_{1}

^{*}

This paper studied the macroeconomic and the term structure of treasury bonds in the Shanghai Stock Exchange Market. Different from previous studies, we used a group of 122 observed macroeconomic data to construct our model’s macro factor. Therefore the macro factor contained more information than previous studies in predicting the excess return of Treasury bond. Based on the Kalman-Filter estimation, the results show that the macro factor’s risk was compensated through the level factor and slope factor, especially the level factor. Further, based on the decomposition of the yield curve into expected future short rate part and risk premium part, we find that there is some correlation between the variability of the risk premium and monetary policy to some extent.

Since the appearance of Ang and Piazzesi [

There are a lot of variables which affect the bond pricing in the literature, and also affect the bond risk premium which we mean the compensation for holding the bonds as an asset. In financial variables, Fama and Bliss [

But it may be difficult to uncover a direct link between macroeconomic activity and bond risk premium. As some macro variables may be latent and impossible to be summarized. And macro variable are imperfectly measured. On the other hand, the models may imperfect descriptions of the price dynamic, and the set of variable used was not perfectly spanned the information the market price showed.

In order to contain more information about the macro variable’s predictability in bond pricing, we form the macro factor based on a group of 122 macro observation according to Ludvigson and Ng [

Following Dufee [

We first form the macro factors based on a group of 122 macro variables. We constructed the macro factor based on the prediction regression of the holding period excess return on the macro factors which is the principle of these group data. According to our results, macro factors can account for about at least 39% of the excess returns, and 62% at most. And the most significant variables among the macro variables which predict excess return were the price index of alcohol and tobacco in CPI, Monetary supply in US, non-staple food processing and short-term loans in the banking and financial institutions.

Then we study the Macro Dynamic Term Structure Model in Shanghai Stock Exchange markets using the constructed macro factors. We find that the macro factor’s risk premium was mainly compensated through the level factor and slop factor. Based on further decomposition of the yield curve, we find that the monetary policy affects the yield curve risk premium. The rest of the paper was organized as follows: the second part demonstrates the model’s set up and estimation procedure. The third part analyses the estimation results, the decomposition of yield curve and impulse response analysis. The last part is summary.

In summary, there seem a lot of macro variables which can be used as factors in Macro Dynamic Term Structure Model, but it seems that they don’t contain so much macro information predicting the excess return. And the macro variable itself seems that it doesn’t contain the same meaning as the theoretic model implied. So the main contribution of this paper is that it contains more information about the macroeconomic and its impact on the term structure and the risk premium of treasury bonds, especially in a transferring economic like China when there might exist some kind of restrictions in the markets.

Following Joslin, Le and Singleton [

To fix notation, suppose that there are N risk factors

Some treat

Suppose that the P dynamic of the factors

where

Absent arbitrage opportunities imply the affine pricing of bonds of all maturities according to Duffie and Kan [

where the loadings

where some conformable

to the canonical form in terms to

Suppose the market price of risks is affine, and satisfies:

where

Therefore the physical dynamic parameters could expressed in the risk premium parameters

observation equation is:

where

And therefore the model’s parameters need to estimated is

The above specification can reduce the models parameters when chosen the appropriate risk premium parameters. Therefore the MLE estimation of the Karlman-Filtering model can quickly reach the global maximization.

Our monthly data extends from March 2006 through April 2015. The data were from National Bureau of Statistic of PRC, Federal Reserve Bank, WIND and CSMAR. The data consisted of groups of data that can represent an aspect of the economic activities or the situations in China. Such as international data about the world commodity price index, the US monetary supply, exchange rate among the main trading partners, domestic industrial production, price index including CPI and PPI, consumption, investment, PMI and so on. All the macro cyclical data was seasonal adjusted.

The full bond price data is calculated from the net transaction price in the last of the month in the CSMAR added up with the accrue interest. The interest is calculated based on the par value and the coupon accrued since the last coupon date. Then we delete the data when the time to maturity of the bond in the transaction is less than 6 months. Thus, based on the data we could get the Fama-Bliss yield data. We chose the following 10 maturity as the regression data, the maturities was 1 to 10 integer years.

We use the dynamic factor analysis as an application of statistical procedures for the cased study here. The presumption of dynamic factor analysis is that the covariance among economic time series is capture by a few unobserved common factors. Stock and Watson [

where

where

We estimated factor from a balanced panel of 122 monthly economic series, each spanned the period March 2006 through April 2015.

