Macroeconomic Announcements and Investor Beliefs at The Zero Lower Bound

Transcription

1 Macroeconomic Announcements and Investor Beliefs at The Zero Lower Bound Ben Carlston Marcelo Ochoa [Preliminary and Incomplete] Abstract This paper examines empirically the effect of the zero lower bound (ZLB) on the response of investors beliefs to macroeconomic announcements. Using information from options on interest rate swaps, or swaptions, we extract conditional volatility, conditional skewness and conditional kurtosis to capture investors ex-ante uncertainty, views on the likelihood of positive or negative changes in interest rates, and perceived probability of a tail event, respectively. We find that the conditional swap rate moments respond most strongly to macroeconomic news when the economy is at the ZLB. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. All errors are our own. Eberhardt School of Business, University of the Pacific, bcarlston@pacific.edu. Federal Reserve Board of Governors, marcelo.ochoa@frb.gov

2 1 Introduction As investors receive information about economic fundamentals, they process the information and update their expectations of the economy s future growth, inflation, and discount rates. However, the same piece of news can have a different impact on investors beliefs about the economy depending on the regime of monetary policy. Our paper addresses the following question: Has the zero lower bound influenced how investors beliefs about the macroeconomy respond to macroeconomic news? This question is particularly important for several reasons. First, from a policy perspective, it is important to have a better understanding of the behavior of investors beliefs in a period when monetary policy effectiveness is very tightly linked to its ability to manage expectations. Second, our paper sheds light on potential asymmetric or nonlinear effects of information shocks, for example, monetary policy shocks on investor s expectations. As new information about the macroeconomy arrives, investors update their beliefs about the macroeconomy. Finance theory tells us that fixed-income prices should vary with macroeconomic news. We use this reasoning, and make use of daily data on options on swap rates or swaptions, to extract the distribution of swap rates for different maturities and different horizons. In particular, we compute the response to scheduled macroeconomic news of: conditional volatility, which proxy ex-ante investor uncertainty; conditional skewness, which captures the likelihood of (or dislike for) positive or negative changes in interest rates; and conditional kurtosis: perceived probability of (or dislike for) a tail event. We obtain detailed information on the timing and content of the major macroeconomic announcements as well as expectations from market participants about each macroeconomic announcement from Action Economics Dealer Survey. Action Economics surveys about 3 market participants on the Friday of the week before the release of each economic indicator. We use the reported median forecast of the survey to infer market expectations. We include information about 12 major announcements. Our data has a number of key features that allow us to address our research question. First, it covers relatively long sample including the almost 7 years the economy has been under the zero lower bound. Second, it contains detailed information on the timing and content of the major macroeconomic announcements. Lastly, our bond market data is observed at daily frequency, so we can more precisely relate asset prices to macroeconomic releases. Our results show that following the release of the employment report and the FOMC statement conditional volatility, skewness and kurtosis decline. We also find that the information content of macroeconomic releases, namely news about non-farm payrolls and news about monetary policy, matter more during the ZLB period. Good news 1

3 about the macroeconomy, a better than expected non-farm payrolls and a less accommodative than expected FOMC decision, is accompanied by an increase in conditional volatility, but a decline in conditional skewness and conditional kurtosis. Our paper is related to a large literature exploring the effect of macroeconomic announcements on financial markets. Papers using fixed-income securities have mainly focused on the level of yields and some on their volatilities. Our paper explores higher order moments that captures different aspects of investors beliefs. Our paper is also related to the literature exploring the asymmetric response of asset prices to macroeconomic news. While some papers focused on recessions vs expansions, we explore the asymmetric response to information shocks during different monetary policy regimes. Two exceptions are Swanson and Williams (214) who focus on the level of Treasury yields and Gilchrist, Lopez-Salido, Zakrajsek (214) who focus on other rates. Furthermore, our focus is on disentangling between changes in preferences and investors beliefs. 2 Data and Methodology 2.1 Macroeconomic Announcements We obtain data on the actual release values and the financial market expectation for 1 of the most important U.S. information releases from Action Economics Dealer Survey (AEDS), formerly known as Money Market Services survey. AEDS surveys about 3 financial market participants on the Friday before each data release, and we use the reported median survey response to capture market expectations. 1 We also collect data on the release date of the Federal Open Market Committee (FOMC) meetings statements and minutes. We consider a comprehensive list of announcements that characterize several aspects of the macroeconomy. In particular, we include the following announcements: the consumer price index (CPI), the unemployment rate, non-farm payrolls, hourly wage earnings, initial jobless claims, housing starts, the Conference Board Leading economic index, the Institute of Supply Management (ISM) Manufacturing Index, durable goods orders and the Federal Open Market Committee (FOMC) meetings statements and minutes. We collect data covering the period from January 24 to July 215. Table 1 presents the list of announcements in our sample and the number of observations over which two announcements are released during the same day. Following Balduzzi et al. (21) and Andersen et al. (23), we construct a mea- 1 Balduzzi, Elton, and Green (21), Andersen, Bollerslev, Diebold, and Vega (23), among others, have shown that forecasts based on surveys are a reasonable proxy for expectations of the data release. 2

