金 融 市 场 学
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金 融 市 场 学. 攀 登. 金融市场学. 债券. 时间价值. 货币是有时间价值的. 金融工具分类与时间价值. 简易贷款 年金 附息债券 贴现债券. 现值和终值. 简易贷款 年金 附息债券 贴现债券. 到期收益率. 简易贷款 年金 附息债券 贴现债券. 利率. 折算惯例 比例法 复利法 名义利率与实际利率 差别在于是否考虑了通货膨胀的影响 即期利率与远期利率 利率水平的决定 可贷资金模型 流动性偏好模型. 利率的结构. 预期假说 市场分割假说 偏好停留假说. 债券特征.

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5178024

金 融 市 场 学

攀 登


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金融市场学

债券


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时间价值

货币是有时间价值的


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金融工具分类与时间价值

  • 简易贷款

  • 年金

  • 附息债券

  • 贴现债券


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现值和终值

  • 简易贷款

  • 年金

  • 附息债券

  • 贴现债券


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到期收益率

  • 简易贷款

  • 年金

  • 附息债券

  • 贴现债券


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利率

  • 折算惯例

    • 比例法

    • 复利法

  • 名义利率与实际利率

    • 差别在于是否考虑了通货膨胀的影响

  • 即期利率与远期利率

  • 利率水平的决定

    • 可贷资金模型

    • 流动性偏好模型


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利率的结构

  • 预期假说

  • 市场分割假说

  • 偏好停留假说


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债券特征

  • 面值(Face or par value)

  • 息票率(Coupon rate)

    • 零息票债券

  • 利息支付方式

  • 债券契约


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各类债券

  • 国债

  • 企业债

  • 地方政府债券

  • 海外债

  • 创新债券

    • 指数化债券

    • 浮动和反向债券


Money markets

Money Markets

  • US Treasury Bills (T-Bills)

  • Certificates of Deposit (CD)

  • Commercial paper (CP)

  • Bankers’ acceptances

  • Eurodollars

  • Repos and Reverses

  • Federal Funds


Us treasury bills

US Treasury Bills

  • Initial maturities are

    • 91-182 days, offered weekly

    • 52 weeks, offered monthly

  • Competitive and noncompetitive (10-20%) bids.

  • The investor buys the instrument at discount

  • bid-ask (spread) represents the profit for the dealer

  • quotes use the bank discount yield.

  • Exempt of state and local taxes.


Bank discount yield

Bank Discount Yield

  • $10,000 par T-bill at $9,600 with 182 DTM.

  • $400(360/182) = $791.21thus the bank discount yield is 7.91% rBD=(10,000-P)/10,000 ·360/n

  • effective annual yield is:(1+400/9600)2-1=8.51%

  • bond equivalent yield is:rBEY=(10,000-P)/P ·365/n


Certificates of deposit

Certificates of Deposit

  • Time deposits with commercial banks.

  • It may not be withdrawn upon demand.

  • Large CDs can be sold prior to maturity.

  • Insured by FDIC up to $100,000

    (Federal Depository Insurance Corporation)


Commercial paper

Commercial Paper

  • Unsecured short term debt (corporations).

  • Maturity is up to 270 days.

  • CP is issued in multiples of $100,000.

  • Small investors buy it through mutual funds.

  • Most issues have credit rating.

  • Treated for tax purposes as regular debt.

  • LC backed (letter of credit) optional.


Bankers acceptances

Bankers’ acceptances

  • Orders to a bank by a customer to pay a given sum at a given date.

  • Backed by bank.

  • Traded in secondary markets.

  • Widely used in international commerce, because the creditworthiness is supplied by a bank.


Eurodollars

Eurodollars

  • Dollar denominated time deposits in foreign banks.

  • Most are for large amounts and with maturity of less than 6 months.


Repos and reverses

Repos and Reverses

  • Repurchase agreements (RPs) used by dealers in government securities.

  • Term repo has a maturity of 30 days or more.

  • Reverse repo is the result of a dealer finding an investor buying government securities with an agreement to sell them at a specified price at a specified future date.


Federal funds

Federal Funds

  • Commercial banks that are members of the Federal Reserve System (Fed) are required to maintain a minimum reserve balance with Fed.

  • Banks with excess reserves lend (usually overnight) to banks with insufficient reserves.


Brokers calls

Brokers’ Calls

  • Brokers borrow funds to loan to investors who wish to buy stock on margin.

  • The broker agrees to repay the loan upon the call of the bank.

  • The rate is higher because of the credit risk component.


Libor

LIBOR

  • London Interbank Offer Rate (LIBOR) is the rate at which the large London banks lend among themselves.

  • This rate serves often as an anchor for floating rate agreements which for example can be set at LIBOR + 3%


Yields on money market instruments

Yields on Money Market Instruments

  • In general, money market instruments are quite safe.

    • However, T-bills are the safest of the money instruments.

  • As a result the other instruments provide a slightly higher yield.


Fixed income capital markets

Fixed-Income Capital Markets

  • T-Notes - initial maturity of 10 years (or less).

  • T-Bonds - initial maturities of 10-30 years.