For each regression, the R^{2} increase as the bonds maturities goes up, from 38.9% to 62.1%. This shows that the macro factors have more prediction information about the short maturity bonds than the longer maturity

Factor 1 | 36.88% | Factor 2 | 50.47% | Factor 3 | 58.49% |
---|---|---|---|---|---|

VAI: General equipment | 0.9354 | PPI: Durable | 0.8205 | VAI: Food process | 0.623 |

IMPI: Non-energy | 0.891 | M2: China | −0.7204 | CPI: Tobacco, Liquor | 0.607 |

VAI: WOODS process | 0.8901 | PPI: Clothing | 0.7175 | M2: US | 0.5576 |

VAI: Paper | 0.8844 | PPI: Daily use | 0.7103 | IMPI: Basic metals | −0.5427 |

Factor 4 | 64.28% | Factor 5 | 69.23% | Factor 6 | 73.62% |

US treasury: 1 year | −0.6241 | CFFI: Total loans | −0.7544 | SH composite index | −0.6453 |

US: Short loans | −0.6093 | Consumer satisfy | 0.5736 | CFFI: Portfolio | −0.5192 |

CFFI: Total loans | 0.587 | M1: US | −0.5551 | SZ composite index | −0.456 |

SZ composite index | 0.5506 | CPI: Clothing | −0.5189 | VAI: Gas production | −0.4263 |

Factor 7 | 76.26% | Factor 8 | 78.47% | ||

VAI: water production | 0.6712 | IAC: Primary Ind. | −0.4503 | ||

CFFI: Portfolio | −0.404 | VAI: Electrical M & E | 0.3576 | ||

IMPI: Woods | 0.3577 | Fiscal expenditure | 0.3543 | ||

VAI: Non-ferrous Metals | −0.353 | VAI: Furniture | 0.3496 |

VAI: value added industry production, PPI: Producer Price Index, CFFI: Credit Funds of Financial Institutions, IAC: Investment Actually Completed. IPI: International Markets Price Index. CSI: consumer satisfaction index.

Variables | R^{2}-Adj^{ } | ||||||||
---|---|---|---|---|---|---|---|---|---|

0.0001 | −0.0053 | −0.0263 | −0.0074 | 0.0387 | −0.0276 | 0.0108 | 0.0067 | 0.6214 | |

(0.0026) | (0.0026) | (0.0038) | (0.0061) | (0.0040) | (0.0085) | (0.0068) | (0.0053) | ||

0.0020 | 0.0033 | −0.0366 | −0.0201 | 0.0536 | −0.0193 | 0.0291 | 0.0191 | 0.5446 | |

(0.0044) | (0.0045) | (0.0064) | (0.0112) | (0.0055) | (0.0140) | (0.0108) | (0.0069) | ||

0.0067 | −0.0074 | −0.0526 | −0.0181 | 0.0898 | −0.0226 | 0.0368 | −0.0140 | 0.4927 | |

(0.0079) | (0.0080) | (0.0121) | (0.0198) | (0.0103) | (0.0252) | (0.0182) | (0.0090) | ||

−0.0017 | −0.0026 | −0.0761 | −0.0311 | 0.1145 | −0.0220 | 0.0221 | 0.0106 | 0.4784 | |

(0.0087) | (0.0093) | (0.0136) | (0.0225) | (0.0120) | (0.0296) | (0.0202) | (0.0127) | ||

0.0015 | −0.0037 | −0.0783 | −0.0272 | 0.1434 | −0.0162 | 0.0454 | −0.0115 | 0.3892 | |

(0.0163) | (0.0143) | (0.0282) | (0.0341) | (0.0222) | (0.0461) | (0.0304) | (0.0269) |

Notes: the table reports the regression of excess bond holding period returns on model factors.

bond.

