Tuesday, May 28, 2013

简单易行的分级基金套利


简单易行的分级基金套利

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欢迎发表评论2012年05月30日14:17 来源:和讯基金  作者:农行财富管理中心 宋艳芬
将本文转发至:
  分级基金最为突出的特点就是它的基础份额(也称母基金)可以按约定比例分级成两只具有不同风险收益特征的优先份额A和进取份额B(两者也称子基金)。分级基金子基金的价格在场内由市场供需关系决定,而母基金净值根据每日投资标的表现来决定,由于价格决定机制不同,分级基金子基金按约定比例所计算出的市场价格与母基金净值之间经常会存在价差。当这种整体性折溢价超出一定范围(高于申购、赎回成本、场内交易成本等)时,就可能存在套利机会。
  分级基金套利的必备条件
  分级基金套利需要条件:只有具备“配对转换”机制的开放式分级基金才能进行套利。分级基金的份额配对转换机制是指在基金的合同存续期内,投资者可以像买入股票一样,在场内按照约定比例分别买入A、B两类子基金份额,然后合并成母基金份额,得到的母基金份额就等同于普通的开放式基金;同时投资者也可以像申购开放式基金一样,申购母基金份额,然后按比例拆分成为A、B两类子基金份额并分别上市交易。
  套利空间计算
  母基金净值可直接在和讯网、好买基金网(博客,微博)等基金公司网站查询。
  母基金市价=A市价*A比例+B市价*B比例(A、B市价在股市上可查询)。
  溢折价率=(母基金市价-母基金净值)/母基金净值
  如结果为正数,那么就是市价溢价比例,就存在着溢价套利的可能;如果为负数,就是市价折价比例,那么就有折价套利的机会。
  分级基金套利:
  分级基金可通过以下三种方式进行套利:
  1.溢折价配对转换套利:
  溢价套利:当溢折价率为正数且大于交易成本时,投资者就可结合着对大势的把握,进行溢价套利。投资者可于T日在场内申购母基金,T+1日确认母基金份额,T+2日申请拆分成A、B份额,然后于T+3日在场内卖出A、B份额,以套取溢价收益。因为由申购场外份额经跨系统转托管至场内后再申请拆分所需要的时间为T+5,因此溢价套利一般均是通过场内申购的方式来操作。
  溢价套利的成本:申购费1.2%(不同的基金会有所差别) + 卖出佣金。
  折价套利:当溢折价率为负数,且绝对数大于交易成本时,投资者就可结合着对大势的把握,进行折价套利。投资者可于T日在场内按约定比例购买A、B份额,于T+1日将A、B份额申请配对转换成场内母基金份额,并于T+2日申请在场内赎回母基金。结束套利。
  折价套利的成本:买入佣金 + 赎回费0.5%(不同的基金会有所差别)。
  案例分析
  通过银华资源基金案例来分析分级基金套利过程。银华资源基金是一只行业指数股票型分级基金,该基金A、B份额比为4:6,即10份银华资源基金分成4份银华金瑞和6份银华鑫瑞
  我们在2月10发现银华资源存在着溢价套利机会。我们于2月10日,申购了1万份银华资源基金,10日的净值为1.0500。2月13日银华资源基金到账,2月14日申请拆分后,获得4000份银华金瑞和6000份银华鑫瑞。两类份额我们花费了10500元。我们于2月15日收盘时卖出上述金瑞和鑫瑞份额,按照2月15日的收盘价计算,银华金瑞0.91元、银华鑫瑞1.417元。上述投资者将分拆的基金全部售出,可以获得12142(4000*0.91+6000*1.417)元。
  考虑到1.2%的申购费,0.1%的佣金等交易成本,最终,投资者可以获得1504元的收益,收益率14%。
  当然,分级基金的溢折价套利不能实现 T+0,而是需要3到4个工作日,因此存在一定的风险。期间因股市波动,会导致母基金净值变化,或者是A、B份额市价变动,从而存在折溢价率收敛风险(折溢价率收敛风险是指套利空间可能受大盘波动而收窄,导致套利亏损)。另外,由于母基金的净值是每一交易日结束后公布,因此盘中的实时折溢价情况存在较大的不确定性,需要对其进行实时预估。
  2、分级基金“T+0”无风险套利
  “T+0”套利的策略是:同时持有母、子基金份额,在享受基础份额净值增长的同时,一旦发现折溢价空间,对母、子基金份额进行相反方向操作,可以实现“T+0” 真正的无风险套利,落袋为安,锁定折溢价套利收益。
  举例说明:
  以银华深证100(159901,基金吧)分级基金为例,我们可以购买20000份该基金,并将其托管到交易所内,保留10000份银华深证100,同时将另10000份拆分成5000份稳进和5000份锐进。分级基金出现溢价的当天,我们就可以同时进行如下操作:将5000份稳进和锐进都在场内卖出,并申购10000份银华深证100,并将以前购买的10000份银华深证100进行拆分。如果出现折价,则反向操作即可。这样操作的结果就是维持持有份额不变的同时,实现了T+0无风险套利。
  因为市价是多方利益体博弈的结果,因而套利不是时时存在的,通常在如下情况下可能会出现套利机会:一是基金折算日前后会出现较大的溢价波动,二是阶段性反弹行情中可能出现更多套利机会;三是指数快速上涨时也会出现较多溢价套利机会。喜欢追求低风险套利收益的投资者,可在详细了解分级基金产品特点的基础上,在容易出现套利的时机,积极把握。 
  