  • Par (also called face or principal) $1,000.

  • Interest (coupons) paid semiannualy.


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RateMo/YrBid AskedChg.Ask Yld

83/4Aug 00n105:16 105:18+87.55

Rate coupon payment 83/4% of $1,000;

paid semiannually; $43.75 per bond each 6 mo.

Maturity = August 2000n = note

Bid =105:16 means 10516/32=105.5

at the price $1055 buyer is willing to buy.

Ask=105:18 means 10518/32=105.5625

at the price $1055.625 seller is willing to sell.


Municipal bonds munis

Municipal Bonds (Munis)

  • Issued by state and local governments and agencies. Interest (not capital gains!) is exempt from federal taxes.

  • General Obligations are backed by the taxing power of the issuer.

  • Revenue bonds are backed only by revenues from specific projects.

  • Industrial Development bond is issued to finance a private projects.


Interest from munis

Interest from Munis

  • Is not subject to federal income tax.

  • Hence the yields are lower:

    r (1- t) = rm

    r- before tax return on taxable bond

    rm- return on municipal bond

    t- marginal tax rate

  • Attractive to wealthy investors.


Corporate bonds

Corporate Bonds

  • Used to generate long-term funds.

  • The primary difference is the default risk.

  • Backed by specific assets (like mortgages).

  • By the financial strength of the firm only (debentures).

  • Callable at a call price (firm).

  • Convertible, may be exchanged to a stock (investor).


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债券条款

  • 信用

  • 赎回条款

  • 转换条款

  • 回售条款

  • 浮动利率


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违约风险和评级

  • 评级公司

    • Moody’s Investor Service

    • Standard & Poor’s

    • Fitch (Duff and Phelps)

  • 两个大类

    • 投资类

    • 投机类


Investment grade

Investment Grade

  • Moody’sS&P=F

  • AaaAAA

  • Aa1AA+

  • Aa2AA

  • Aa3AA-

  • A1A+

  • A2A

  • A3A-

  • Baa1BBB+

  • Baa2BBB

  • Baa3BBB-


Speculative grade

Speculative Grade

  • Moody’sS&P=F=D&P

  • Ba1BB+

  • Ba2BB

  • Ba3BB-

  • B1B+

  • B2B

  • B3B-

  • CCC+

  • CaaCCC

  • CCC-

  • CaCC

  • CC


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评级机构使用的指标

  • 偿债能力(Coverage ratios)

  • 杠杆比率(Leverage ratios)

  • 流动性比率(Liquidity ratios)

  • 盈利能力(Profitability ratios)

  • 现金流(Cash flow to debt)


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违约风险保护

  • 偿债基金

  • 未来债务

  • 红利限制

  • 抵押


Bond pricing

债券定价(Bond Pricing)

PB =债券价格

Ct = 利息

T=付息次数

R =要求收益率


10 1000 8

10年期,面值1000, 8%息票率,半年付息一次

PB =$1,148.77

Ct=40

P=1000

T=20 periods

r=3%


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债券价格与要求收益率之间的关系

  • 要求收益率高则债券价格低

  • 要求收益率为零则债券价格为未来现金流之和


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Price

Yield

价格和要求收益率


10 1000 7 950

10 年期,面值1000,息票率 = 7%,当前价格= $950

则,收益率r = 3.8635%


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收益率折算

折算为年收益率

7.72% = 3.86% x 2

实际年收益率

(1.0386)2 - 1 = 7.88%

当期收益率

$70 / $950 = 7.37 %


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实现的收益率和到期收益率

  • 再投资假设

  • 持有期收益

    • 利率变化

    • 利息的再投资

    • 价格变化


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持有期收益

I = 利息

P1 = 卖出价格

P0 = 买入价格


Example

Example

息票率= 8% 要求收益率 = 8%

期限 =10年P0 = $1000

由于要求收益率降到 7%

P1 = $1068.55

HPR = [40 + ( 1068.55 - 1000)] / 1000

HPR = 10.85% (半年)


Accrued interest

Accrued Interest

  • Additional payment for part of the coupon

$

time


Price quotes and accrued interest

Price Quotes and Accrued Interest

  • Assume that the par value of a bond is $1,000.

  • Price quote is in % of par + accrued interest

  • the accrued interest must compensate the seller for the next coupon.


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债券投资的基本策略

  • 积极策略

    • 预测利率走势

    • 寻找市场的非有效性

  • 消极策略

    • 控制风险

    • 平衡风险与收益


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债券定价基本性质

  • 价格和收益率的反向关系

  • 收益增加比收益减少引起的成比例的价格变化较小

  • 长期债券的价格比短期债券的价格对利率的敏感性更强

  • 随着到期日的增加,价格敏感性的增加呈下降趋势

  • 利率敏感性与息票率呈反向关系

  • 当债券以一较低的到期收益率出售时,债券价格对收益变化更敏感


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久 期

  • A measure of the effective maturity of a bond

  • The weighted average of the times until each payment is received, with the weights proportional to the present value of the payment

  • Duration is shorter than maturity for all bonds except zero coupon bonds

  • Duration is equal to maturity for zero coupon bonds


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久期的计算


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8%

Time

Payment

PV of CF

Weight

C1 X

Bond

years

(10%)

C4

.5

40

38.095

.0395

.0198

1

40

36.281

.0376

.0376

1.5

40

34.553

.0358

.0537

2.0

1040

855.611

.