This is also the case for the other factors. The other factors have a rising coefficients in absolute, even though they were significant only in some of the short maturities bonds’ regressions. We show that the coefficients in

where excess return

where

To specific the risk premium parameters in Equation (8), we follow Cochrane and Piazzesi’s [

On the other hand,

Thus we finished the four factors Gaussian Dynamic Term Structure model’s set up. The state space model is estimated by Kalman-Filtering, and the parameters’ standard error was calculated through outer product and delta method. The result is presented in

As is shown in

The second line of

According to the above Q parameters and P dynamics, we can decompose the yield curve into average of expected future short term rates and yield risk premium. According to expectation hypothesis, the yield curve

−0.0526 | −0.0536 | −0.0559 | −0.0559 | 0.0022 |

(0.0932) | (0.1123) | (0.0929) | (0.1233) | (0.8903) |

−0.0067 | 0.7444 | −0.1079 | −2.2547 | 9.3813 |

(0.0270) | (0.2300) | (0.1746) | (0.1242) | (0.2588) |

0.0145 | −0.0224 | 0.3600 | 0.0164 | −0.3527 |

(0.0092) | (0.0219) | (0.0792) | (0.0176) | (0.0827) |

0.0119 | ||||

(0.0354) |

Note: standard errors are in parenthesis.

−0.0031 | −0.0520 | 0.0160 | −0.1075 | −0.0286 |

(0.0018) | (0.0315) | (0.0242) | (0.0450) | (0.1315) |

0.0112 | 0.2848 | −0.2959 | −0.1875 | 0.5620 |

(0.0070) | (0.0760) | (0.0728) | (0.0216) | (0.0345) |

−0.0024 | −0.0328 | 0.0476 | −0.0798 | 0.4203 |

(0.0020) | (0.0210) | (0.0166) | (0.0374 | (0.0234) |

0.0013 | 0.0341 | −0.0311 | 0.0267 | −0.1535 |

(0.0010) | (0.0059) | (0.0099) | (0.0081) | (0.0119) |

Note: standard errors are in parenthesis.

follows:

where

Thus, we can get the yield curve decomposition.

We can see that normally that the 1-year yield is below the 3-year yield, but it seems that 1-year yield sometimes is greater than 3-year yield after the second quarter of year 2011. And the risk premium is large in that period.

The relationship between monetary policy and yield risk premium is important for the policy maker. When the risk premium component is high, it suggests the weak economic condition for policy easing.

It seems that the risk premium is affected by the monetary policy measures in

has been token before or lasting to the observed month. We can see that in March to August in 2006, the distant between the 3-year yield and 1-year yield is large, it means the risk premium is large. And we find that in this period the central bank has rose the Require Reserve Ratios for several times. They also rose the bank lending rate and deposit rate. We can see sharp increase in the first half of 2007. In year 2007, central banks continues to increase the RRR and rose the loan rate and deposit rate. We can see large risk premium in second half of 2007 to early 2008. Then in the fourth quarter of 2008 the central bank turn from the restraint policy to easing policy, so after the decreasing of the Require Reserve ratio, decreasing of bank loan rate and deposit rate, we can see sharp decrease in both in interest rate and the risk premium. This is the same situation for the period from April 2011 to August 2011 when the risk premium is high for the period.

This paper uses a canonical macro dynamic term structure model (MTSM) to study the term structure of treasury bonds in the Shanghai Stock Exchange Market, and the macro factor’s effect on the risk premium. The canonical form has the advantage of separation of the P dynamic and Q dynamic into different sets of parameters relatively less and easily estimated. We set the model in parameters by the Q dynamic parameters and the risk premium parameters for our study. And we set the risk premium parameters according to the empirical relationship between the model factors factor loadings and covariance matrix with the excess returns. And different from the specification where the risk parameters is only in level factors, we include more free parameters regarding the level and slope factor because the models’ macro factor just explains part of the excess holding period return of the bond.

The other difference from other MTSMs is our model’s macro factors. In order to contain more information about the macro variable’s predictability in bond pricing, we constructed the model’s macro factor based on 122 observation series depicting different aspects of the economics.

Our results show that the constructed macro factor can explain 62.14% at most of the excess holding period returns. It shows that the macro variables can explain the bond excess returns. And further, the estimated MTSM results show that the compensation of the model’s macro factor is mainly through the level factor; this means that the macro factors affect the level factor dynamic and then the excess returns of the bonds.

Based on the study of the yield decomposition, we find some relation between the risk premium and the monetary policy. We find that the high risk premium in some periods may have some relationship with the central bank’s monetary measures in that period. This may be the results of the market structure of the economics, and can be thought as a further topic for researchers.

This work is support by Research Innovation Foundation of Shanghai University of Finance and Economics under Grant No.CXJJ-2013-327. And I am especially grateful to Professor Jianping Ding for his support and encouragement. All errors are my own.

XiaoweiWu, (2016) The Risk Premium of Treasury Bonds in China. Journal of Mathematical Finance,06,156-165. doi: 10.4236/jmf.2016.61015