Building A More Stable, Low-Risk Hedging Portfolio


Building A More Stable, Low-Risk Hedging Portfolio
May 27 2013, 14:20 | by Leif Peterson | includes: FXC, FXE, FXY, HYG, IYR, PSQ, SH, SXL, TLT
Portfolio managers periodically assess the performance of asset-preserving or hedging portfolios comprised of assets that are typically less risky than high-return assets, in order to prepare for periods of prolonged instability or deep market corrections. To evaluate several current possibilities, portfolios rebalanced on a quarterly basis were generated using a variety of techniques to determine the stability in returns. A heat map of 6-year correlation coefficients is shown below for a basket of "collar" type hedging assets. As usual, the Japanese Yen (FXY) has not correlated with the majority of other currencies. This is also evident for long-term treasuries (TLT), shorting ETF (SH) for the S&P 500 Index, and shorting ETF (PSQ) for the NASDAQ-100 Index.
(click to enlarge)

Using the correlation matrix R and covariance matrix C for these assets, eight types of portfolios was constructed, five of which involved transformations applied to the log-return data (MinVar, EWMA, RES, MP, RESMP) and three types which involved covariance matrix "shrinkage" methods (DK, LW, and SS). Covariance matrix shrinkage techniques attempt to reduce the covariance matrix to an identity matrix. Recall, the more a covariance matrix is like an identity matrix, the more homogeneous the eigenvalues, since if the covariance matrix is truly an identity matrix, R=I, and all of its eigenvalues will be one. This follows the property that the determinant of an identity matrix I is one, since the product of all of its eigenvalues, Πλ, is unity. The MinVar portfolio is a Markowitzian minimum variance portfolio (not tangency). The EWMA portfolio uses an exponential weighted moving average determination of returns and their standard deviations. The RES approach employs "component subtraction" (see Chap 28) to remove the effect of the first principal component (eigenvector) of the correlation matrix on returns. (this is also known as removing the "market" effect from returns, since the eigenvector of R associated with the greatest eigenvalue typically reflects widespread market correlations. The MP, or Marčenko-Pastur technique, uses component subtraction to remove the effect of noise eigenvectors (whose λ<λ+) on returns. The RESMP approach includes component subtraction to remove effects of both the principal eigenvector and noise eigenvectors below the MP cutoff. Lastly, the DK (Daniels-Kass), LW (Ledoit-Wolf), and SS (Schäfer-Strimmer) methods focus on various covariance matrix "shrinkage" methods, which attempt to [i] stabilize R by forcing it to be positive definite with non-zero eigenvalues, [ii] become well-conditioned so that the ratio of the largest to the smallest eigenvalue is not too large, and [iii] reduce variance related to bias-variance decomposition. All portfolios included dividends, and did not involve tangency weights, but rather the minvar weights. Portfolio weights were determined quarterly using a 60 trading-day (3 months with 20 trading days per month) testing period and historical 180-day training period. Portfolio weights after each rebalance were also adjusted by multiplying each weight by one minus the tail probability (significance test p-value) for testing that the right-tail slope is greater than the left slope [when abs(log-return) was regressed on percentiles of log-returns] and also by multiplying the previously adjusted weights by the asset's 96-day Hurst exponent. No shorting was allowed, and weights were always constrained to sum to unity after each adjustment. Portfolio rebalancing involved purchase of assets according to the weights, using all existing proceeds in the portfolio. The 6-year wealth plot below shows results for the eight portfolios after an initial $100,000 investment during the first rebalance using the adjusted weights obtained. For comparison purposes, an initial purchase of $100,000 was made in the S&P500 index (^GSPC from Yahoo), which remained unbalanced. For a quarterly rebalance, the DK shrinkage portfolio resulted in approximately $180k 6 years after April 30, 2007.
(click to enlarge)

