(2)对数收益率的优点 1)多期收益情形,对数多期收益等于单期连续复利的和: (k)=log(1+R(k)=log(1+R)(1+R-)(1+R-) log(1+R)+log(1+R-)+…+og(1+R) 对数收益率使收益率的统计建模更为简单。 2)价格取对数,能够降低数值: 3)价格取对数,能够消除某些过程的非平稳性,既当方差为均值的 某种函数形式时,取对数可以消除这方面的影响,从而得到常数方差。 4)为了估计变量弹性的需要 (3)对数收益率的缺点: 对于投资组合收益Rn=∑vnR,但投资组合的对数收益率不等 于资产的对数收益率的和,即=∑m。当M→0,则→∑v 因此,当我们研究资产之间关系时,一般使用简单收益率;而当研究 收益的跨期行为时,使用对数收益率。 4.剩余收益(收益率溢价) 即考察资产收益和另外一种参考资产(如无风险资产)的收益的 比较,表示为 Zi=Rt-ror, ==rt -ror 这种溢价可以认为是一种套利投资组合,此投资组合中资产为多头 参考资产为空头。因此,净投资为零,所以称为套利投资组合。 (二)风险 1.风险的定义:是指在决策过程中,由于各种不确定因素的作用, 决策方案在一定时间内出现不利结果的可能性以及可能损失的程度。 包括损失的概率、可能损失的数量以及损失的易变性 2.风险的分类
6 （2） 对数收益率的优点： 1）多期收益情形，对数多期收益等于单期连续复利的和： () () ( ) (( )( ) ( )) ()( ) ( ) 1 1 1 1 1 1 log 1 log 1 1 ... 1 log 1 log 1 ... log 1 .... t t t t tk t t tk t t tk rk Rk R R R RR R rr r − −+ − −+ − −+ =+ = ++ + = + + + ++ + =+ + + 对数收益率使收益率的统计建模更为简单。 2）价格取对数，能够降低数值； 3）价格取对数，能够消除某些过程的非平稳性，既当方差为均值的 某种函数形式时，取对数可以消除这方面的影响，从而得到常数方差。 4）为了估计变量弹性的需要。 (3) 对数收益率的缺点： 对于投资组合收益 1 N Rpt ip it = ∑ w R ，但投资组合的对数收益率不等 于资产的对数收益率的和，即 1 N pt ip it r wr ≠ ∑ 。当∆t → 0，则 1 N pt ip it r wr → ∑ 。 因此，当我们研究资产之间关系时，一般使用简单收益率；而当研究 收益的跨期行为时，使用对数收益率。 4．剩余收益（收益率溢价） 即考察资产收益和另外一种参考资产（如无风险资产）的收益的 比较，表示为 Zit it t = − R R0 ， it it t 0 z rr = − 这种溢价可以认为是一种套利投资组合，此投资组合中资产为多头， 参考资产为空头。因此，净投资为零，所以称为套利投资组合。 （二） 风险 1．风险的定义：是指在决策过程中，由于各种不确定因素的作用， 决策方案在一定时间内出现不利结果的可能性以及可能损失的程度。 包括损失的概率、可能损失的数量以及损失的易变性。 2．风险的分类：
1)信用风险 credit risk: The risk of a trading partner not fulfilling his obligations in full on due date or at any time Including aggregation probability of default and expected loss measurements 2)市场风险 Market Risk: an institution 's financial condition resulting from adverse movements in the level or volatility of market prices of interest rate instruments, equities, commodities and currencies. Market risk is usually measured as the potential gain/loss in a position/portfolio that is associated with a price movement of a given probability over a specified time horizon. This is typically known as value-at-risk (VAR) 3)清算风险 Settlement risk: Settlement risk is the risk that a settlement in a transfer system does not take place as expected. settlement risk comprises both credit and liquidity risks The former arises when a counterparty cannot meet an obligation for full value on due date and thereafter because it is insolvent. liquidity risk refers to the risk that a counterparty will not settle for full value at due date but could do so at some unspecified time thereafter; causing the party which did not receive its expected payment to finance the shortfall at short notice 4)其它风险 Other risks: (1)流动性风险 liquidity risk, which comes in two forms. Market liquidity risk arises when a firm is unable to conclude a large transaction in a particular instrument at anything near the current market price Funding liquidity risk is defined as the inability to obtain funds to meet cashflow obligations (2)法律风险 legal risk, which is the risk that a transaction proves unenforceable in law or because it has been inadequately documented; (3)操作风险 operational risk,ie. the risk of unexpected losses arising from deficiencies in a firm's management information, support and control systems and procedures
7 1）信用风险 credit risk：The risk of a trading partner not fulfilling his obligations in full on due date or at any time。Including aggregation, probability of default and expected loss measurements。 2）市场风险 Market Risk：an institution's financial condition resulting from adverse movements in the level or volatility of market prices of interest rate instruments, equities, commodities and currencies. Market risk is usually measured as the potential gain/loss in a position/portfolio that is associated with a price movement of a given probability over a specified time horizon. This is typically known as value-at-risk (VAR). 3）清算风险 Settlement Risk：Settlement risk is the risk that a settlement in a transfer system does not take place as expected. settlement risk comprises both credit and liquidity risks. The former arises when a counterparty cannot meet an obligation for full value on due date and thereafter because it is insolvent. Liquidity risk refers to the risk that a counterparty will not settle for full value at due date but could do so at some unspecified time thereafter; causing the party which did not receive its expected payment to finance the shortfall at short notice. 4）其它风险 Other Risks： （1）流动性风险 liquidity risk, which comes in two forms. Market liquidity risk arises when a firm is unable to conclude a large transaction in a particular instrument at anything near the current market price. Funding liquidity risk is defined as the inability to obtain funds to meet cashflow obligations. （2）法律风险 legal risk, which is the risk that a transaction proves unenforceable in law or because it has been inadequately documented; （3）操作风险 operational risk, i.e. the risk of unexpected losses arising from deficiencies in a firm's management information, support and control systems and procedures