4 sure of the news component for each macroeconomic release as difference between the realized value and the expected value of the data release, S k,t = A k,t X k,t σ k (1) where A is the value of the main statistic released in announcement k, and X is the corresponding median survey forecast. We normalize this measure of surprise to compare regression coefficients across different announcements. In the case of the release of the FOMC statement and minutes, we use the change in the 2-year Treasury yield around a small interval that brackets the policy announcement to infer the monetary policy surprise associated with the policy announcement as in Hanson and Stein (215) and Gentler and Karadi (215). 2.2 Daily Conditional Moments of Swap Rates From Barclays, we obtain data of options on interest rate swaps, or swaptions, along three dimensions: the maturities of the underlying swaps, the expiries of the options, and the option strikes. This three-dimensional grid of prices is known as the swaption cube. In our database, we have price information for nine swap tenors ranging from 1- to 3-years (1-5, 7, 1, 2, and 3 years), with ten option expiries from 1-month to 1 years (1, 3, and 6 months and 1-5, 7 and 1 years), and thirteen degrees of moneyness, defined as the strike price minus the forward rate swap, (±2, ±15, ±1, ±75, ±5, ±25 and bps). Our swaptions are denominated in USD and the data covers the dates of November 3, 24 to July 27, 215. We also collect data on swap rates over the same time period from the Federal Reserve Statistical Release H.15. We can infer the conditional moments of an underlying future swap rate using the implied volatility smile where the time horizon is equal to the option expiry. For example, using the prices of the 1-year option on the 1-year swap across different strikes, we can obtain the conditional variance, skewness, or kurtosis of the 1-year swap rate at a 1-year horizon. We choose to focus on the conditional moments as opposed to the entire conditional densities because they are less sensitive to the chosen numerical technique. To compute the conditional moments of the future swap rates we follow closely Trolle and Schwartz (214). Consider a fixed versus floating interest rate swap that occurs during the period T m to T m where the fixed rate is K. Each period, T j, within the predetermined dates T m+1 to T n the fixed leg will pay τ j 1 K and the floating leg will pay τ j 1 L(T j 1, T j ), where τ j 1 is the year fraction between periods T j 1 and T j and L(T j 1, T j ) is the LIBOR rate determined at date T j 1. Assuming that the short rate has the same credit and liquidity risk as the LIBOR, the value of the swap from 3

5 the perspective of the fixed rate payer is, V m,n (t) = P (t, T m ) P (t, T n ) KA m,n (t) (2) where n A m,n (t) = τ j 1 P (t, T j ) (3) j=m+1 is the swap annuity factor and P (t, T j ) is the time-t price of a zero coupon bond that matures at time T j. Let S m,n (t) be the time-t forward swap rate. S m,n (t) is the rate on the fixed leg that makes the present value of the swap contract equal to zero and can be calculated as S m,n (t) = P (t, T m) P (t, T n ) A m,n (t) Note that at time T m, the forward swap rate will become the spot swap rate. A payer swaption is the option to enter into an interest rate swap paying the fixed rate and receiving the floating rate. Let P m,n (t, K) be the value at time t of a European payer swaption expiring at time T m and paying fixed rate K from periods T m to T n. At time t < T m, its price is given by (4) P m,n (t, K) = A m,n (t)e A t [ (Sm,n (T m ) K) +] (5) where the expectation is done under the annuity measure using A m,n (t) and the numeraire (see Jamshidian (1997)). Similarly, the receiver swaption has a price at time t of R m,n (t, K) = A m,n (t)e A t [ (K Sm,n (T m )) +]. (6) Reviewing Eq. (5) and Eq. (6), the payer swaption represents a call option while the receiver can be seen as a put option on the underlying swap rate. It can be shown that the conditional mean of the future swap rate is the current forward swap rate µ t = S m,n (t). (7) The following expressions for the conditional variance, skewness, and kurtosis can be shown to be V ar A t (S m,n (T m )) = E A t = [ (Sm,n (T m ) µ t ) 2] 2 A m,n (t) ( P m,n (t, K)dK + S m,n(t) Sm,n(t) R m,n (t, K)dK ) (8) 4