A chart of the rebalance-specific weights for the 6-year quarterly-rebalanced DK shrinkage portfolio is shown below, where the most recent non-zero weights for the last rebalance period (May 1, 2013) were HYG(48.8%), TLT(20.7%), FXY(17.5%), FXE(7.8%), FXC(4.5%), and IYR(0.7%). (weights for other portfolios using different adjustments and time frames are provided here). Note that this is a hedging portfolio focusing on asset preservation. That weights were adjusted for right-tail events may minimize exposure to assets with left-tail ("black-swan") dominance. Adjusting weights at each rebalance by the epoch-specific historical 96-day Hurst exponent provides more weight for assets with greater stability.
(click to enlarge)

Regarding risk and stability of assets considered for portfolio input, the chart below shows an example of a 2-year historical summary of an asset [Sunoco Logistics (SXL)] whose price returns are more right-tail dominant and stable. In the upper left panel, it can be readily observed that the frequency of occurrence of log-returns is greater in the right tail. This was verified quantitatively by regressing abs(log-return) on percentiles, for which the slope for right tail returns was significantly greater than the slope for left tail returns (slope of green fitted line vs. red fitted line). The regression coefficient for a test of equal slopes (13.78) is listed in the chart title, along with the significance level, which is important but not less than 0.05. The upper right panel shows the 12-, 24-, 48-, and 96-day fractal dimension, D, which by definition fall in the range [1,2]. Values of D near 1 suggest high stability, whereas values approaching 2 suggest instability. Since the Hurst exponent, H, is equal to 2-D, values in the range 0.5<H<1 are termed "persistent" (like the frequency of ocean waves), whereas values of 0<H<0.5 are "anti-persistent," similar to fractal Brownian processes. Persistent time series processes tend to go up after a previous increase and down after a previous decrease, which is not true for anti-persistent time series. On May 1, 2013, SXL had a low 96-day D near 1.2, and therefore, over longer periods, SXL tended to be stable. Recently, however, the 12-, 24-, and 48-day D's for SXL are picking up, suggesting that the price return time series is becoming more unstable (breaking up). This can be seen in the lower right panel, which reflects that the price return is starting to become more choppy.
(click to enlarge)

Below are listed the risk and stability characteristics of the assets with non-zero weights in the quarterly-rebalanced 6-year DK portfolio, ordered by their 6-year 96-day Hurst exponents. The 2-years histories and calculations are provided to gain a better view of their price fractal dimension.
FXY-CurrencyShares Japanese Yen Trust
Percentile values of daily loss(gain) in per cent
0.5
1
5
10
25
50
75
90
95
99
99.5
-0.03
-0.02
-0.01
-0.01
0.00
0.00
0.00
0.01
0.01
0.01
2.52
Daily log-return distribution fitting results
Distribution
Location, a
Scale, b
Laplace
0.387
0.260
Linear regression results [Model: y=log(percentile of log-return), x=|log-return|]
Variable
Coef
s.e.
t-value
P-value
Constant
-0.774
0.091
-8.544
0.0000
|log-return|
-200.603
13.739
-14.601
0.0000
I(right-tail)
0.130
0.130
1.006
0.3148
|log-return|*I(right-tail)
-80.430
23.055
-3.489
0.0005
Hurst exponent (of daily return price)
12-day
24-day
48-day
96-day
0.091
0.541
0.723
0.936
(click to enlarge)

IYR- iShares Dow Jones US Real Estate ETF
Percentile values of daily loss(gain) in per cent
0.5
1
5
10
25
50
75
90
95
99
99.5
-0.05
-0.04
-0.02
-0.01
0.00
0.00
0.01
0.02
0.04
0.05
2.15
Daily log-return distribution fitting results
Distribution
Location, a
Scale, b
Logistic
0.038
0.102
Linear regression results [Model: y=log(percentile of log-return), x=|log-return|]
Variable
Coef
s.e.
t-value
P-value
Constant
-1.017
0.090
-11.333
0.0000
|log-return|
-84.104
6.120
-13.743
0.0000
I(right-tail)
0.301
0.121
2.487
0.0132
|log-return|*I(right-tail)
-14.743
8.838
-1.668
0.0959
Hurst exponent (of daily return price)
12-day
24-day
48-day
96-day
0.593
0.850
0.832
0.726
(click to enlarge)

