https://marketwatch.creatavist.com/story/7571
Mile wide, inch deep
Bond market liquidity dries up
Mile wide, inch deep
Bond market liquidity dries up
Brownian movement 涨落与耗散过程
生物仿生原理与应用 - 厦门大学生物仿生与软物质研究院
3.2.2 涨落—耗散定理
方程(3.31)及(3.37)中的“扩散系数”
/ B D k T , (3.38)
其中 是表征系统微观分子的“涨落”引起的粘滞(或者摩擦),即Brownian
粒子的扩散过程是由于液体分子的涨落过程引起的阻尼过程。而阻尼本质上是
耗散过程。关系式(3.38)将涨落与耗散过程联系在一起,所以被称为“涨落—
耗散定理”。
多数情况下(除热等离子体外),等离子体中的电子温度和离子温度相差很大,整体来说是远离平衡的体系。
一般认为,粒子间的相互碰撞是输运现象的微观过程。但是在等离子体中,
由于长程的电磁相互作用及大量运动模式的存在,波对带电粒子的散射成为输
运过程的重要原因——在很多情况下,甚至是主要原因。因此导致“反常”的
输运、耗散。这也是非平衡态等离子体物理所要研究的重点之一。
2.1 Boltzmann 方程
基于“气体是由大量相互作用的粒子构成的”这一模型,非平衡态统计物理
学的先驱Ludwig Boltzmann在19世纪下半叶发展起来了描述微观粒子在速度
空间的分布函数满足的方程:Boltzmann 方程。
这个方程的推导见于统计物理的教科书。我们在这里直接给出最后的结果:
速度分布函数 f (x, v,t)满足的方程
( , , )
c
f t f
t m t
v F x v
x v
, (2.01a)
其中的 Boltzmann 碰撞项
1 1 1 ( )
c
f d d f f f f
t
v , (2.01b)
这里的 d 是碰撞立体角元, 是碰撞散射截面。这就是著名的Boltzmann 积
分—微分方程。在推导这个方程时,我们假设了:1)二体碰撞(忽略了三体及
多体相互作用与关联,Boltzmann 用的是“稀薄气体”);2)短程相互作用——
Boltzmann 用的是“刚球模型”; 3)“分子混沌性”——碰撞过程中两个粒子
的分布是是相互独立的,即碰撞过程只与双粒子的分布12 1 2 12 f f f G 中的 1 2 f f
有关,而与粒子间的关联无关。
2.2 H 定理与熵
Boltzmann 方程的最重要的贡献是通过H 定理证明了热力学第二定律——
发展的时间箭头。而热力学第二定律不仅在物理学和自然科学中,而且在社会
科学领域里也有重要应用。我们下面就来证明H 定理。
Boltzmann 在1872 年引进这样一个H 函数:
H dxdv f (x, v,t) ln f (x, v,t) 。 (2.02)
将这个 H 函数对时间求全微分,并利用Boltzmann 方程,并假设积分域的边界
时绝热的,我们得到下面的关系式:
1 1 1 1 1
1 ( )(ln ln )
4
dH d d d d f f f f f f f f
dt
x v v 。 (2-03)
因为被积函数的两个因子 1 1 ( f f f f )和 1 1 (ln f f ln f f )的符号总是相同的,所以
总有
dH 0
dt
。 (2-04)
这里等号只有在 1 1 f f f f 的情况下成立。
这就是著名的 H 定理:在孤立体系中,分布函数的辩护总是使得H 函数减
小,除非体系已经达到这样一种平衡状态——分子间的碰撞不再引起分布函数
的变化。
从 H 定理可以知道,H 函数具有描述系统演化时间箭头的性质,即具有“熵”
的性质。通过与热力学熵的比较,Boltzmann 得到在第一性原理意义上的“熵”
的定义:
2.3 细致平衡原理
H 定理和热力学第二定律的微观第一性原理证明引起物理学界的争论:既然
Boltzmann 方程具有宏观不可逆性质,那么作为其出发点的微观物理规律的可
逆性呢?