6 [ Skew A t (S m,n (T m )) = EA t (Sm,n (T m ) µ t ) 3] V art A (S m,n(t m )) 3/2 ( 6 A m,n(t) S (K S m,n(t) m,n(t))p m,n (t, K)dK + ) S m,n(t) (K S m,n (t))r m,n (t, K)dK = V art A (S m,n(t m )) 3/2 (9) [ Kurt A t (S m,n (T m )) = EA t (Sm,n (T m ) µ t ) 4] V art A (S m,n(t m )) 2 ( 6 A m,n(t) S (K S m,n(t) m,n(t)) 2 P m,n (t, K)dK + ) S m,n(t) (K S m,n (t)) 2 R m,n (t, K)dK = V art A (S m,n(t m )) 2 (1) For each strike price we calculate the implied volatility. We then interpolate across the implied volatilities and convert back to the prices that are used in the numerical integration for computation in equations (8), (9), and (1). Table 2 displays the results for the conditional volatility (annualized and measured in basis points) of the future swap rate for different swap maturities and at different horizons. It reports the the sample means of the slopes of the volatility surface along both the swap maturity and horizon dimensions. On average, the conditional volatility is hump shaped across the horizon for shorter swap maturities while swap maturities of 5 years or longer are a decreasing function of the horizon on average. The same pattern holds across maturities. On average, for future swaps with a more immediate horizon (under 1 year), the conditional volatility exhibits a hump shape across maturities. For the horizons of 2 years and beyond, the conditional volatility is generally a decreasing function of swap maturity. Conditional volatility exhibits significant variation over time. For example, the upper panel of Figure 1 displays the slope of the conditional volatility term structure along horizons for different swap tenors. The difference between the conditional volatility of the swap rate ten years ahead less the conditional volatility 1 month ahead. As you may see, as the financial crisis ended and the economy entered the period of unconventional monetary policy, the conditional uncertainty of rates at short horizons declined (the slope declined in absolute value). However, the slope has been more volatile after the zero lower bound, reflecting fluctuations in uncertainty about rates at short horizons, for example, in episodes such as the so called taper tantrum when we see an increase in the slope. Table 3 displays the for the conditional skewness of future swap rate for different swap maturities and at different horizons. Again, it also reports the sample means 5

7 of the slopes of the skewness surface along both the swap maturity and horizon dimensions. Conditional skewness is positive for nearly all option expiries and swap maturities, but for longer horizons it declines nearly to zero. A positive conditional skewness implies that OTM payer swaptions will be more expensive than OTM receiver swaptions. Additionally, the conditional skewness is a decreasing function of swap maturity for any given horizon where the magnitude of the slope is generally decreasing as the horizon lengthens. For a given swap maturity, the conditional skewness is humped shaped across expirations. Similar to conditional volatility, conditional skewness also shows variation over time. In particular, as shown in the middle plot of Figure 1, the dynamics of conditional skewness has shifted after the zero lower bound. During this time of unprecedented low rates, conditional skewness has become more volatile and typically more positive across maturities and horizons. Table 4 displays the for the conditional kurtosis of future swap rate for different swap maturities and at different horizons. Included in the table are the sample means of the slopes of the skewness surface along both the swap maturity and horizon dimensions. For horizons of 1 year or less, we see that the conditional kurtosis is generally at or above 3 across all maturities. For these shorter horizons, the kurtosis also decreases as the maturity increases. For horizons of 2 years and beyond, the conditional kurtosis generally decreases, for any given horizon, as time to maturity increases. Additionally, for the longer horizons, the conditional kurtosis is on average less than 3. Over time, the conditional kurtosis seems to be more volatile during the period of the zero lower bound for swaps with short horizons. Specifically, looking at the conditional kurtosis of the 1- and 2-year maturity swap contracts with a horizon of 1 month there is a marked increase in volatility during the years after the financial crisis. The tails of the short horizon swap rate distributions have become even fatter during the period of zero interest rates. To briefly summarize the findings regarding the conditional moments of future swap rates, we found that conditional volatility about short-term rates declines but the volatility of the conditional volatility increased. Swap rates have become more positively skewed and the conditional kurtosis of the short horizon swap contracts has become more volatile during the period of the zero lower bound on interest rates. With an increase in kurtosis and its volatility, we see investors believe a rare event is more likely in the current environment than in previous settings possibly because the Federal Reserve can no longer lower interest rates should the economy begin to fall back into a recession. 6

