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This study examines the random walk behavior of Indian bond market. Bond indices published by Clearing Corporation of Indian (CCIL) were used in this study. The hypothesis is tested with multiple variance ratio tests from daily and weekly data, from 3-Jan.-2011 to 30-Dec.-2016. This paper also applies the bootstrap procedure on all the tests used because it shows desirable small sample properties under conditional heteroscedasticity. Variance test ratios show that Indian bond market does not follow random walk behavior.

In the recent seven years, Indian bond market has seen tremendous growth. G- Sec market has grown by more than 500% in the last seven years, 29.1% compounded growth rate per annum.

The possibility that the Indian debt market will become the primary debt market in Asia suggests the importance of understanding the efficiency of Indian debt market.

This study examines the efficient market hypothesis (EMH) for Indian G-Sec

Markets | Mar.-15 (in Billions) | Apr.-08 (in Billions) | Growth | CAGR |
---|---|---|---|---|

CBLO | 1794.44 | 673.98 | 266% | 15.02% |

Market Repo | 1097.57 | 382.99 | 287% | 16.23% |

G-Sec | 553.07 | 92.58 | 597% | 29.09% |

91-Day (T-Bill) | 33.31 | 3.68 | 905% | 36.99% |

182-Day (T-Bill) | 12.09 | 2.02 | 599% | 29.13% |

364-Day (T-Bill) | 19.02 | 8.39 | 227% | 12.40% |

Source: Data base on Indian Economy, RBI’s data warehouse. CAGR: Calculated by (Mar.-15/ Apr.-08)^(1/7)-1.

market through variance ratios. The idea of asset prices following random walk comes from Efficient Market Hypothesis (EMH). The assumption is that investors act immediately to any informational advantage, thereby, eliminating profit. Hence, prices fully reflect the information. This condition leads to a random walk behavior, random sequence of price changes, where the market is efficient. A random walk is defined as price changes are independent. If the Indian bond market follows random walk behavior, then the market is weak form of efficient and therefore, not predictable. This means it is impossible for a trader to generate excess return overtime by speculation. Otherwise, if the Indian bond market is predictable, then the market is not weak-form efficient, which means that traders can make excess profit by speculative positions. There have been many researches which test for the efficient market hypothesis of stock price.

A number of studies tested the efficient market hypothesis for diffident class of assets. Ojah and Karemera [

Ajayi and Karemera [

While many studies available for foreign market, only few studies reported for Indian stock market and no studies found for debt market in India to test EMH, at least to the knowledge of author. Bhattacharya et al. [

There have been numerous empirical studies which test the market efficiency through different methods however majority of the researchers have applied variance ratio test for testing random walk behavior of assets. Hence, this paper applies variance ratio test to test RWH. Many researchers have studied RWH for different markets such as stock market, forex market, commodity market etc. No studies have been found to understand the efficiency of Indian bond market at least to the knowledge of the author. As the Indian bond market has gaining attentions of the international investors, it is imperative for the investors to know efficiency of the market whereby investors can adjust their risk level for investment in the bond market or try to make speculative profits.

The most popular statistical tool to test the RWH is variance test ratio [_{t} ? Y_{t}_{−q}), of the time series Y_{t} is q times the sample variance of one-period return (Y_{t} − Y_{t}_{−1}). Hence, variance ratio at lag q is defined as the ratio between (1/q)th of the q-period return to the variance of one-period return. Thus, the variance computed at each lag should be equal to unity. Thus, the variance ratio test evaluates the hypothesis that a given time series follows a random walk return sequence. The variance ratio, VR(q), is defined as follows.

V R ( q ) = σ 2 ( q ) σ 2 ( 1 ) (1)

where σ 2 ( q ) is the unbiased return variance of q period (X_{t} ? X_{t}_{−q}) and σ 2 ( 1 ) is variance of one period (X_{t} ? X_{t}_{−1}). The null hypothesis of random walk behaviour is that VR(q) is not statistically different from unity.

The estimator of q period return variance σ 2 ( q ) using q period returns ( X t + ⋯ + X t − q + 1 ) calculated using overlaping on horizon returns (q-period) as advocated by Lo and Mackinlay [

σ 2 ( q ) = m − 1 ∑ t = q T ( x t + x t − 1 + ⋯ + x t − q + 1 − q μ ) 2 (2)

where μ = T − 1 ∑ t = 1 T x t and m = q ( T − q + 1 ) ( 1 − q T − 1 ) . The value of m is such

as σ 2 ( q ) is an unbiased estimator of q period return variance when σ 2 ( 1 ) is stationary over time.