HYG-iShares iBoxx $ High Yid Corp Bond
Percentile values of daily loss(gain) in per cent
0.5
1
5
10
25
50
75
90
95
99
99.5
-0.02
-0.02
-0.01
0.00
0.00
0.00
0.00
0.01
0.02
0.02
2.69
Daily log-return distribution fitting results
Distribution
Location, a
Scale, b
Laplace
0.326
0.184
Linear regression results [Model: y=log(percentile of log-return), x=|log-return|]
Variable
Coef
s.e.
t-value
P-value
Constant
-1.062
0.086
-12.336
0.0000
|log-return|
-181.256
13.254
-13.676
0.0000
I(right-tail)
0.407
0.122
3.346
0.0009
|log-return|*I(right-tail)
-29.503
18.858
-1.565
0.1183
Hurst exponent (of daily return price)
12-day
24-day
48-day
96-day
0.807
0.863
0.628
0.665
(click to enlarge)

FXC-CurrencyShares Canadian Dollar Trust
Percentile values of daily loss(gain) in per cent
0.5
1
5
10
25
50
75
90
95
99
99.5
-0.02
-0.01
-0.01
-0.01
0.00
0.00
0.00
0.01
0.01
0.01
5.88
Daily log-return distribution fitting results
Distribution
Location, a
Scale, b
Logistic
0.340
0.253
Linear regression results [Model: y=log(percentile of log-return), x=|log-return|]
Variable
Coef
s.e.
t-value
P-value
Constant
-0.649
0.094
-6.911
0.0000
|log-return|
-268.174
17.793
-15.072
0.0000
I(right-tail)
0.129
0.136
0.952
0.3417
|log-return|*I(right-tail)
-47.485
27.319
-1.738
0.0828
Hurst exponent (of daily return price)
12-day
24-day
48-day
96-day
0.615
0.404
0.614
0.524
(click to enlarge)

FXE-CurrencyShares Euro Trust
Percentile values of daily loss(gain) in per cent
0.5
1
5
10
25
50
75
90
95
99
99.5
-0.02
-0.02
-0.01
-0.01
0.00
0.00
0.00
0.01
0.01
0.02
4.38
Daily log-return distribution fitting results
Distribution
Location, a
Scale, b
Logistic
0.129
0.275
Linear regression results [Model: y=log(percentile of log-return), x=|log-return|]
Variable
Coef
s.e.
t-value
P-value
Constant
-0.589
0.097
-6.099
0.0000
|log-return|
-219.984
14.582
-15.086
0.0000
I(right-tail)
0.106
0.140
0.759
0.4483
|log-return|*I(right-tail)
-47.599
22.919
-2.077
0.0383
Hurst exponent (of daily return price)
12-day
24-day
48-day
96-day
0.450
0.531
0.557
0.518
(click to enlarge)

TLT-iShares Barclays 20+ Yr Treas.Bond
Percentile values of daily loss(gain) in per cent
0.5
1
5
10
25
50
75
90
95
99
99.5
-0.03
-0.03
-0.02
-0.01
-0.01
0.00
0.01
0.02
0.03
0.04
3.36
Daily log-return distribution fitting results
Distribution
Location, a
Scale, b
Logistic
0.283
0.221
Linear regression results [Model: y=log(percentile of log-return), x=|log-return|]
Variable
Coef
s.e.
t-value
P-value
Constant
-0.654
0.102
-6.395
0.0000
|log-return|
-133.370
9.356
-14.255
0.0000
I(right-tail)
0.134
0.137
0.980
0.3273
|log-return|*I(right-tail)
3.957
12.427
0.318
0.7503
Hurst exponent (of daily return price)
12-day
24-day
48-day
96-day
0.718
0.774
0.557
0.368
(click to enlarge)

Before considering assets for portfolio construction, it is helpful to characterize whether the log-return distribution is left or right tail dominant, and how persistent the price return time series is. Certainly, the fundamentals concerning valuation, surprises in future earnings growth, economic moat, and shocks from geopolitical or legal events may drastically change price return characteristics. As usual, there are other ways to study risk and stability of times series; however, emphasis on right-tail dominance and greater Hurst exponents may minimize risk and increase stability in the near term. Additional unbalanced and quarterly-rebalanced 2-,5-, and 10-year portfolios for the Dow 30, Vanguard Funds, Fidelity Funds, dividend assets, volatilty (collar) assets, commodities, sector ETFs, and gold stocks are provided at RandomMatrixPortfolios. Readers interested in detailed algorithms and computational aspects of correlation and covariance matrices, eigendecomposition, the Marčenko-Pastur limit distribution of eigenvalues for a random matrix, component subtraction for the RES, MP, and RESMP methods, and covariance matrix shrinkage techniques can refer to chapters 12 and 28 of a new book on machine learning and computational intelligence approaches to pattern discovery and classification.
Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.