FRM前导课程第一篇

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FRM 前导课程

概率论与统计学

Pre-course4.1 Probability

1. Basic concepts in Probability

A. Random Variable随机变量

A variable whose possible values are uncertain

B. Outcomes结果（随机变量的结果）

The possible values of a random variable

C. Event事件（一系列的结果）

A specified set of outcomes

a. Mutually Exclusive events互斥事件

概率之和＜1。 两件事情不能同时发生（例：投擲骰子A≤3,B＞4）

b. Exhaustive Events 完备事件

概率之和＞1。 事件包含所有结果（例：投擲骰子A≤3,B＞2）

c. 互斥且完备事件

概率之和=1。 （例：投擲骰子A≤5，B＞5）

d. Independent event 独立事件

掷骰子掷两次

2. Unconditional and conditional Probability

Unconditional Probability非条件概率

Conditional Probability条件概率

Independent events独立事件

假如A跟B为independentevents独立事件，P(A/B)=P(A); P(B/A)=P(B)；P(AB)=P(A)*P(B)。 P(A)=要衡量的概率，P(B)=前提条件。

Dependent events非独立事件

Joint Probability联合事件

P(AB)=P(A/B)P(B)

3. The General Addition Rule加法法则

A发生或B发生的概率。 P(A+B)=P(A)+P(B)-P(A and B)非条件概率减条件概率

4. Multiplecation Rule乘法法则

P(A/B) = P(AB) / P(B)。 B发生的情况下，A发生的概率是多少？

5. Total Probability Rule全概率法则

求的是非条件概率！（路径相乘后相加） B1,B2~Bn完备且互斥事件组（概率之和等于1），P(A)=P(AB1)+P(AB2)+...+P(ABn)。 （画树图最方便）

6. Bayes' Formula贝叶斯法则

求的是条件概率。 （分母：路径相乘相加；分子：求的路径） （透过画树图求答案）

7. Combination and Permutation排列组合（区别：是否考虑顺序问题）

是 Permutation排列

否 Combination组合

Pre-course 4.2 Expected Value, Variance, Covariance and Correlation

1. Expected Value平均值，期望值

平均值=发生概率*数值

衡量整体，缺点：不能反应波动情况

衡量平均收益

2. Variance方差

方差衡量数据波动性，数据越大，数据之间波动（风险）越大。 距离平方的平均值。 步骤1. 求均值，2. 相减，3. 平方，4. 乘概率。

衡量风险

3. Standard deviation标准差

（波动率）方差开根号

4. Covariance斜方差

衡量两个资産相关性。 ＞0，两资産正相关（同向变动）；=0，两资産不相关；＜0，两资産负相关（反向变动）。

取值无意义，正负号有意义。 缺点：两资産数据大，得出结果就大。 无法衡量相关的程度。 只能衡量线性关系

衡量相关性

5. Correlation相关系数

消除斜方差取值无意义的情况。 取值范围-1～1。 ρ=1，完全正相关；0＜ρ＜1，正相关； ρ=0，不相关（没有直线关系）； -1＜ρ＜0，负相关； ρ=1，完全负相关。

缺点：只能衡量线性关系

衡量相关性

6. Portfolio组合

Expected Value of a portfolio组合的平均收益

资産1占比*预期收益+资産2占比*预期收益

Standard deviation of a portfolio组合的标准差

Pre-course4.3 basic statistics and return distributions

Statistics

1. Descriptive statistics描述性统计量

拿到数据怎么去描述数据特征？（通过描述得到最基本的特征）

2. Inferential statistics推断性统计量

Simple→populations用样本去推断总体

①Population总体: all members of a specified group ②Sample样本：a subset of a population ③Parameter参数：any descriptive measure of a population characteristic用来描述总体特征的质 ④Sample statistic统计量: any descriptive measure of a sample characteristic用来描述样本的特征 ⑤Frequency distribution频率分布图: tabular display of data summarized into a relatively small number of intervals.数据分组描述数据特征 --❶ Relative frequency distribution相对频率分布：the percentage of dividing absolute frequency of each interval by the total number of observations.（通常%表示) --❷ Cumulative frequency distribution累计频率分布：shows the percentage of observations less than the upper bound of each interval.

3. Arithmetic mean算数平均值

全部数据相加除数据的数量∑

4. Geometric mean几何平均值

全部数据相乘开根号数据的数量（例如：时间加权收益率）

5. Weighted mean 加权平均值

数据加上权重表示，权重之和=1

6. Median中位数

先数据排序，后取最中间的数（not affected by extreme values as arithmetic mean不易受极端值影响）

7. Mode众数

the appears most often出现频率最高的数

8. Quantiles分位数

Cut points dividing the range of a probability distribution into continuous intervals with equal probabilities数据分几等分就是几分位数（例：quartiles四分位数，decile十分位数，percentile百分位数）

9. Variance方差

总体方差及样本方差

10. Chebyshev's inequality切比雪夫不等式

适用范围：任意分布，估计范围，概率范围，均值方差都是已知的情况。 1-1/k²,(k＞1)，（例：1-1/2²=75%）

11. Skewness偏度

Indicating the degree of symmetry of return distributions.衡量分布是否对称。 (Sk=0,symmetrical distribution对称；Sk＞0，positively skewed distribution右偏; Sk＜0, negatively skewed distribution左偏）⊕看长尾巴落在哪~

12. Kurtosis峰度

Leptokurtic尖峰肥尾：Kurtosis＞3, Excess kurtosis＞0； Mesokurtic正态分布：Kurtosis=3, Excess kurtosis=0； Platykurtic低峰薄尾：Kurtosis＜3, Excess kurtosis＜0

Pre-course4.4 Common Probability distribution

1. Distribution of Probability

A. Probability distribution概率分布

Specifies the probabilities of all possible outcomes for a random variable

B. Discrete Random Variable离散随机变量

画表，取值有限且可列无数个（例：掷骰子）

C. Continuous Random Variable连续随机变量

f(x)，取值范围无限多个（例：衡量股票价格或人身高体重）

D. Discrete Distribution离散分布

The distribution of discrete random variable.

E. Continuous Distribution连续分布

The distribution of the continuous random variable.

2. Probability Functions概率函数

A. Probability Function离散型随机变量

①取值的概率0≤P(X)≤1，②∑P(X)=1，画表格列出

B. Probability Density Function (pdf)概率密度函数

f(X)连续型随机变量，都在X轴上方且面积=1，f(x)≥0, P(x)≥0,

C. Cumulative Probability Function (cdf）累积概率函数

离散跟连续都可以计算累积概率，F(x)=P(X≤x)

D. Bernoulli Distribution伯努力分布（离散型）

Bernoulli Trial伯努力实验（例：抛硬币）

只有两种情况，一方概率P, 另一方概率1-P。

Binomial Distribution二项分布

n=实验次数，p=事件发生概率，1-p=不发生概率

E. Continuous Uniform Distribution（连续型）

a. 均匀分布

概率密度函数（PDF）: 取值无限多个，一般找范围。 面积等于1。 取值范围a＜x＜b。 偏度=0。 ∵对称。

累积概率（CDF）: ①F(X)=0,X≤a ; ② F(X)=X-a/b-a, a＜X＜b ; ③ F(X)=1, X≥b。

b. Normal Distribution正态分布

①Symmetric about the mean (skewness=0)，偏度=0 ②Kurtosis(a measure of peakedness),峰度=3。 ③若随机变量X服从一个数学期望为μ、方差为σ^2的正态分布，记为N(μ，σ^2)。 其概率密度函数为正态分布的期望值μ决定了其位置，其标准差σ决定了分布的幅度。当μ = 0,σ = 1时的正态分布是标准正态分布。