This paper also consider joint variance ratio test of Chow and Denning [

Lo and Mackinlay [

To control the error in conventional variance ratio test, Chow and Denning [

V R ( p ) = 1 ( 1 − k / T ) 4 π T σ 2 ∑ j = 1 ( T − 1 ) / 2 W q ( ϑ i ) Δ x ϑ j (3)

where

Δ x ϑ j = 2 π T − 1 | ∑ i = 1 T ( y − y ( t − 1 ) − μ ) exp ( − i ϑ t ) | 2

W q ( ϑ i ) = ∑ | j | < q ( 1 − | j | q ) exp ( − i j ϑ )

A non-parametric alternative to conventional asymptotic VR tests using ranks and signs also applied. The tests based on ranks are exact under the independence and identical distribution assumption [

R j ( q ) = ( ( T q ) − j ∑ t = q T ( r j , t + ⋯ + r j , t − k + 1 ) 2 T − 1 ∑ t = q T r j , t 2 ) X ∅ ( q ) − 1 / 2 (4)

Using several q values would lead to an over rejection of the null hypothesis. To control this problem, Belaire-Franch and Contreras [

The data examined consist of the daily and weekly index return for bond indices published by Clearing Corporation of India (CCIL). CCIL publishes bond indices for different tenors. All bond index (BI), sovereign bond index (SV), tenor indices such as zero to five (0 to 5), five to ten (5 to 10) years, ten to fifteen (10 to 15) and fifteen to twenty (15 to 20) and twenty to thirty (20 to 30) are examined in this paper. The data span from January 4, 2011 to December 30, 2016, namely 2185 and 313 observations for the daily and weekly data respectively. For weekly data, the prices were observed on Wednesday or on the following day if the market is closed on Wednesday.

For the weekly data (

Tables 4-7 report results of individual and multiple variance test for the daily and weekly index return of Indian bond market. The holding periods q considered are 2, 4, 8, 16 as suggested by Deo and Richardson [

The random walk hypothesis for Indian bond market is rejected as per the variance ratio test. The p values for all the small period k (2, 4, 8, 16) are less than 5% for VR(q). This indicates that players in the Indian bond market do not take risky positions in short term. The random walk hypothesis is rejected for the weekly data as well for all the indices.

The estimates of variance ratios are shown in the main row, the VR(q) statitics are in parenthesis, the p-values are in brackets.

Mean | Std. Dev. | Skewness | Kurtosis | JB | LB (10) | LB2 (10) | LM (10) | |
---|---|---|---|---|---|---|---|---|

0 to 5 | 0.00022 | 0.00135 | −0.48850 | 63.35802 | 331608.1* | 32.57* | 329.58* | 59.17* |

5 to 10 | 0.00024 | 0.00214 | 0.29549 | 91.07838 | 705991.7* | 28.12* | 204.37* | 50.38* |

10 to 15 | 0.00026 | 0.00290 | 1.32367 | 100.68970 | 869076.8* | 34.68* | 167.7* | 14.37* |

15 to 20 | 0.00027 | 0.00317 | 0.72653 | 64.02131 | 339039.8* | 21.85* | 76.66* | 95.16* |

20 to 30 | 0.00027 | 0.00347 | 0.34913 | 63.87009 | 337214.7* | 23.66* | 79.47* | 92.02* |

BI | 0.00025 | 0.00228 | 0.83081 | 94.79217 | 766999.2* | 25.76* | 129.42* | 21.90* |

SB | 0.00025 | 0.00229 | 0.76452 | 82.71783 | 577981.8* | 20.04* | 105.88* | 25.84* |

Bond type | Mean | Std. Dev. | Skewness | Kurtosis | JB | LB (10) | LB2 (10) | LM |
---|---|---|---|---|---|---|---|---|

0 to 5 | 0.001545 | 0.003258 | 1.70988 | 14.00902 | 1727.61* | 23.56* | 149.38* | 12.02** |

5 to 10 | 0.001694 | 0.005306 | 0.77518 | 8.02916 | 360.05* | 19.96* | 223.11* | 52.74* |

10 to 15 | 0.001776 | 0.007457 | 1.19397 | 10.00555 | 712.14* | 15.85* | 160.16 | 5.10 |

15 to 20 | 0.001891 | 0.008715 | 1.11177 | 9.07152 | 543.50* | 25.55* | 111.78* | 10.00* |

20 to 30 | 0.001902 | 0.0102 | 1.06948 | 8.97137 | 523.03* | 24.16* | 128.33* | 22.62* |