细致平衡原理告诉我们 Boltzmann 方程的微观可逆性:
1 1 f f f f 。 (2.07)
也就是说,如果 dt 时间段的元碰撞引起的分布函数变化
( )
1 1
f c f f ddxdtdvdv
与相同时段反元碰撞引起的分布函数变化
( )
1 1
f i f f ddxdtdvdv
相等,则我们说体系处于“细致平衡”状态。而这个状态就是平衡态。即体系
达到平衡状态的充分必要条件是达到“细致平衡”——这就是细致平衡原理。
[PDF]非平衡态统计物理导论 - 北京大学物理学院
...
Brownian movement 涨落与耗散过程
生物仿生原理与应用 - 厦门大学生物仿生与软物质研究院
rwz.xmu.edu.cn/a/yanjiulingyu/
轉為繁體網頁
结冰必须由水中的水纳米级颗粒的引发,抗抗冻蛋白抗冻机理是由于抗冻蛋白对纳米颗粒界面阻隔结冻引起的。 ..... (C) 在形成稳定核之前,成核团蔟的涨落。 .... 生物化学中基本的质量作用定律和细致平衡定理都不能适用于局域钙信号的模型研究中。轉為繁體網頁
3.2.2 涨落—耗散定理
方程(3.31)及(3.37)中的“扩散系数”
/ B D k T , (3.38)
其中 是表征系统微观分子的“涨落”引起的粘滞(或者摩擦),即Brownian
粒子的扩散过程是由于液体分子的涨落过程引起的阻尼过程。而阻尼本质上是
耗散过程。关系式(3.38)将涨落与耗散过程联系在一起,所以被称为“涨落—
耗散定理”。
多数情况下(除热等离子体外),等离子体中的电子温度和离子温度相差很大,整体来说是远离平衡的体系。
一般认为,粒子间的相互碰撞是输运现象的微观过程。但是在等离子体中,
由于长程的电磁相互作用及大量运动模式的存在,波对带电粒子的散射成为输
运过程的重要原因——在很多情况下,甚至是主要原因。因此导致“反常”的
输运、耗散。这也是非平衡态等离子体物理所要研究的重点之一。
2.1 Boltzmann 方程
基于“气体是由大量相互作用的粒子构成的”这一模型,非平衡态统计物理
学的先驱Ludwig Boltzmann在19世纪下半叶发展起来了描述微观粒子在速度
空间的分布函数满足的方程:Boltzmann 方程。
这个方程的推导见于统计物理的教科书。我们在这里直接给出最后的结果:
速度分布函数 f (x, v,t)满足的方程
( , , )
c
f t f
t m t
v F x v
x v
, (2.01a)
其中的 Boltzmann 碰撞项
1 1 1 ( )
c
f d d f f f f
t
v , (2.01b)
这里的 d 是碰撞立体角元, 是碰撞散射截面。这就是著名的Boltzmann 积
分—微分方程。在推导这个方程时,我们假设了:1)二体碰撞(忽略了三体及
多体相互作用与关联,Boltzmann 用的是“稀薄气体”);2)短程相互作用——
Boltzmann 用的是“刚球模型”; 3)“分子混沌性”——碰撞过程中两个粒子
的分布是是相互独立的,即碰撞过程只与双粒子的分布12 1 2 12 f f f G 中的 1 2 f f
有关,而与粒子间的关联无关。
2.2 H 定理与熵
Boltzmann 方程的最重要的贡献是通过H 定理证明了热力学第二定律——
发展的时间箭头。而热力学第二定律不仅在物理学和自然科学中,而且在社会
科学领域里也有重要应用。我们下面就来证明H 定理。
Boltzmann 在1872 年引进这样一个H 函数:
H dxdv f (x, v,t) ln f (x, v,t) 。 (2.02)
将这个 H 函数对时间求全微分,并利用Boltzmann 方程,并假设积分域的边界
时绝热的,我们得到下面的关系式:
1 1 1 1 1
1 ( )(ln ln )
4
dH d d d d f f f f f f f f
dt
x v v 。 (2-03)
因为被积函数的两个因子 1 1 ( f f f f )和 1 1 (ln f f ln f f )的符号总是相同的,所以
总有
dH 0
dt
。 (2-04)
这里等号只有在 1 1 f f f f 的情况下成立。
这就是著名的 H 定理:在孤立体系中,分布函数的辩护总是使得H 函数减
小,除非体系已经达到这样一种平衡状态——分子间的碰撞不再引起分布函数
的变化。
从 H 定理可以知道,H 函数具有描述系统演化时间箭头的性质,即具有“熵”
的性质。通过与热力学熵的比较,Boltzmann 得到在第一性原理意义上的“熵”
的定义:
2.3 细致平衡原理
H 定理和热力学第二定律的微观第一性原理证明引起物理学界的争论:既然
Boltzmann 方程具有宏观不可逆性质,那么作为其出发点的微观物理规律的可
逆性呢?