一般正态分布转化标准正态分布的过程： Standardizing标准化 Z=X - μ / σ Z分布指的就是标准正态分布 表格给的是：累积概率

c. t-Distribution t分布

①Symmetrical (bell shaped)偏度=0 ②Fatter tails than a normal distribution比正态分布尾巴厚，极端事件概率较大。 ③degrees of freedom (df),自由度，df=n-1, ④As df increase, t-distriburion approaches normal distribution。

d. Longnormal Distribution对数正态分布

①定义式：正态分布经指数变换后即为对数正态分布；对数正态分布经对数变换后即为正态分布。 ②It is positively skewed. 对数正态总是右偏的。(看尾巴），S＞0。 ③Lognormal random variable is bounded from below by zero。取值范围＞0。 ④It is used to model assest price.最适合衡量资産价格。 ⑤正态分布适合衡量收益率，有赚有赔。

Pre-course4.5 Sampling and Estimation 样本推断总体（估计总体）

1. Sample and Estimation

Sample样本（n）

Statistic统计量：描述样本数据的指标。 S²样本方差，S样本标准差，

Population总体(N)

Parameter总体参数：μ总体均值，σ²总体方差，σ总体标准差。

2. Time-Series data and Cross-Sectional Data

Time-Series Data时间序列数据

A sequence of data collected at discrete and equally spaced intervals of time.(例：股票过去30天收盘价。)自己和自己比较

Cross-Sectional Data截面数据

Data st a single point in time.同一个时间段不同指标，自己和其他人比较

3. Simple Random Sampling and Stratified Random Sampling

Simple Random Sampling简单随机抽样

Sampling method that each element of the population has an equal Probability of being selected to the subset.随机抽取，抽到的概率相等。缺点：太过于随机，没代表性，误差大。

Stratified Random Sampling分层抽样

A Sampling method in which the population is first divided into strata.Then a simple Random sample is taken from each stratum. 先分割在抽样,准确些。

4. Sampling Distribution and Sampling Error

Sampling Distribution样本分布

The distribution of sample statistics for repeated samples of size n. N次抽样后把样本汇集起来，所形成的分布。

Sampling Error抽样误差

Any difference between the sample meanand the population mean.用样本估计总体，样本跟总体的误差，估计误差。

5. Central Limit Theorem中心极限定理

Given certain conditions,the arithmetic mean of a sufficiently large number of iterates of independent Random variables, each with a well-defined expected value and well-defined variance,will be approximately normally distributed,regardless of the underlying distribution.描述抽样分布，样本分布服从正态分布。 n＞30,样本均值分布就服从正态分布。

6. Standard Error of Sample Mean

样本均值标准差（标准误）：样本均值/标准差，方差大，误差越大， ①已知总体标准差，标准误=σ/√n （σ总体标准差，n样本大小）。 ②已知样本标准差，标准误=S/√n (S样本标准差，每次抽样的标准差）。 这一系列的样本均值标准差

7. Desireable Properties of Estimators

Unbiased无偏性

The expected Value equals the parameter it is intended.估计量期望等于总体参数

Efficient有效性

The unbiased estimator of the population parameter has a Sampling distribution with smallest Variance.所有满足无偏性估计量中，找一个最有效的，方差最小。 方差越小，估计越准确。

Consistency一致性

The probability of estimates close to the value of the population parameter increases as sample size increases.当样本大小增加时，估计准确性会越好，方差越小越好。

8. Point estimate and Confidence interval

Point Estimate 点估计

一对一的估计，用一个样本均值去估计总体均值。 缺点：抽样误差

Confidence lnterval区间估计

运用正态分布的置信区间， 置信水平：1-α（α：显著性水平) Point estimate（点估计）± Reliability Facot (Z值) * Standard Error（样本均值标准差，整体标准差/√n） 将点估计±标准差 = 区间估计 (例如：90%的置信区间，找1.65倍标准差）

Example

9. Biases on Sampling抽样误差

Data-Mining Bias数据挖掘偏差

Misuse of data referring to the repeatedly "drilling" in the same data until finding the statistically significant patterns.偶然结果当成结论。

Sample selection Bias样本选择偏差

Certain databasesare excludedfrom the analysis. 数据缺失不完整（例：Survivorship Bias生存者偏差：Only Sampling from existing database.只考虑活着的数据，导致高估。 ）

Look-Ahead Bias前视偏差

Using information that was not available on the test date. 用未来的信息来确定今天的交易信号。比如说用当日的最高价格来决定当日的买入信号。实盘里这种信息是不可能取得的。

Time-period Bias时间周期偏差

Based on a time period that may make the results time-period specific.周期太长太短都不好。

Pre-course4.6 Basics of Hypothesis Testing假设检验 样本检验总体（检验总体）

1. Statistical Hypothesis Test统计假设检验

用样本检验总体（均值，标准差，方差）。 之前总体不知道，现在总体知道（已经告诉你了！）。 检验已知总体的值是否正确！

2. Hypothesis and Hypothesis Steps步骤

①State the Motivated (Alternative) Hypothesis Hₐ.想检验的是什么？总体的均值？方差？标准差？ ②State the null hypothesis H₀. ③You select the probability of "error", or the a significance level. α=0.05 or α=0.01.选择判断的标准（显著性水平，小概率水平）不会发生直接省略 ④You choose the size n of the random sample.确定样本的大小 ⑤Select a random sample from the appropriate population and obtain your data. ⑥Calculate the decision rule. ⑦Decision.决策 A) Reject the null Hypothesis and claim that your alternative Hypothesis was correct the difference is significant at a 100% level. B) Fail to Reject the null Hypothesis correct the difference is not significant at a 100% level.

3. Null Hypothesis and Alternative Hypothesis（①互斥且完备事件，②所有等号都放原假设上，③≤，≥，＞，＜：单尾检验 ；=，≠：双尾检验。 ）

Null Hypothesis原假设H₀

（例：原假设身高H₀:均值≥1. 7）

Alternative Hypothesis备择假设Hₐ

我们想要证明的假设（例：想证明身高Hₐ：均值＜1. 7）

4. Two-tailed Tests of Hypotheses 双尾检验假设

原假设H₀: μ=1.7 , 备择假设Hₐ: μ≠1.7 样本均值∽μ 样本均值∽N( μ, σ²/n) 样本均值∽N( 1.7, σ²/n) 假设α=5%，95%双尾，±1.96倍标准差σ/√n 假设拿到样本均值1. 71，属于大概率事件，Not Reject H₀，Hₐ错误 假设拿到样本均值1. 4，属于小概率事件（不会发生），Reject H₀，Hₐ正确

5. One-Tailed Tests of Hypotheses单尾检验假设

H₀: μ≤1.7, Hₐ（拒绝方）: μ＞1.7，找样本均值看落点

6. Type l Error, Type ll Error, Level of significance, Power of test

Type l Error第一类错误

(弃真) Is the incorrect rejection of a true null Hypothesis (a "false positive"),H₀是真时，我们却拒绝了它。

子主题

Type ll Error第二类错误

(取伪) Is the failure to Reject a false null Hypothesis (a "false negative"), H₀是错误时，我们却没有拒绝它。

Power of Statistical test 检验势

The probability of power of test is equal to (1-β），P( power of test)= 1-P (type ll Error)

7. P-Value and its Application in Hypothesis Testing p值法

原假设发生的概率（例：H₀: μ=1.7 , Hₐ: μ≠1.7） If P-value=4% ＜α=5% ：Reject H₀

8. Hypothesis Test Concerning a Single Mean

Test statistic for Hypothesis Tests of population mean With Variance （左 known） ； （右unknown）

金融市场简介

Pre-course 7.1 introduction to Financial Market

Definition of Financial Markets

A Financial market is a market in which people trade financial securities and derivatives at relatively low transaction costs. 是指由货币资金的借贷、金融工具的发行与交易以及外汇资金买卖等所形成的市场，是资金供求双方运用各种金融工具、通过各式各样的金融交易活动，实现资金余缺的调剂的场所。

Summary of Classification of Financial Markets

Classification by nature of claim未来求偿权

A claim to a stream of payments in the future.对未来现金流索取的权利

Debt market 债务市场（债权债务关系）

Interest payment and face value at maturity到期时得到利息及本金

Coupon securities付息债

Make interest payments- usually semiannually.