BI | 0.001741 | 0.006212 | 1.24213 | 11.08382 | 929.76* | 20.09* | 131.63 | 6.17 |

SI | 0.001749 | 0.006494 | 1.01796 | 9.23810 | 556.18* | 17.12* | 145.72* | 6.99 |

2 | 4 | 8 | 16 | |
---|---|---|---|---|

0 to 5 | 0.5549 | 0.2609 | 0.1285 | 0.0826 |

(−4.6645) | (−4.6827) | (−4.2328) | (−3.8094) | |

[ | [ | [ | [0.0001] | |

5 to 10 | 0.5561 | 0.2712 | 0.1254 | 0.0845 |

(−3.7082) | (−3.7308) | (−3.4169) | (−3.0818) | |

[0.0002] | [0.0002] | [0.0006] | [0.0021] | |

10 to 15 | 0.5290 | 0.2553 | 0.1229 | 0.0816 |

(−3.3161) | (−3.3126) | (−3.081) | (−2.8275) | |

[0.0009] | [0.0009] | [0.0021] | [0.0047] | |

15 to 20 | 0.5186 | 0.2603 | 0.1311 | 0.0839 |

(−4.6061) | (−4.4957) | (−4.0906) | (−3.7348) | |

[ | [ | [ | [0.0002] | |

20 to 30 | 0.5398 | 0.2703 | 0.1354 | 0.0903 |

(−4.5526) | (−4.4608) | (−4.0519) | (−3.7096) | |

[ | [ | [0.0001] | [0.0002] | |

Bond Index | 0.5667 | 0.2733 | 0.1320 | 0.0879 |

(−3.305) | (−3.4467) | (−3.2122) | (−2.974) | |

[0.0009] | [0.0006] | [0.0013] | [0.0029] | |

Sovereign Bonds | 0.5706 | 0.2778 | 0.1352 | 0.0896 |

(−3.485) | (−3.6419) | (−3.408) | (−3.1782) | |

[0.0005] | [0.0003] | [0.0007] | [0.0015] |

QB | CD(r) | CD(s) | |
---|---|---|---|

0 to 5 | 4.683 | 19.892 | 12.136 |

[ | [ | [ | |

5 to 10 | 3.731 | 18.368 | 10.937 |

[0.001] | [ | [ | |

10 to 15 | 3.316 | 18.333 | 10.937 |

[0.001] | [ | [ | |

15 to 20 | 4.606 | 19.016 | 12.435 |

[ | [ | [ | |

20 to 30 | 4.553 | 18.749 | 11.964 |

[0.002] | [ | [ | |

Bond Index | 3.447 | 16.755 | 11.108 |

[0.001] | [ | [ | |

Sovereign Bonds | 3.642 | 17.326 | 12.392 |

[ | [ | [ |

2 | 4 | 8 | 16 | |
---|---|---|---|---|

0 to 5 | 0.4888 | 0.2233 | 0.1465 | 0.0619 |

(−3.3372) | (−2.8197) | (−2.1248) | (−1.7222) | |

[0.0008] | [0.0048] | [0.0336] | [0.085] | |

5 to 10 | 0.5068 | 0.2295 | 0.1510 | 0.0668 |

(−3.1283) | (−2.8273) | (−2.2452) | (−1.8862) | |

[0.0018] | [0.0047] | [0.0248] | [0.0593] | |

10 to 15 | 0.4967 | 0.2221 | 0.1413 | 0.0664 |

(−3.5888) | (−3.1658) | (−2.3835) | (−1.859) | |

[0.0003] | [0.0015] | [0.0171] | [0.063] | |

15 to 20 | 0.5563 | 0.2317 | 0.1567 | 0.0726 |

(−3.9881) | (−3.9447) | (−2.8257) | (−2.1263) | |

[0.0001] | [0.0001] | [0.0047] | [0.0335] | |

20 to 30 | 0.5164 | 0.2324 | 0.1530 | 0.0698 |

(−3.568) | (−3.36) | (−2.5474) | (−2.003) | |

[0.0004] | [0.0008] | [0.0109] | [0.0452] | |

Bond Index | 0.5011 | 0.2254 | 0.1480 | 0.0675 |

(−3.4821) | (−3.1395) | (−2.3742) | (−1.8409) | |

[0.0005] | [0.0017] | [0.0176] | [0.0656] | |

Sovereign Bonds | 0.4985 | 0.2330 | 0.1498 | 0.0683 |

(−3.6401) | (−3.235) | (−2.4767) | (−1.9398) | |

[0.0003] | [0.0012] | [0.0133] | [0.0524] |

QB | CD(r) | CD(s) | |
---|---|---|---|

0 to 5 | 3.337 | 7.120 | 4.933 |

[0.0034] | [ | [ | |

5 to 10 | 3.128 | 6.328 | 4.547 |

[0.007] | [ | [ | |

10 to 15 | 3.589 | 7.248 | 5.727 |

[0.0013] | [ | [ | |

15 to 20 | 3.988 | 6.429 | 4.933 |

[0.0003] | [ | [ | |

20 to 30 | 3.568 | 6.742 | 4.593 |

[0.0014] | [ | [ | |

Bond Index | 3.482 | 6.584 | 5.274 |

[0.002] | [ | [ | |

Soverign Bonds | 3.640 | 6.684 | 5.500 |

[0.0011] | [ | [0.001] |

This study employed individual and multiple variance tests to assess the random walk hypothesis of Indian bond market using bond indices published by the CCIL. Analyzing the data from 3^{rd} Jan. 2011 to 30^{th} Dec. 2016 daily and weekly data, RWH is rejected for Indian bond market. Variance tests applied to test the RWH are robust to heteroscedasticity and non-normality. The outcome of the analysis suggesting that possibility of abnormal returns through speculation in the Indian bond market by traders is present to a great extent.

Babu, A.S. (2017) Testing for Random Walk Behavior in Indian Bond Market. Theoretical Economics Letters, 7, 728-736. https://doi.org/10.4236/tel.2017.74052