细致平衡原理告诉我们 Boltzmann 方程的微观可逆性:
1 1 f f f f 。 (2.07)
也就是说,如果 dt 时间段的元碰撞引起的分布函数变化
( )
1 1
f c f f ddxdtdvdv
与相同时段反元碰撞引起的分布函数变化
( )
1 1
f i f f ddxdtdvdv
相等,则我们说体系处于“细致平衡”状态。而这个状态就是平衡态。即体系
达到平衡状态的充分必要条件是达到“细致平衡”——这就是细致平衡原理。
[PDF]非平衡态统计物理导论 - 北京大学物理学院
www.phy.pku.edu.cn/~fusion/forum/download.php?id...
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倒易关系是“细致平衡定理”的“宏观”体现——在线性近似下,非平衡态体 ... 将微观物理量的涨落与宏观的耗散联系起来,是非平衡态统计物理的基石之一。 在Einstein轉為繁體網頁
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qikan.cqvip.com/article/detail.aspx?id=26636810
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[PDF]第八期 - 中国流变学学会-- Chinese Society of Rheology
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rwz.xmu.edu.cn/a/yanjiulingyu/
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结冰必须由水中的水纳米级颗粒的引发,抗抗冻蛋白抗冻机理是由于抗冻蛋白对纳米颗粒界面阻隔结冻引起的。 ..... (C) 在形成稳定核之前,成核团蔟的涨落。 .... 生物化学中基本的质量作用定律和细致平衡定理都不能适用于局域钙信号的模型研究中。轉為繁體網頁
[PDF]基于内变量热力学的黏弹性本构方程及其基本性质研究 - 中国 ...
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A new reality
Dan Fuss likes to describe the structure of the corporate bond market as resembling an ice cream sandwich: bonds change hands between the two crispy wafers on either side, but there’s a fluffy layer in between that facilitates each transaction.
“It’s a good sandwich if there’s a whole bunch of ice cream on the inside,” says Fuss, a bond market veteran who runs the $21.9 billion Loomis Sayles Bond Fund. But in recent years, that creamy inner layer, commonly known by the less appetizing title of “dealer,” has been melting.
Dealers were once powerful arms of Wall Street’s biggest investment banks, such as Merrill Lynch, J.P. Morgan and Lehman Bros. They used their large trading desks to make markets for investors to buy and sell securities. But the shifting roles of these large banks since the financial crisis, often pinned on financial regulations like the Volcker Rule, has caused a steep drop in the volume of debt securities these investment banks hold.
The cushion protecting fixed-income investors from market shocks, particularly in the $6.6 trillion corporate bond market, is melting, which is creating a new form of risk when it comes to buying these securities. In response, investors are reevaluating how they hold bonds sold by companies from Apple Inc. to Ford Motor Co. to DreamWorks Animation, as well as reshaping how they interact in the secondary trading market. The changes have served as a key factor eroding the traditional conviction that the bond market shields investors from risk.