Zero-coupon零息债

①make no interest payments 到期前不支付利息 ②sold at price well below face Value发行小于面值。

Tax exempt免息债券

Interest earned is not taxed利息收益不用课税，一般指国债。

Perpetuals永续债券

Bond with no maturity date, pay interest forever。 债券无到期日，永远支付债券利息。

Equity market股票市场（股票分红，股票价值对企业的求偿权）

Dividends and sales price when sold得到企业未来分红及卖出股票得到的价值

Stock represents ownership

Stockholders股东

Owns part of the corporation and receives dividends from the issuer公司的所有者，分红给股东

Capital Gains资本利得

Difference between price initially and amount received when stock is sold买卖价差

Types of stock分类

Preferred stock优先股（特别股）

Fixed dividends, priority over common stock优先取得分红权利，固定分红。

Common stock普通股

Variable dividends,base on company's profits。 不固定分红，取决于企业收益。

Convertible可转股

Preferred stock that can be converted into common stock at a stated price。 优先股以预先设定好的价格转成普通股

Classification by maturity of claim到期时间求偿权

Money market 货币市场（＜1年）

The Money market

Exchange of short-term instrument (less than one year)小于一年的短期工具（特点：高流动性，低风险）

U.S. Treasury bills美国国库券

美国国债 发行时间小于1年： Bill 发行时间1~10年：notes 发行时间10年以上： Bond

Short-term debts of US government

Bank Certificate of Deposits存单

Liabilities of issuing bank,interest bearing to corporations that hold them定期存款，发行人银行

Commercial paper商业票据

Short-term liabilities of prime business firms and finance companies发行人：企业

Federal Funds联邦基金

Exchange of excess / deficient reserves between banks on an overnight basis银行之间进行相互借贷

Capital market资本市场（＞1年）

The capital market

Exchange of long-terms securities (more than one year)资本市场大于一年的长期证券

Stock market股票市场

Largest part of capital market and held by private and institutional investors组成企业的大部分资本结构都是透过发行股票

Corporate bond market公司债

Held by insurance companies, pension and retirement funds公司债通常由保险公司，养老金，退休基金购买

Local and state government bonds地方政府债

Primarily held for tex-exempt feature免税的债券

Government securities

Held by commercial banks, the Fed,individual Americans/foreigners,and dealers商业银行，美国人，外国人，贸易商等都会去购买

Classification by seasoning of claim新旧程度求偿权

Primary market一级市场（新股发行市场）

①Market for issuing a new security and disrtibuting to saver-lenders新的债权债务关系，(IPO首次公开发行) ②investment Banks- information and marketing specialists for newly issued securities.参与方: 投资银行投行部门 承销发售

Secondary market二级市场（股票流通市场）

Market where existing securities can be exchanged (over-the-counter market OTC市场，场外交易)投资者与投资者间相互交易已经存在的金融産品

By immediate delivery of future delivery当下交割与否

Cash or spot market现货或即期市场

Buyers pay the market price for securities, currency, or commodities on the spot, just as you would pay cash for groceries or other consumer products.一手交钱一手交货，股票交易所

Derivative market远期市场（衍生品市场）

Contractual agreement between two parties to exchange an asset in the future at a stated price现在约定价格好在未来时间点来对商品交割

Derivative financial instruments衍生金融産品

Derive value from underlying assests透过标的资産衍生的金融産品（例：股票做标的资産派生衍生品股票期货）

Long多头

Buyer of the contract, receivecommodity in the future买入衍生品的合约

Short空头

Seller of the contract, provide commodity in the future卖出衍生品合约

Speculators投机者

Gamble on price fluctuations and hope to profit

Hedgers对冲者

Eliminate the risk of price fluctuations对冲自己手头风险

Classification by organizational structure市场交易机制

Auction market 竞价市场

Is one where buyers and sellers enter competitive offers at the same time ; matching bids and offers are paired together and executed.价格配对成功即可撮合成交 （Bid兢买：the price of a buy willing to pay） （Ask兢卖：the price of a sell willing to receive）

Over-the-counter market OTC市场，柜台交易，场外交易市场

Is a decentralized market (without a central physical location),where market participants trade with one another through various communication modes such as the telephone,email,and proprietary electronic trading systems 去中心市场，通过电话邮件方式交易

dealers交易商，act as market-makers by quoting prices at which they will buy and sell a security,currency,or other financial products报价交易商品，赚取中间价差

A trade can be executed between two participants in an OTC market without others being aware of the price at which the transaction was completed AB之间的交易，行为不用被披露出去

Typically less transparent than exchanges and are also subject to fewer regulations 整体透明度不高，监管较不严

Intermediated market中间人市场

Is a market or a situation in which one or more financial institutions stands in between counterparties in a financial transaction中介

Classification by types of instruments

Stock markets

Bond markets

Commodity markets

Money markets

Derivatives market

Futures markets

Insurance markets

Foreign Exchange markets

Economic Function of financial markets

Interactions of buyers and sellers determines price

Interactions of buyers and sellers determines price买卖双方供需决定价格

Price discovery process价格发现者

Provides a mechanism to sell提供卖的机制

Liquidity流动性

Reduces transaction costs降低融资交易成本

Search cost寻找资金成本

Information costs讯息成本

Pre-course 7.2 Financial intermediaries金融中介机构

Role of financial intermediaries中介机构的角色

Act as agents in transferring funds from savers-lenders to borrowers-spenders资金提供方的钱转移到资金需求方里

Acquire funds by issuing their liabilities to public and use money to purchase financial assess 从投资者那发行负债，筹集资金，并将钱拿来购买金融资産

Earn profits on difference between interest paid and earned

Diversify portfolios and minimize risk分散化投资策略降低风险

Lower transaction costs交易成本降低

Competition lowers interest rates beneficial to economic growth相互竞争压力利率，有利企业成长

Commercial Banks商业银行

Most prominent financial institution最常见的金融机构

Range in size from huge to small

Major sources of funds银行资金来源

Used to be demand deposits of public 向公众吸收活期存款

Also accept savings and time deposits定期存款

Now rely more on "other liabilities"

Uses of funds资金用途

Short-term government securities购买短期国债

Long-term business loans企业长期贷款

Home mortgages房贷

Investment banks

Is a financial institution that assists individuals, corporations, and government in raising financial capital by underwriting or acting as the client's agent in the issuance of securities 等于国内证券公司，帮助个人或者企业筹集资金，通过承销和发行证券的方式筹集资金

Activities

Management buyouts管理层杠杆买断

Initial public offerings IPO首次公开发行

Cross-border transaction跨境交易

Valuation and Fairness Opinions估价和公平意见

Raising Debt and Equity Capitial

Bank's own investments

Mergers and acquisition企业兼并与收购

Research and analysis

Corporate finance企业融资

Corporate restructurings

Life Insurance Companies人寿保险

Insure against death保人健康生命

Receive funds in form of premiums收取保费

Use of funds is based on mortality statistics -predict when funds will be needed死亡率统计指标精算，理赔需支付多少钱，倒推保费收取金额

Invest in long-term securities -high yield购买长期资産，可以产生较高收益

Long-term corporate bonds购买长期公司债

Long-term commercial mortgages购买长期商业贷款

Property and Casualty Insurance Companies财产保险

Property insurance财产保险

Insure homeowners and business against losses or damage caused by various perils危险.(i.e. fire, lighting, windstrom or tornado)对财产的损失进行保险，