8 3 Empirical Analysis To study the response of conditional volatility, conditional skewness and conditional kurtosis of forward swap rates of different maturities and at different horizons to macroeconomic announcements, we estimate for each announcement k the following regression: with, m (m,n) t = α (m,n) k + β (m,n) k (z t )S k,t + H h k β (m,n) k (z t ) = β (m,n) 1,k (1 I zt ) + β (m,n) 2,k I zt β (m,n) h (z t ) + ɛ t where m (m,n) t represents the day-to-day change in either the conditional volatility σ (m,n), the conditional skewness γ (m,n) 1, or the conditional kurtosis γ (m,n) 2 of the forward swap rate with maturity n, m periods ahead. In this specification, α (m,n) k captures the unconditional response of the forward swap rate moments to the release of the macroeconomic announcement k, while β (m,n) k (z t ) captures the impact of the content of news. We allow different announcement surprises to have different effect on the forward swap rate moments and we allow these effects to be different between the two monetary policy regimes: the period of conventional monetary policy, when the federal funds target rate was the primary policy instrument, and the period of unconventional monetary policy, a period during which the primary policy instrument was at its effective lower bound, and the FOMC conducted monetary policy primarily by altering the size and composition of the Federal Reserve s balance sheet. Also, it issued various forms of forward guidance regarding the trajectory for the fed funds target rate. We follow Gilchrist, Lopez-Salido, Zakrajsek (214), and set the indicator function, I zt equal to one after November 25 of 28, when the Federal Reserve Board announced that it will start purchasing the debt obligations of Government Sponsored Enterprises (GSEs) and agency-backed Mortgage-Backed Securities (MBS). We control for all concurrent announcements in order to isolate the marginal effect of each announcement type. 3.1 Results For brevity, we will report the response to the employment report and the FOMC statement release, the most influential news events. The Online Appendix has a detailed analysis of all news considered in our sample. The upper panel in Figures 2 to 4 displays the unconditional response of conditional volatility to the release of the employment report (α), and the lower panel of the same figures displays the effect of a one standard deviation surprise on conditional volatility 7

9 for news about non-farm payrolls for different horizons (β(z t )). The red line shows the effect during the ZLB period, and the blue line the effect before the ZLB period. For short- and medium-term rates we find that conditional volatility declines, at all horizons, and most of the intercepts are statistically significant. The decline is a bit larger for longer-term rates, and the impact is significant across horizons. The impact decreases quickly with the horizon, though it remains statistically significant. Looking at the bottom panels, we find that news about non-farm payrolls matter more during the ZLB period, and the impact is economically more important. As shown in the figures, at all horizons the red line is below the blue line. This pattern is consistent, for short-term rates as you see here, and for medium- and long-term rates as you see in the following plot. Figures 5 to 7 show similar plots for the release of the FOMC statement. Again, we find that estimates of the unconditional response of conditional volatility are all negative. Looking at the news content sensitivity, we find that news about the FOMC decisions have a more pronounced impact on conditional volatility during the ZLB period. If the FOMC decision is perceived as less accommodative than expected, that is a positive surprise, then volatility rises. But it rises more and the increase is statistically and economically significant during the ZLB period. For the conditional skewness, the intercept is small and negative, though only significant for most cases. What is again more interesting, is the asymmetric impact of news. Good news about the labor market are accompanied by a decline in skewness, at all horizons. However, as shown in Figures 8 to 1, news about non-farm payrolls are more important during the ZLB period, and this is particularly true for long-term rates at all horizons. News about the FOMC statement has no effect on skewness before the ZLB period, while after the ZLB period an FOMC statement interpreted as less accommodative than expected leads to a decline in skewness (see 11 to 13). We also find an asymmetric impact of news for conditional kurtosis (see Figures 14 to 16. Positive surprise about non-farm payrolls leads to a decline in conditional kurtosis after the ZLB. The effect is economically significant for short- and mediumterm swap rates at all horizons. Similarly, news about the FOMC decision have a larger impact on conditional kurtosis after the ZLB. A less accommodative than expected FOMC statement leads to a decline in conditional kurtosis. 4 Conclusion Following the Great Recession, we entered new period of monetary policy also known as the ZLB. We further examine the question of whether the zero lower bound has influenced investors beliefs about the economy in response to various macroeconomic 8