Liquidity drought
Created by Terrence Horan
The financial crisis forced the surviving Wall Street banks to reduce risk in a hurry. Many have downgraded their roles as market-makers for corporate bonds, taking fewer bonds onto their books for future sale. Market participants blame the constricting regulatory forces of capital requirements and the post-crisis Volcker Rule. Regulators have pinned the blame back on the banks, which raced to shed less-liquid assets even before regulations were enacted.
At the same time, a surge in new bond sales has increased the size of the market even as dealers, the key facilitator to helping those bonds change hands in the secondary market, have become less willing to handle them. The result is a bond market which is flush with new securities but hobbled when it comes to pricing and trading these securities after the initial sale. As liquidity evaporated in the wake of the financial crisis, it has adjusted the way large asset managers hold and trade bonds, which then impacts the retail investors who put money into mutual and exchange-traded funds (read one institutional investor's story). Here's what's at stake:
- Buyers are paying a premium to own liquid bonds
- Investors who need to sell bonds in a hurry are finding less stable prices
- A chaotic exit from the bond market could cause yields to spike and portfolio values to drop
These market shifts are set against the backdrop of a widespread fear that investors will leave the bond markets en masse as interest rates rise. Concerns about low bond-market liquidity mounted this summer as investors ditched bonds in what bond guru Jeffrey Gundlach has called a liquidation cycle (see what investors were saying at the time). The 10-year Treasury note yield spiked by more than 1.3 percentage points over the summer, briefly touching 3%, on concerns about a Federal Reserve wind down of its bond-buying stimulus program, which was announced last week. The benchmark note traded near 3% on Dec. 27.
The summer bond selloff propelled the corporate bond market to a brief correction characterized by wild movements in prices, though investment-grade prices rapidly recovered. If an event in the credit or rates market provokes another panicked rush to the exits, without the help of dealers as a cushion, it could strain the market and further exacerbate price swings. The fear is that what might have been a moderate selloff could cascade into a rout, sending costs on mortgages and corporate debt sky high.
“I think people have gotten too comfortable, nay complacent, with how this exit process works,” says Tom Murphy, sector leader for investment grade credit at Columbia Management. Investors have piled money into corporate bonds in the years since the financial crisis, but that could translate to chaos if sentiment reverses all at once.
But there’s always a silver lining, and the liquidity struggles facing the market may finally be heralding a broader discussion about whether and how the bond market can better meet the needs of investors. Buyers of debt would ideally like to be able to trade large blocks of bonds quickly and cheaply. The holy grail for many investors is something akin to the way equities trade: in high volumes with tight differentials between the price of a buyer and seller.
Fragmentation
"The market is a mile wide and an inch deep.” — Will Rhode, director of fixed income, TABB Group.
That’s a difficult proposition, if not impossible. The corporate bond market is by nature fragmentary: while a company has one ticker symbol on a stock exchange, that same firm can have dozens of outstanding bonds, each with their own peculiarities. The wide range of differentiation allows companies easier capital markets access and it provides opportunities for investors who can parse the relative value of different issuances. It’s also at the heart of what makes it so hard to ensure a liquid market.
“The market is a mile wide and an inch deep,” says Will Rhode, director of fixed income at research firm TABB Group.
With liquidity making trading more difficult in the corporate bond market, there’s a growing recognition that a solution is needed, and that it may have to go beyond simply adjusting the point of interaction between dealers and investors. The whole market may need to evolve -- from standardizing the way bonds are issued to funneling the market toward a new trading structure.
The issue has long been top-of-mind among market insiders, but isn’t as widely discussed among the vast pool of investors who buy into the bond market for its perceived security. MarketWatch interviewed a range of corporate bond market participants in recent months to assess the origins of this shift, the reconsideration of trading strategies that it’s spurred among bond investors, and a possible path towards a better functioning bond market.
The dealer folds
Before the financial crisis, dealer market-making held a powerful place in the nation’s biggest investment banks. The fresh-out-of-college traders that shuffled in and out of Manhattan bank buildings each day handled the banks' inventories of bonds worth hundreds of millions of dollars, which they used as starting capital to make their own trades, says Lawrence McDonald, a former Lehman Bros. corporate bond trader. The holdings, which were used to make markets for each type of corporate security, would fit into two categories, or books.