Liability Insurance责任险

Covers the insured's legal liability arising out of property damage or bodily injury to others第三者责任险

①Property and casualty Insurance = property and liability Insurance财产伤亡险=财产责任险 ②Receive premiums收取保费 ③Need to be fairly liquid due to uncertainty claims保持流动性因为有些不确定的求偿 ④Purchase a variety of securities High-grade stocks and bonds 购买高评级股票债券 Short-term money market instruments for liquidity购买短期货币市场基/産品

Pension and Retirement funds养老金退休金

Pension funds are investment pools that pay for employee retirement commitments承诺事项. Funds are paid for by either employees, employers, or both.企业给员工开设养老金跟退休金帐户，受益者为雇主及员工

Concerned with long run关注长期收益

Receive funds from working individuals资金来源企业个人

Prediction of future use of funds预测未来资金使用

Invest mainly in long-term corporate bonds and high-grade stock投资于长期公司债和高评级股票

Mutual funds共同基金

Is an investment vehicle made up of a pool of money collected from many investors for the purpose of investing in securities such as stocks,bonds,money market instruments and other assets.是一种投资工具，由许多投资者收集的资金组成，用于投资股票，债券，货币市场工具和其他资产等证券。类似我国公募基金

Are operated by professional money managers, who allocate the fund's investment and attempt to produce capital gainsand/or income for the fund's investors.专业基金经理做投资决策，基金经理做分配而产生资本利得及收益

A mutual fund's portfolio is structured and maintained to match the investment objectives stated in its prospectus募股章程 共同基金投资目标与投资招募说明书相匹配

Investing in wide variety of securities may diversify risks投资多种类型産品以分散化风险

Money market Mutual Funds货币市场共同基金

Fund invests in highly liquid short-term money market instruments投资高流动短期金融産品

Large-size negotiable CD's可转让存单

Treasury bills一年内到期美国国债

High-grade commercial paper企业商业票据

Hedge funds对冲基金

Is an investment fund that pools capital from accredited individuals or institutional investors and invests in a variety of assets, often with complex portfolio construction and risk-management techniques.面向机构投资者或资质跟净值高的投资者，会做非常复杂的投资策略

Hedge fund are made available only to certain sophisticated or accredited investors and cannot be offered or sold to the general public对冲基金对老练/被认可的投资者募资，不对社会公众公开募资

Private Equity私募股权

Private equity typically refers to investment funds organized as limited partnerships that are not publicly traded and whose investors are typically large institutional investors, university endownments, or wealthy individuals. 私募股权通常是指由有限合伙制组织的投资基金，这些合伙制不是公开交易的，其投资者通常是大型机构投资者，有钱人。

Savings and Loan Associations( S and L 's) 存贷机构

Traditionally acquired funds through savings deposits资金来源，吸收存款

Used funds to make home mortgage loans 吸收存款后，进行买房抵押贷款发放

Now perform same functions as commercial banks类似商业银行

Issue checking accounts支票业务

Make consumer and business loans消费者 企业发放贷款业务

Commercial and consumer Finance Companies商业和消费者金融公司

Consumer finance companies are those that help consumer finance a purchase of receive loans for various purposes商业贷款给消费者提供融资去购买消费者想要买到的商品

Acquire funds primarily by selling short term loans(commercial paper)资金来源发行短期票据去筹集资金

Lend money for consumer purchases or business firms to fiance inventories资金用途给消费者或者企业购买商品

Finance companies are more willing to accept risky customers than commercial banks比银行更愿意承担更多风险

Credit Unions信用社信用联合

Organized as cooperatives for people with common interest合作性团体是一帮有共同利益的团体

Members buy shares (deposits) and can borrow会员入股来成立信用社

Changesin the law in 1980 broadened their powers

Checking (share) accounts支票

Make long-term mortgage loans长期贷款

固定收益类投资基础

Pre-course 9.1 Introduction to Bonds

1. Fixed-income fundamentals

Fixed income security固定收益证券

Issuer(borrower)agrees to make income payments fixed by contract发行人借款人会去支付固定金额给投资人

Bonds债券

Borrow makes interest payments向投资人支付固定利息

Preferred stock优先股

An equity issue with fixed income payments of dividends支付固定股息

Term to maturity 到期时间

Date when debt ceases, with maturity being that exact date 债务到期那天and term 期限denoting 表示the number of years till that date剩余的天数

Par Value (maturity Value, face value)面值

Amount issuer agrees to pay at maturity到期那天债务人承诺支付的金额

Coupon息票

Periodic interest payment made to bondholders每期支付的利息

Coupon rate息票率

Rate of interest usually paid semiannually for U.S. issues; multiplied by par value yields dollar value of coupon每期支付的金额占面值的多少 息票率×面值=每期支付的利息

2. Bond features债券特点

What is bond?

Debt issued by a corporation or a government body由企业或者政府发行者为资金借款人

A bond represents a loan made by investors to the issuer债券代表投资人借钱给发行人的一个凭证

In tern for his/her money, the investor receives a legal claim on future cash flows of the borrower投资人得到对未来现金流(利息及本金)的索取权

The issuer promises to发行人(债务人)承诺

Make regular coupon payments ever period until the bond matures, and pay the face (par) value of the bond when it matures承诺支付定期的利息，到期时支付面值

Default违约

An issuer who fails to pay is subject to legal action on behalf of the lenders( bondholers)债务人未履行承诺支付现金流(未按时未按量),债权人采取法律措施

3. Bond fundamentals债券基本原理

Zero-coupon bonds零息债券

No periodic interest payments; principal and interest paid at term在到期日之前，不支付利息

Floating rate bonds浮动利率债券

Coupon rate is reset periodically定期重新设置利率

4. U.S. Treasury securities美国国债

Bills

Mature in one year or less, issued at a discount到期日小于1年，折价发售

Notes

Matures between 2~10 years, issued as a coupon security期限2～10年

Bonds

Maturities longer than 10 years期限大于10年

Treasury inflation protection securities (TIPS)抗通胀债券

Principal is indexed to CPI with real rate being fixed到期时债券偿还的本金跟CPI(消费者物价指数)挂钩

5. Quotation convention for Treasury bills期限小于一年的国债报价

Yd: 银行贴现率 D:折价金额 F:面值 t:天数

6. Price quotation convention for Treasury coupon securities期限大于一年的债券报价

Notes and bonds trade on a dollar price basis in units of 1/32 of 1% of par($100), 1/32的最小变动价格0. 03125元，(例：quote of 92-14 = 92 and 14/32 ; with basis of $100,000 par value a change in price of 1% = $1000 with 1/32 = $31.25）

7. Stripped Treasury securities本息分离债券

STRIPS : U.S. Treasury program issues these direct obligations of the U.S. government, ending trademark and generic receipts 把该债券的每笔利息支付和最终本金的偿还进行拆分，然后依据各笔现金流形成对应期限和面值的零息债券。零息债券(ZERO-COUPON)是指以低于面值的折扣价出售，在债券存续期间不发生利息支付，到期一次性按面值进行偿还的债券。正如其名字一样，零息债券不是周期性地支付息票利息，其利息是体现在债券的价值随着时间越来越接近到期日而增加，在到期日，债券价值等于面值，按全部面值赎回，债券面值与发行价格之间的差额就是利息总额

Treasury strips( zero-coupons or stripped Treasury securities)

Treasury coupon strips利息打包卖出

Created from the future coupon

Treasury principal strips 本金打包卖出

Created from the principal payment at maturity

8. Federal agency securities美国联邦政府机构债券

Government-sponsored enterprises政府创办企业债券 securities market

Federally related institution 美国联邦政府所属机构发行债券securities markets

Only the Tennessee Valley Authority(TVA) has done so recently, these issues are backed by the full faith and credit of the U.S. government美国政府背书

