. We also analyze the hedging capacity of stocks at sectorial level and calculate the hedging measures for various sub-indices. We find positive inflation hedging capacity of various sub-indices. As mentioned above, Boudoukh et al. (1994) report that the stocks of the non-cyclical sectors have positive inflation hedging attributes. However, our results show that cyclical sectors such as Oil & Gas and Industries exhibit positive inflation hedging attributes. The pattern of the inflation hedging 7 See for instance, Modigliani and Cohn (1979), Schotman and Schweitzer (2000), Hoevenaars et al (2008). 19