“The front book is the facilitation book. That’s the book for client liquidity. The back book is your prop position. That book was responsible for a lot of profits on the Street in 2007, and that today pretty much doesn’t exist,” said McDonald, who authored A Colossal Failure of Common Sense, a bestseller about the bank's demise.
That system crumbled in the years after the financial crisis. The facilitation books shrank in size while the proprietary trading books became virtually non-existent. Dealer balance sheet sizes fell to a fraction of what they once were.
The smaller amount that dealers hold on their books means they can’t unconditionally buy bonds that investors are trying to sell, especially in large blocks. But there’s another issue at play: the low interest-rate environment that characterized much of the post-crisis economy has brought many new issuers into the market. New corporate bond sales have surged as issuers rushed to take advantage of still attractive rates and investors sought the relatively higher income of corporate debt.
The combination of smaller holdings by dealers and a surge in the amount of outstanding corporate debt suggests that there’s more inventory to change hands with fewer institutions willing to facilitate those transactions. Whereas dealers once held about 4% of all outstanding corporate debt on their balance sheets, they now hold closer to 0.5%, according to Oliver Randall, a professor of finance at Emory University, who has done research on corporate bond market liquidity (see more about his research).
Even as most sides recognize there’s a lack of liquidity in the market, there’s a fundamental disagreement about what caused it. Market participants are quick to point to new regulations that limit proprietary trading by dealers and increase the amount of reserves required to be held by banks. In that sense, the liquidity drought has provided ammunition for critics who believe financial reform has been destructive to the markets. But government officials are equally quick to suggest that banks have become less tolerant of risk.
The Volcker Rule was passed as part of the Dodd-Frank financial reform bill in 2010. It banned banks from trading securities with their own money, or proprietary trading. The rule has become one of the more controversial pieces of the regulatory regime, even though the final regulations were only laid out in early December. Nonetheless, banks had already wound down their proprietary trading operations in anticipation of the rule taking effect, and market participants say the lack of clarity about how much of dealers' standard trading activity would be considered proprietary further cut into their market-making ability ahead of the release of the final regulations (read NYSE CEO Niederhauer's take on the Volcker Rule and bond markets) .
The other focal point of regulatory reform is the Basel III capital regulations, which force banks to hold higher levels of reserves as a buffer against the type of bank leverage that expedited Lehman's fall into bankruptcy and kicked off the financial crisis. It’s making the dealer arms of banks less able to deploy capital to make markets in corporate bonds, market-makers told Treasury officials .
Lawmakers have cited broader shifts in trading practices as possible reasons for the decline in market-making ability.
New York Federal Reserve economists did research on the summer 2013 bond selloff, looking at how market-making ability changed as investors left the bond market as a whole. They concluded that even though dealers stepped back from their roles as intermediaries during the selloff, the dealers for whom there was more regulatory breathing room to take on risk actually took less risk. That indicated market-making ability was driven less by capacity limitations from regulations, and more by self-imposed limits on risk.
Finger pointing aside -- and excluding other reasons, such as hesitancy of trading outside the benchmarks set by pricing-disclosure platform Trace -- there tends to be a widespread recognition that the historic ability to take on risk has evaporated, forcing a shift in the way investors trade bonds. The bottom line, says Fuss of Loomis Sayles, is that it’s, “rules, both written and internal, as to the risk [dealers] can take carrying inventory.”
Investors play their hand
The total amount of trades in the high-grade corporate bond market has actually increased in the last five years, which seemingly contradicts the idea that liquidity is drying up. But alongside that rise, trade sizes have shrunk markedly, indicating that investors trying to route their trades through Wall Street have had to break up their trades to accommodate smaller balance sheets.
This change has given small firms an unusual advantage on Wall Street, where mammoth investors often have an edge because of their size.