9. Corporate bonds企业债

The issuer agrees to make coupon payments and repay the principal value of bond at maturity. If the institution cannot pay, it is in default. Bondholders have first claim to the income and assets of a corporation.支付利息及本金在到期的时候， 如果企业未按时按量支付即违约，债权人对于企业资産有第一求偿权

Embedded option内嵌期权

Option are embedded in the bond issue

Bare option 裸期权

Trades separately from the underlying security

Term bonds (bullet)期限债

Can be retired by payment at final maturity or paid off earlier if so stated in the bond indenture or contract到期日同一天

Serial bonds系列债（分期偿还债）

Specified principal amounts are due on specified dates

Mediun-term notes中期票据

Continuously offered to investors over a period of time注册期内可以连续发行债券

10. Security for bonds债券担保

Beyond the general credit standing, real or personal property may be pledged抵押 不动产个人资産都可以拿来抵押担保

Basically, a pledge is a very serious formal promise 抵押是非常严肃及重要的承诺

In Financial market, a pledge is bailment that conveys possessory title to property owned by debtor (the pledgor) to a creditor (the pledgee) to secure repayment for some debt or obligation and to the mutual benefit of both parties 在金融市场中，质押是将债务人（质押人）拥有的财产的所有权转让给债权人（质押人）的担保，以确保偿还某些债务或义务并达到双方的共同利益

The term is also used to denote the property which constitutes the securities

A pledge is type of securities interest抵押是一种类型的担保权益

11. Municipal securities地方政府债

These debt obligations are issued by state and local governments. Their structures are either serial maturity or term maturity.由地方政府发行

Serial maturity一系列到期日

Portion of debt is retired each year

Term maturity一次性偿还

Debt is retired in maturities ranging from 20~40 years with sinking fund provisions偿债基金条款 beginning 5~10 years prior to maturity

Type of municipal securities地方政府债类型

General obligation bonds一般义务债券

Many general obligation bonds are secured by the issuer's unlimited taxing power.(一般义务债券是指获得发行政府信贷及“征税权力”担保，而不是一个项目的收入的市政债券。)

Limited-tax general obligation bonds

Backed by taxes that are limited as to revenue source 虽然用税收做担保，但有法定上限

Full faith and credit obligations

Used by larger issers who have access to taxes beyond property taxes担保税收不仅仅限于财产税

Double-barreled双管债券

Revenue source includes fees, grants, etc. As well as taxing power税收 补助金 作为偿债担保

Revenue bonds收入债券(以具体项目做偿债担保)

Hybrid bonds混合债券

Insured bonds投保债券

Backed by insurance policies written commercially in addition to the credit of municipal issuer债券担保人除了地方政府以外，加上保险公司做担保

Refunded bonds (prerefunded bonds)

Originally issued as G.O. or revenue bonds but are now secured by an escrow fund consisting of U.S. government obligations地方政府已经持有美国国债且将美国国债放在第三方帐户存管

12. Eurobonds欧洲债券

A Eurobonds is泛指海外

Underwritten by an international syndicate 用外币发行的债券，承销方是国外机构

Offered, at issuance, simultaneously to investors in a number of countries同时向不同国家进行发行

Issued outside the jurisdiction管辖权 of any single country不受任何国家管辖

Mostly traded in OTC market 场外柜台市场交易

Euro straights传统债券

fixed-rate coupon bond with annual coupons每年支付固定利息

Dual currency issues双币债券

Interest and principal are paid in different currencies利息跟本金货币不相同的债券，利息通常是投资者所在的货币单位，本金是发行者所在国家货币

Convertible Eurobond可转换债券

Can be converted to another asset可以被转换成其他资産

13. Preferred stock优先股

Is not a debt instrument, but a senior security with dividends set at a percentage of par value (dividend rate).不是债权是股权，优先级别大于普通股，股利是用面值的百分比描述

Dividends are a distribution of earnings. However, 70% of this income is exempt from federal taxation if the recipient is a qualified corporation. 股息是收益的分配。 但是，如果接收者是合格的公司，则该收入的70％免征联邦税。

Promise returns to holders of preferred are fixed公司对优先股股东有义务支付固定红利

Preferred holders have priority over common stockholders for dividends and liquidation distributions优先股在公司清算时有优先索取权

Cumulative preferred可累计优先股

If issuer cannot make a payment, the dividend accrues until fully paid

Non-cumulative preferred不累计优先股

If issuer cannot make a payment, owner forgot the payment

Perpetual preferred 永续优先股

Issues without a maturity date

Pre-corse 9.2 Provisions Bonds债券条款

Sinking-fund privision偿债基金条款

An indenture is a legal and binding contract between a bond issuer and the bondholders契约是债券发行人与债券持有人之间的具有法律约束力的合同

Indenture requires issuer to retire a specified portion of an issue each year in order to reduce credit risk条款要求发行人每年赎回一些比例债务来降低信用风险

If only part is paid, reminder is a balloon maturity债务每年被赎回时，剩下没被赎回的部分就叫balloon maturity

Provisions for paying off bonds

Are conditions or requirements in a legal document(indenture). There can be a lot of provisions for a bond issuance条款就是在这个合约内对双方权利及义务文件性说明

Call and refund provisions提前赎回条款

Call provision提前赎回条款

Issuers want to be able to take advantage of falling interest rates in the future (i.e. lower their debt costs) and call provisions are an embedded option for the issuer 赋予债务人权利，债务人在利率下降时，有权将债务赎回，目的更低的利率再融资

Corporate bonds are usually callable at a premium above par with the amount declining as the bond approaches maturity, often reaching par after a certain number of years have passed since issuance公司债约定赎回价格在面值之上，赎回价格也不定，临近到期会下降接近面值

Refunding筹资条款

Issuer cannot redeem bonds during first 5~10years following issue unless the funds come from other than lower-interest cost money (cash flow, common stock sale proceeds)发行人在开始的5到10年不可以赎回债券，除非来自低息现金流或普通股出售收益

Puttable bonds卖出条款

①Bondholer can sell the issue bake to the issuer at par value on designated dates ②if interest rates rise after bond is issued, which lowers the bond value,the bondholdercan put the bond to issuer for par ③investor receives：❶ Non-puttable corporate bond ❷ Long put option on the bond 赋予债权人(投资人)权利，可以以事先约定好的价格(面值)，在卖回企业，利率上涨，债券价格下跌，低于面值时，债权人用面值卖还给企业

Sinking-fund provision偿债基金条款

Is a fund established by an economic entity by setting aside revenue over a period of time to fund a future capital expense, or repayment of a long-term debt企业将收入部分预留出来，存管到第三方帐户，只能用来偿还债务

Sinking fund can be satisfied by偿债基金资産来源

Making a cash payment of the face amount of the bond to be retired to the corporate trustee信托 who then bonds using a lottery system现金存到信托里，随机抽取投资人手上债券被赎回

Delivering bonds to the trustee with a total face value = amount that must be retired from bonds purchased in the open market债券存在信托手里，用债券市场价值进行偿还

Convertible and exchangeable bonds可转换条款

Concertiable bonds可转债

Bondholder has the right to convert the bond to a predetermined amount of common stock of the issuer债权人有权利按照事先约定好的价格或比例，转换成普通股（ A公司转A公司普通股）

Exchangeable bonds 可交换债券

Bondholderer has the right to exchange the bonds for common stock of a firm other than issuer债权人有权将债券转换成普通股（A公司转B公司普通股）

Issues of debt with warrants附认股权证条款

Warrants may allow holder the权证赋予投资者（债权人）权利

Right to purchase a designated security at a specified price有权去购买某类资産或者证券以事先约定好的价格

Right to purchase the common stock of the debt issuer or another firm有权去购买发行公司或其他公司普通股