10 announcements. During the ZLB period, macroeconomic announcements seemed to have a great effect on investors beliefs. From a policy perspective, it is important to better understand the behavior of investor beliefs during the ZLB because it is a period where the effectiveness of monetary policy is heavily dependent on the ability to manage expectations. During the Great Recession, the Federal Reserve went to great lengths to increase the transparency of their future policy decisions in an effort to better manage investors fears and beliefs. Furthermore, we are able to better understand the potential asymmetric effects of information shocks on investor beliefs. Using the Action Economics Dealer Survey we are able to obtain detailed information on market expectations of macroeconomic announcements. Every Friday of the week prior to the release of macroeconomic data, Action Economics surveys 3 market participants about their expectations. We also use swaptions data to extract the conditional volatility, conditional skewness and conditional kurtosis. These measures capture investors ex-ante uncertainty, views on the likelihood of positive or negative changes in interest rates, and perceived probability of a tail event respectively. When looking at the dynamics of the conditional moments from swaptions data we find that on average the conditional volatility is hump shaped across the horizon for shorter maturities while swap maturities of 5 years or longer are a decreasing function of the horizon. When looking across maturities, future swaps with a more immediate horizon exhibit a hump shaped conditional volatility. For horizons of less than a year, we find conditional kurtosis is generally above 3 across all maturities. We also find that conditional kurtosis generally decreases as time to maturity increases. As we look at the response of these conditional moments to macroeconomic releases, we focus on the response to the employment report and the FOMC statement releases as we found them to be the most influential of the news events. We refer the interested reader to the Online Appendix for a detailed analysis of all the news considered in our sample. For short- and medium- term rates we find that conditional volatility decreases with the release of the employment report and FOMC statements. While it remains significant, the impact does decrease in magnitude as the horizon increases. News regarding the non-farm payrolls is statistically significant during the ZLB period and also has a greater impact economically. Similarly for conditional skewness, we find that news about the non-farms payroll are more important during the ZLB period. In summary, we find that macroeconomic news has an asymmetric effect on investors beliefs during the ZLB period. This increased sensitivity to macroeconomic news further illustrates the need to manage investors expectations in order for monetary policy to be effective when short-term rates are near the zero lower bound. 9

11 References Andersen, T.G., T. Bollerslev, F. X. Diebold, and C. Vega. 23. Micro effects of macro announcements: Real-time price discovery in foreign exchange. American Economic Review 93: Balduzzi, P., E. J. Elton, and T.C. Green. 21. Economic news and bond prices: Evidence from the US Treasury market. Journal of Financial and Quantitative Analysis 36: Gentler, M. and P. Karadi Monetary policy surprises, credit costs, and economic activity. American Economic Journal: Macroeconomics 7: Gilchrist, S., D. Lopez-Salido, and E. Zakrajsek Monetary policy and real borrowing costs at the zero lower bound. NBER Working Paper. Hanson, S.G. and J.C. Stein Monetary policy and long-term real rates. Journal of Financial Economics 115: Jamshidian, F Libor and swap markets models and measures. Finance and Stochastics 1: Swanson, E. T. and J. C. Williams Measuring the effect of the zero lower bound on medium- and longer- term interest rates, NBER Working Paper. Trolle, A. B. and E. S. Schwartz The swaption cube. Review of Financial Studies 27:

12 Figure 1: Slope of the term structure of future swap rates conditional moments Conditional Volatility Slope 5 Zero Lower Bound period starts -5 Basis points year 5-year 1-year Year (a) Slope of conditional volatility Conditional Skewness Slope 1.5 Zero Lower Bound period starts 1.5 Basis points year 5-year 1-year Year (b) Slope of conditional skewness Conditional Kurtosis Slope Basis points year 5-year 1-year Zero Lower Bound period starts Year (c) Slope of conditional kurtosis 11