Trade size
“I haven’t seen any problems with liquidity, but the size I trade in isn’t really a problem.” — Chris Keith, Adviser Investments
Chris Keith manages portfolios for individuals at Newton, Mass.-based Adviser Investments, which has roughly $2 billion in assets under management. When he’s in the market, he’s trading in smaller quantities than the major asset managers, which means he doesn’t risk overwhelming the Street with his inventory.
“I haven’t seen any problems with liquidity, but the size I trade in isn’t really a problem,” Keith said. “I think it’s when you have bigger trades, you get a concern there.”
For larger investors, another trick to circumvent liquidity issues is to deal in more liquid synthetic securities such as derivatives contracts, which can be used to bet on the credit quality of a company without having to deal with the same liquidity problems of the bond market.
Douglas Peebles, chief investment officer and head of AllianceBernstein fixed income, says he finds himself using more derivatives. These allow buyers to invest in the same underlying assets, but in many cases, they can be assured of more liquidity that the actual bond. Bond guru Bill Gross, who runs the world’s biggest bond fund, also concedes that he has begun using derivatives in his Pimco Total Return Fund.
Peebles has also shifted the way his trading desk works. His traders now have experience in independently pricing the debt securities they’re looking to buy and sell, reducing reliance on dealers to provide fair prices for trades.
“Before, you could go into the marketplace, and go ask five guys for the price of a bond, and get five similar prices. Now, we need to know the price,” he said.
Assessing the inherent value of a bond also includes knowing the price premium of liquidity. There's a growing gap between which bonds are liquid and which ones aren't, so the more liquid a bond is the higher the price tends to be, and the lower the yield.
A November Goldman Sachs report estimates that the premium that a bond pays over Treasurys is roughly 10% larger when a bond is illiquid, a large increase over pre-crisis levels. Shown the other way, liquid bonds on average yielded about 0.1 percentage points less between 2011 and mid-2013, according to BlackRock. That may not seem like much, but in a low-rate environment, every basis point counts over the life of a bond.
As investors adjust to this environment, innovation is beginning to take shape. Electronic-trading networks, which provide a more efficient connection between investors and dealers as well as other investors, have been slowly catching on (Read about MarketAxess as a case study). Such platforms run the gamut: some simply connect an investor to a dealer in a computerized equivalent of a phone call, while some open up the possibility of trading between all investors and all dealers at the same time.
Market participants have also been gravitating toward a variety of new market structures that redefine how corporate bonds trade (Rhode, of Tabb Group, puts these new structures into three groups).
The bottom line is that bond investors are getting used to the idea that liquidity has dried up. And here’s where the rubber meets the road. If all is calm in the bond market, with dependable and reliable flows into and out of bond funds, investors can methodically work around the issue. In that sense, a robust secondary market is simply a luxury.
But if there’s a mass exodus from the market, a functioning mechanism to trade bonds is necessary. Retail investors pulled money from corporate bond funds over the summer of 2013, forcing the sale of underlying assets, as the Federal Reserve contemplated scaling back its bond-buying program. When big bond investors had to sell into a down market, inconsistencies in the pricing became more exaggerated (See how investors fled bond funds this summer ).
The 10-year Treasury note, a benchmark often used to price sectors of the corporate bond market, recently traded near its highest level in over two years, though the corporate bond market recovered quickly from the summer selloff. If that sentiment again reverses -- a subject of much discussion due to shifts in monetary policy as well as any number of other market factors (see: the Great Rotation debate) -- a healthy trading mechanism is a necessity.
A solution may prove difficult because the bond market itself is fragmented, with issuers of many different sizes each selling specific types of debt. That was the case long before the financial crisis, but in the end the whole market may need to evolve, says Richard Prager, head of trading and liquidity strategies at BlackRock. The firm has been testing an internal bond trading platform (Read about BlackRock's Aladdin bond-trading platform). If trading in the bond market is to become like trading in the stock market, the adaptation has to begin with issuers, who could streamline the way they issue debt, with all of the other groups of market participants pitching in.
“This is a journey,” says Prager. “This is not an overnight market structure shift. I don’t know if this a three-year, five-year, or decade-long journey. In the equity market it took a decade to change.”
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