Right to purchase a debt obligation of the issuer有权购买发行人新发行的债券

Warrants can be sold separately from the bond权证跟标的债券分开交易

Floating-rate securities设置浮动利率条款

Coupon interest is reset periodically based on some contrived interest rate 票息利率会定期重置，根据人为定的标杆( i.e. Spread over Treasury bill, or LIBOR)

LIBOR ①London inter-bank Offered Rate伦敦银行隔夜拆借利率缩写 ②is the average interbank interest rate at which a selection of banks on the London money market at prepared to lend to one another银行间互相借款收取的利率，反应市场资金链的紧张程度 ③Traditionally, LIBOR is a very important benchmark rate for floating-rate securities整体市场的标杆或基准点

Special features in high-yield bonds高收益相关特殊条款

补充：Credit ratings评级

Ratings can be applied to both the issue and issuer

Issuer ratings: are an opinion as to the issuers ability to meet its obligations 发行人评级：对发行人履行其义务能力的看法 ( Junk bond垃圾债券=speculative bond投机债券= High-yield bond 高收益债券)

Special features in high-yield bonds

High-yield or Junk bonds have a rating below triple B. When used for an LBO or recapitalization, where cash flow is severely restricted, deferred coupon structures are created 高收益债券跟垃圾债券指的是评级机构评级低于3B级，会在LBO(管理层杠杆买断)级及企业重组，此时现金流紧缺，因此发行高收益债券，并增加额外三种情况的条款

Deferred interest bonds递延利息债券

Sell at deep discount and do not pay interest for 3-7 years 允许债券发行人，以深度折价方式发行，且允许发行人在最开始的3到7年不支付利息

Step-up bonds递增息票债券

Low coupon rate for initial period and then increases to a higher rate the remainder of the term债券发行初始的一段时间，以低息票利率，随时间推移，利率会增加，

Payment-in-kind (PIK) bonds实物支付债券

Issuer can pay cash at a coupon date or give the bondholder a similar bond equal to the amount of the cash payment不用现金支付债券利息，用相似债券支付债券利息

Embedded option

Many provisions can be viewed as embedded options本质上是嵌入式选择权

Pre-Course 9.3 Basic Valuation of Bonds债券定价方法

Valuation of Bonds and Stock

By discounted cash flow method

First principles第一大原则

Value of financial securities = PV of expected future cash flows金融证券合理价值等于预期未来资産折现现金流的现值

To value bonds we need to

Estimate future cash flows : size (how much) and timing (when) 预估现金流大小及发生的时间点

Discount future cash flows at an appropriate rate 合理折现率对现金流进行折现

Pure-Discount (Zero-Coupon) Bonds零息债

Information needed for valuing pure discount bonds

①Time to maturity (T)= Maturity date - today's date ②Face value (F) ③Discount rate (r) Value of pure discount bond: PV= F/ (1+r)ᵀ

Example

Coupon Bonds息票债券

Information needed to value level-coupon bonds

①Coupon payment dates and Time to maturity (T) 支付几期的利息 ②Coupon (C) per payment period 每期支付的利息and Face value(F) 到期面值 ③Discount rate Value of a Level-coupon bond: PV = C/(1+r)+ C(1+r)²+... +C/(1+r)ᵀ+F/(1+r)ᵀ = PV of coupon payments利息折现 + PV of face value本金折现

Example 计算机按就可以 （PV为+，现金流流入） （PV为-，现金流流出） Discount bonds 折价债券 Par bonds 面值债券 Premium bonds 溢价债券

Yield-To-Maturity到期收益率

The discount rate used in the bond pricing formula is also known as the bond's yield to maturity (YTM) or yield

A bond's YTM is the unique discount rate at which the market price of the bond equals the present value of the bond's cash flows 已知市场价格以及债券现金流现值，推算到期收益率（折现率）

Example

Yield Curve 收益率曲线

信用等级要一致

Pre-course 9.4 Interest Risk of bonds

Interest risk of bonds

Decreasing yield cause bond prices to rise, but long-term bonds increase more than short-term收益率下降导致债券价格上升，长期债券上升幅度比短期多

Increasing yields cause long-term bonds to decrease in price more than short-term bonds收益率上升导致债券价格下降，长期债券下降幅度比短期多

Duration久期

Approximately measures a bond's sensitivity to interest rate changes 衡量债券价格相对于利率变化的敏感度

代表利率每上升（下降）1%， 价格会下降（上升）3%

也用久期算债券价格变化 We also use Duration to approximately get a bond's price change due to interest rate change

△P/P =0.1%×10=1% △P= 1%× 140(P)=1.4

Macauley Duration麦考利久期

For a bond, it can be proven that Duration is related(not equal) to the average maturity of cashflow对于债券来说，可以通过数学证明久期跟现金流平均到期日息息相关

So in many book, the duration of a bond is defined as the weighted-average period of time before the cash flow involved are received 债券久期定义很多书定义为未来现金流加权到平均期时间

Macaulary Duration麦考利久期

More specifically, Duration is a weighted average of individual maturities of all the bond's separate cash flows 未来现金流的加权平均值

The weight is the present value of the payment divided by the bond price加权是每一笔现金流的现值占债券价格的百分比

Price change and Macaulay Duration

Macaulay can be used to compute the percentage change in a bond's price, with some "modification修正" ( suppose m compounding periods per year) m为每年支付利息几次

Modified Duration修正久期

修正久期是对于给定的到期收益率的微小变动，债券价格的相对变动与其麦考利久期的比例

Summaries总结

Summarizes properties of duration

①Bond prices move with interest rates. 债券价格跟收益率（利率）呈负相关

②The longer the maturity of a bond, the more sensitive is it's price to a change in interest rates( larger Duration) 对于债券来说，如果他的期限越长，未来现金流加权时间越长，麦考利久期越大，修正久期也越大，代表债券价格变化敏感度越大，利率风险越大。

③Foe zero-coupon bond: Macaulary Duration = maturity 对于零息债券来说，麦考利久期 等于 到期时间 因为没有现金流流出

金融衍生品基础

Pre-Course 10.1 Introduction to Derivatives Market

1. Introduction to derivatives介绍衍生品

In finance, a derivative is a financial contract that derives its value from the performance of an underlying entity 金融衍生品价值取决于基础资産（标的资産）派生出来的价值

Sometimes, we also define a derivative as a financial instrument whose value depends on (or derives from) the values of other, more basic, underlying variable. However,derivatives can be dependent on almost any variable. 有时，我们还将衍生工具定义为一种金融工具，其价值取决于（或衍生自）其他更基本的基础变量的价值。 然而，衍生品几乎可以依赖于任何变量。

This underlying enity can be an asset, index, or interest rate, and often called the "underlying" 标的资産可以是资産指数，利率，股票，利率

2. Derivatives exchanges衍生品在交易所场内

A derivatives exchange is a market where individuals trade standardized contracts that have been defined by the exchange. Derivatives exchanges have existed for a long time. 衍生品在交易所内买卖，交易所就是买卖双方交易的场所，利用标准化合约使得买卖进行交易

The Chicago Board of Trade (CBOT) 芝加哥交易所was established in 1848 to bring farmers and merchants together. Initially its main task was to standardize the quantities and qualities of the grains that we're traded. Within a few years the first future-type contract was developed.芝加哥交易所（CBOT）芝加哥交易所成立于1848年，旨在将农民和商人聚集在一起。 最初，其主要任务是标准化我们所交易谷物的数量和质量。 在几年之内，第一个未来型合同被开发出来。

Speculators投机者 soon became interested in the contract and found trading the contract to be an attractive alternative to trading the gain itself 投机者很快对合同产生了兴趣，发现交易合同的交易收益本身具有吸引力

A trial future exchange, the Chicago Mercantile Exchange (CME), was established in 1919. Now futures exchanges exist all over the world. 1919年建立了试验性的期货交易所，即芝加哥商品交易所（CME）。现在，期货交易所遍布世界各地。