13 Figure 2: Response of the 2-year swap rate conditional volatility to the release of the employment report.5 Impact of employment report Impact of Non-farm Payrolls News No zlb zlb 12

14 Figure 3: Response of the 5-year swap rate conditional volatility to the release of the employment report.5 Impact of employment report Impact of Non-farm Payrolls News No zlb zlb 13

15 Figure 4: Response of the 1-year swap rate conditional volatility to the release of the employment report.5 Impact of employment report Impact of Non-farm Payrolls News No zlb zlb 14

16 Figure 5: Response of the 2-year swap rate conditional volatility to the release of the FOMC statement.5 Impact of FOMC announcement Impact of FOMC News No zlb zlb 15

17 Figure 6: Response of the 5-year swap rate conditional volatility to the release of the FOMC statement.5 Impact of FOMC announcement Impact of FOMC News No zlb zlb 16

18 Figure 7: Response of the 1-year swap rate conditional volatility to the release of the FOMC statement Impact of FOMC announcement Impact of FOMC News No zlb zlb 17

19 Figure 8: Response of the 2-year swap rate conditional skewness to the release of the employment report.15 Impact of employment report Impact of Non-farm Payrolls News No zlb zlb 18

20 Figure 9: Response of the 5-year swap rate conditional skewness to the release of the employment report Impact of employment report Impact of Non-farm Payrolls News No zlb zlb 19

21 Figure 1: Response of the 1-year swap rate conditional skewness to the release of the employment report Impact of employment report Impact of Non-farm Payrolls News No zlb zlb 2

22 Figure 11: Response of the 2-year swap rate conditional skewness to the release of the FOMC statement.15 Impact of FOMC announcement Impact of FOMC News No zlb zlb 21

23 Figure 12: Response of the 5-year swap rate conditional skewness to the release of the FOMC statement Impact of FOMC announcement Impact of FOMC News No zlb zlb 22

24 Figure 13: Response of the 1-year swap rate conditional skewness to the release of the FOMC statement Impact of FOMC announcement Impact of FOMC News No zlb zlb

25 Figure 14: Response of the 2-year swap rate conditional kurtosis to the release of the employment report.1 Impact of employment report Impact of Non-farm Payrolls News No zlb zlb 24

26 Figure 15: Response of the 5-year swap rate conditional kurtosis to the release of the employment report.15 Impact of employment report Impact of Non-farm Payrolls News No zlb zlb 25

27 Figure 16: Response of the 1-year swap rate conditional kurtosis to the release of the employment report.2 Impact of employment report Impact of Non-farm Payrolls News No zlb zlb 26

28 Figure 17: Response of the 2-year swap rate conditional kurtosis to the release of the FOMC statement.15 Impact of FOMC announcement Impact of FOMC News No zlb zlb 27

29 Figure 18: Response of the 1-year swap rate conditional kurtosis to the release of the FOMC statement.15 Impact of FOMC announcement Impact of FOMC News No zlb zlb 28

30 Table 1: Macroeconomic Announcements Announcement Concurrent announcements Consumer Price Index Core Consumer Price Index Durable Goods Orders Hourly Earnings Non-farm payrolls Unemployment Initial Jobless Claims Housing Starts CB Leading Economic Index NAPM Index FOMC statement FOMC minutes 12 This table presents the announcements and the number of times two announcements are concurrent, that is, released during the same day. 29

31 Table 2: Conditional Volatility of Future Swap Rates Tenor Option Expiry 1-m 3-m 6-m 1-year 2-years 3-years 4-years 5-years 7-years 1-years 2-years 3-years Slope 1-year year year year year year year year year Slope This table shows the mean of conditional volatility of future swap rates. Conditional volatility is measured as the square-root of conditional variance, annualized, and measured in basis points. 3

32 Table 3: Conditional Skewness of Future Swap Rates Tenor Option Expiry 1-m 3-m 6-m 1-year 2-years 3-years 4-years 5-years 7-years 1-years 2-years 3-years Slope 1-year year year year year year year year year Slope This table shows the mean of conditional skewness of future swap rates. 31

33 Table 4: Conditional Kurtosis of Future Swap Rates Tenor Option Expiry 1-m 3-m 6-m 1-year 2-years 3-years 4-years 5-years 7-years 1-years 2-years 3-years Slope 1-year year year year year year year year year Slope This table shows the mean of conditional kurtosis of future swap rates. 32