3. Open outcry and Electronic markets

Traditionally derivatives exchanges have used what is known as the open outcry system最开始用公开喊价的方式

This involves traders physically meeting on the floor of the exchange, shouting, and using a complicated set of hand signals to indicate the trades they would like to carry out 这涉及交易者在交易所现场进行实际会面，大喊，并使用一组复杂的手势来表示他们想要进行的交易

Exchanges are increasingly replacing the open outcry system by electronic trading. This involves traders entering their desired trades at a key board and a computer being used to match buys and sellers 交易所越来越多地通过电子交易取代公开喊价系统。 这涉及交易者在键盘上输入他们想要的交易以及一台买卖双方的电脑

The open outcry system has its advocates, but, as time passes, it is becoming less and less common. 公开喊价制度有其倡导者，但随着时间的流逝，它变得越来越不普遍。

4. Over-the-counter markets场外交易市场

The over-the-counter markets is an important alternative to exchanges这些市场因为没有集中的统一交易制度和场所，因而把它们统称为场外交易市场，又称柜台交易或店头交易市场，指在交易所外由证券买卖双方当面议价成交的市场。它没有固定的场所，其交易主要利用电话、电报、传真及计算机网络进行，交易的证券以不在交易所上市的证券为主。

It is a telephone- and computer- linked network of dealers. 交易双方通过电话电脑进行协商

Trades are done over the phone and are usually between two financial institutions or between a financial institutions and one of its clients 交易双方可以是两个金融机构或金融机构跟客户

If measured in terms of the total volume of trading, OTC market has become much larger than the exchange-traded market. 若只有衡量交易量来说场外市场远大于场内市场

A key advantage of the over-the-counter market is that the terms of a contract do not have to be those specified by an exchange. Market participants are free to negotiate any mutually attractive deal. 场外市场的大优点，由于双方进行协商交易，交易合约不需要被指定，市场参与者可以自由协商订制个性化条款。

A disadvantage is that there is usually some credit risk in an over-the-counter trade. 缺点就是场外市场有较大的信用风险 信用风险主要是两个 ①Counterparty risk 对手方风险,亏钱可能不还钱 ②Settlement risk 交割结算风险，给了钱没给货

5. Types of plain vanilla derivatives衍生品类型

Forward远期合约

A customized contract between two parties to buy or sell an asset at a specified price on a future date 买卖双方签订订制化场外合约，约定好价格在未来时间点，买卖某个资産

Future期货

A standardized forward contract and is traded in an exchange 跟远期一样，但签订的是标准化合约，且在场内交易所交易

Swap互换

A customized contract between two parties to buy or sell assets at a specified price on a serial future dates 双方约定好一系列到期日的买卖资産的订制化合约

Option选择权

Represent a right to buy or sell an asset in the future 买卖双方某一方有权利（可以执行或不执行）在未来某个时间点，买入或者卖出资産的权利

6. Participants of derivative market衍生品参与者

Hedger对冲者

Takes steps to reduce the risk of an investment by making an offsetting investment. 在衍生品市场建立与现在市场相反的策略，已降低风险

Speculator投机者

Analyzes and forecasts future price movement, trading contracts with the hope of making a profit. 分析和预测未来的价格走势，买卖合约希望能获取利润

Arbitrageur套利者

Attempts to profit from price inefficiencies in the market by making simultaneous that offset each other to capture risk-free profits. 尝试通过使彼此抵消的同时发生来获取无风险利润，从而从市场低价中获利。

Pre-Course 10.2 Introduction to Forwards

Forward contracts远期

Forward contract is relatively a simple derivative. It is an agreement to buy or sell an asset at a certain future time for a certain price. 远期合约是一个简单的衍生品。 一个买卖双方的约定合约，约定在未来的时间段点协议好的价格买卖某一项资産

Typically, the price at maturity is called strike price执行价, denoted by K or X.

It can be contrasted with a spot contract现货, which is an agreement to buy or sell an asset today 即期合约就是当下进行资産买卖

Typically, the spot price is denoted by S. 现货市场价格用S表示

A forward contract is traded in the over-the-counter market- usually between two financial institutions or between a financial institution and one of its clients 远期合约在场外交易市场交易，参与者通常是两家金融机构，或者一家金融机构和客户签订的合约

One of the parties to a forward contracts assumes a long position and agrees to buy the underlying asset on a certain specified future date for a certain specified price. 远期合约买方（多头方）：其中一方参与者约定在未来确定时间用未来确定价格同意购买远期合约资産就叫买方（多头方）

The other party assumes a short position and agrees to sell the asset on the same date for the same price. 另外一方参与者约定在未来确定时间用未来确定价格同意卖出远期合约资産就叫卖方（空头方）

Forward contracts on foreign exchange are very popular, and can be used to hedge foreign currency risk. 汇率当作远期合约标的资産，过去常用来对冲汇率风险

A向B购买未来远期汇率欧元商品，买100份，每商品售价1. 2美元，A多头，B空头。 S现货价格 K执行价格

Payoffs from forward contracts

The payoff from a long position in a forward contract on one unit of an asset is S-K or S-X 多头，价格涨赚钱，现货—合约价格 The payoff from a short position in a forward contract on one unit of an asset is X-S or K-S 空头，价格跌赚钱，合约—现货 0和游戏

Deliveries of forward contracts远期合约结算

A forward contract can be customized to any commodity, amount and delivery date. 远期契约可以是任何大众商品，双方协商约定好买卖数量，价格跟交割日期。

A forward contract settlement can occur on a cash or delivery basis到期时有两种结算方式，现金跟实物交割

When the contract settles in actual delivery of the underlying asset, that final stage is called forward delivery 当合同结算相关资产的实际交割时，该最后阶段称为远期交割

Otherwise, the contract settles for cash ( or cash settlement)

Forward rate agreement FRA

A forward rate agreement (FRA) is a cash-settled OTC contract between two counterparties, where the buyer is borrowing (and the seller is lending) a notional sum at a fixed interest rate (the FRA rate ) and for a specified period of time starting at an agreed date in the future. 远期利率合约，现金交割差值结算，场外市场， 契约买方约定好固定利率在未来的某个时间点，进行资金的借入 (卖方，借出）

By entering into an FRA, the parties lock in an interest rate for a stated period of time starting on a future settlement date, based on a specified notional principal amount.FRA里，双方将借款利率锁定，从T1开始锁定时间, 持续时间直到T2, 约定好名义(虚拟不真正发生借款)本金

The long position of FRA (borrower资金借入方), can benefit from an increase of interest rate, to protect against rate increase.

The short position of FRA (lender资金借出方), can benefit from a decrease of interest rate, to protect against rate decrease.

Pre-Course 10.3 Introduction to Futures

Introduction to Futures

A future contract is an agreement to buy (if you are long) or sell (if you are short) something in the future, at an agreed upon price (the future price). 期货合约是在未来以约定的价格（期货价格）购买（做多）或卖出（做空）的协议。

Futures exist on financial assets (debt instruments, currencies, stock indexes), and real assets (gold, creude oil, wheat, cattle, cotton,etc) 期货存在于金融资产（债务工具，货币，股票指数）和商品（黄金，原油，小麦，牛，棉花等）上

Comparison of Futures and Forward

Both types of contracts specify a trade between two counter-parties

There is a commitment to take delivery of an asset (this is the buyer, or the long) 某一方有义务去收取资産，那就叫买方，多头

There is a commitment to deliver an asset (this is the seller, or the short) 某一方有义务交割资産，那就叫卖方，空头

Many times,future contracts and forward contracts are substitutes. 本质相似，很多时候可以互换

However, at a specific times, the relative costs, liquidity, and convenience of using one market versus the other will differ. 但是在某些情况下考虑到交易成本，流动性，交割方便性的问题，交易方可能会选取某个市场。

Marketing to market, Example

Marking to market refers to the daily settlement of gains and losses due to changes in the market value of the security / contract. 每日结算（盯市）

Some features of Futures Contracts期货合约特征

i. Some Futures contracts have daily price limits 期货价格有每日涨跌停限制

ii. Some features contracts(Euro, T-bills, stock index futures,currencies) have one specific delivery date ；Others (T-bonds, crude oil) give the short the option of choosing which day (usually in the delivery month) to make delivery. 有一些期货合约 （例：外汇，股指，外汇）都有确定的交割日交易所规定好标准化交割日 其他期货合约 ( 例：长期国库债券，原油）给卖方有选择权利，在时间范围内进行交割

iii. Some futures contracts (e.g., T-bonds) let the seller choose the quality of goods to deliver, within a specific quality range. 有些期货合约允许卖方在范围内选择交割资産的品质（例如国债）

iv. Some futures contracts (Euro, stock index Futures, feeder cattle)are cash settled. 有些期货合约是现金交割的

v. Note that a future contracts is like a portfolio of forward contracts (time series). 期货合约有点像是组合的远期合约

Futures Contracts Payoff Profiles

多头盈亏：F - K 空头盈亏：K - F

Margin Requirements保证金

Futures exchanges require good faith money from counter-parties to futures contracts, to act as a guarantee that each will abide by the terms of the contract. This money is called margin. 期货交易需要从对方到期货合约的诚信金，以保证每个交易方都遵守合约条款。 这笔钱称为保证金。

Each futures exchange is responsible for setting the margin requirements for their futures contracts 交易所会对每个合约都有保证金的比例要求

The initial margin初始保证金 is the money a trader must deposit into a trading account (margin account) when establishing a future position. 交易所要求每个交易员，一开始需要存入的保证金，建立期货合约时需要缴纳

If If the equity in the account falls to, or below, the maintenance margin level维持保证金, the exchange will send a margin call to the trader, and additional funds must be deposited to restore the account balance to the initial margin level. 如果如果账户中的净值下降到维持保证金水平或以下，则交易所将向交易者发出催缴保证金通知，并且必须存入额外的资金以将账户余额恢复到初始保证金水平 。

The margin that is deposited in order to meet margin calls is called variation margin. 为了满足追加保证金要求而存入的保证金称为变动保证金。

If the trader does not promptly meet the margin call, the trader's position will be liquidated 如果交易者未及时满足追加保证金要求，则交易者的头寸将被平仓

Pre-Course 10.4 Introduction to Options

Options选择权

Options are right to buy or sell assets in the future 在未来某个时间点买入或卖出标的资産的权利(某一方有权利选择买或不买）

Options are contingent claims 期权交易有可能发生有可能不发生

Options are traded both on organized exchanges and OTC 期权可以在场内可以在场外交易

There are two types of option

Call option gives the holder the right to buy the underlying asset by a certain date for a certain price 看涨期权，认购期权：期权持有人有权利在到期时以一定的价格购买标的资産

A call option gives its holder the right to buy an assest

At the exercise or strike price (X) 行权价格

On or before the expiration date (T) 合约约定到期时间

Exercise the option to buy the underlying asset if market value (ST) ＞ strike (X) 当市价大于行权价格时，买方才会行权

Premium权利金: 2.18元 执行价格为130元 当市价低于130元时 买方不行使权利 因为行权价高于市价 市场买就可以了 所以买方不行权 130元价格加上2. 18元权利金=损益平衡点 132. 18元 也就是在132. 18价格之上，买方收益才是正的

买进买权 Buyers of calls

卖出买权 Seller of calls

Put option gives the holder the right to sell the underlying asset by a certain date for a certain price 看跌期权，认沽期权：期权持有人在到期时有权利以一定的价格出售标的资産

A put option gives its holder the right to sell an asset

At the exercise or strike price (X)

On or before the expiration date (T)

Exercise the option to sell the underlying asset if market value (ST) ＜ strike (X) 市价小于行权价格时，买方才会行权

Premium权利金: 4.79元 行权价格：130元 市场价格大于130元时，不行权

买进卖权 Buyer of puts

卖出卖权 Seller of puts

The purchase price of the option is called the premium期权费，权利金

Sellers (writers) of options receive premium income 期权卖方收到期权权利金作为最初始收入

If holder excercises the option, the option writer must make (call) or take (put) delivery of the underlying asset. 期权买方可以选择行权或者不行权， 如果买方行权，那么卖方有义务将标的资産交割给买方

Moneyness of Options选择权价位状态

In the Money 实值期权，价内期权，行权有利润

Exercise of the option would be profitable

Call

Exercise price ＜ Market price

Put

Exercise price ＞ Market price

Out of the Money 虚值期权，价外期权，行权无利润

Exercise of the option would not be profitable

Call

Market price ＜ Exercise price

Put

Market price ＞ Exercise price

At the Money 在值期权，平价期权

Exercise price = Asset price

American Options vs European Options

American options 美式期权

The option can be exercised at any time before expiration or maturity 在到期日之前的任何时间点都可以行使权利

European options 欧式期权

The option can only be exercised on the expiration or maturity date 只能在到期日的那天才可以行使权利

In the U.S., most options are American style, except for currency and stock index options 在美国，多半是美式期权，外汇，股指标的选择权用欧式期权

Options Types

Stock Options股票期权

Index Options股票指数期权

Futures Options期货期权

Foreign Currency Options外汇期权

Interest Rate Options利率期权

Pre-Course 10.5 Introduction to Swaps

Swaps contracts: Definitions

In a swap, two counterparties agree to a contractual arrangement wherein they agree to exchange cash flows at periodic intervals 双方签订协议规定在未来的时间段互相交换现金流或者资産

A swap can be viewed as a portfolio of forwards with different maturities 一系列远期合约的投资组合不同时间段

There are two types of interest rate swaps 利率作为标的的交换

Single currency interest rate swap :" Plain vanilla" fixed—for—floating swaps are often just called interst rate swaps 单种利率互换，用固定利率换浮动利率

Cross-Currency interest rate swap: This is often called a currency swap; fixed for fixed rate debt service in two (or more) currencies多种利率互换，可以是浮动可以是固定利率，涉及两种或两种以上货币

Currency swap

A 公司需要美元，但手上有日元 B 公司需要日元，但手上有美元

The Swap Bank

Swaps are usually traded in OTC market 场外交易

A swap bank is a genetic term to describe a financial institution that facilitates swaps between counterparties 掉期银行作为市场金融机构主要中介角色

The swap bank can serve as either a broker or a dealer 掉期银行可以作为经纪商或交易商

As a broker, the swap bank matches counterparties but does not assume any of the risks of the swap. 经纪商来说，他代表A跟B进行交易，掉期银行与交易对手匹配，但不承担掉期的任何风险。

As a dealer, the swap bank stands ready to accept either side of a currency swap, and then later lay off their risk, or match it with a counterparty. 作为交易商，交易商手上会有许多的头寸积累，掉期银行随时准备接受货币掉期的任何一方，然后放开风险，或与对手进行对等。

Risks of Interest Rate and Currency Swaps

Interest Rate Risk

Interest rates might move against the swap bank after it has only gotten half of a swap on the books, or if it has an unhedged position 在掉期银行只获得账面掉期的一半之后，或者如果它有未对冲头寸，利率变动时就会有利率风险

Exchange Rate Risk

In the example of a currency swap given earlier, the swap given earlier, the swap bank would be worse off if the pound appreciated

Credit Risk

This is the major risk faced by a swap dealer- the risk that a counter party will default on its end of the swap

Sovereign Risk主权国家政策风险

The risk that a country will impose Exchange rate restrictions that will interfere with performance on the swap