8871

1.7742

sum

964.540

1.000

1.8853

一个例子


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久期与价格之间的关系

=连续复利

=年复利

修正久期D* = D / (1+y)


Rules for duration

Rules for Duration

  • Rule 1 The duration of a zero-coupon bond equals its time to maturity

  • Rule 2 Holding maturity constant, a bond’s duration is higher when the coupon rate is lower

  • Rule 3 Holding the coupon rate constant, a bond’s duration generally increases with its time to maturity

  • Rule 4 Holding other factors constant, the duration of a coupon bond is higher when the bond’s yield to maturity is lower


Rules for duration cont d

Rules for Duration (cont’d)

  • Rules 5 The duration of a level perpetuity is equal to:

  • Rule 6 The duration of a level annuity is equal to:

  • Rule 7 The duration for a corporate bond is equal to:


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免疫

F(x)

x


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被动管理

  • Bond-Index Funds

  • Immunization of interest rate risk

    • Net worth immunization

      • Duration of assets = Duration of liabilities

    • Target date immunization

      • Holding Period matches Duration

  • Cash flow matching and dedication


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Price

Pricing Error from convexity

Duration

久期和凸性

Yield


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$

r


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p

$10,000

0 8% r


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凸性修正

Correction for Convexity:


Active bond management swapping strategies

Active Bond Management: Swapping Strategies

  • Substitution swap

  • Intermarket swap

  • Rate anticipation swap

  • Pure yield pickup

  • Tax swap


Yield curve ride

Yield Curve Ride

Yield to Maturity %

1.5 1.25 .75

Maturity

3 mon 6 mon 9 mon


Contingent immunization

Contingent Immunization

  • Combination of active and passive management

  • Strategy involves active management with a floor rate of return

  • As long as the rate earned exceeds the floor, the portfolio is actively managed

  • Once the floor rate or trigger rate is reached, the portfolio is immunized


Callable bond

Callable bond

  • The buyer of a callable bond has written an option to the issuer to call the bond back.

  • Rationally this should be done when …

  • Interest rate fall and the debt issuer can refinance at a lower rate.


Embedded call option

regular bond

strike

callable bond

Embedded Call Option

r


Puttable bond

Puttable bond

  • The buyer of a such a bond can request the loan to be returned.

  • The rational strategy is to exercise this option when interest rates are high enough to provide an interesting alternative.


Embedded put option

puttable bond

Embedded Put Option

regular bond

r


Convertible bond

Stock

Convertible Bond

Straight Bond

Convertible Bond

Payoff

Stock


Merton s model

Merton’s model

$

firm

equity

debt

DV


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金融市场学

股票


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基本面分析

  • 基本面分析

    • 全球经济

    • 国内经济

    • 行业分析

    • 公司分析

  • 从上到下的方法


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全球经济

  • 国家和地区之间的巨大差异

  • 政治风险

  • 汇率风险

    • Sales

    • Profits

    • Stock returns


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关键经济变量

  • Gross domestic product

  • Unemployment rates

  • Interest rates & inflation

  • Consumer sentiment


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政府政策

  • 财政政策

    • 直接的效果

    • 缓慢的实施过程

  • 货币政策

    • Open market operations

    • Discount rate

    • Reserve requirements


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冲击

  • 需求

    • 税收

    • 政府支出

  • 供给

    • 价格变化

    • 劳动力教育水平

    • 科技进步


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经济周期

  • 经济周期

    • 波峰

    • 波谷

  • 行业与经济周期

    • 敏感

    • 不敏感


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指标

  • 领先

    • 资本品的订单数

    • 消费者信心指数

    • 股价~~~~~

  • 同步

    • 工业产量

    • 制造品与贸易销售额

  • 滞后

    • 消费品价格指数

    • 失业平均期限


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行业分析

  • 对经济周期的敏感度

  • 影响敏感度的因素

    • 产品销售对经济周期的敏感程度

    • 经营杠杆比率

    • (DOL=净利润变化/销售额变化)

    • 财务杠杆比率

  • 行业生命周期


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行业生命周期

StageSales Growth

Start-upRapid & Increasing

ConsolidationStable

MaturitySlowing

Relative DeclineMinimal or Negative


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行业结构

  • 进入威胁

  • 现有企业之间的竞争

  • 来自替代品厂商的压力

  • 购买者的谈判能力

  • 供给厂商的谈判能力


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2009年中国统计数据

  • 国内生产总值335353亿元,比上年增长8.7%。

    • 第一产业增加值35477亿元,增长4.2%;第一产业增加值占国内生产总值的比重为10.6%,比上年下降0.1个百分点;

    • 第二产业增加值156958亿元,增长9.5%;第二产业增加值比重为46.8%,下降0.7个百分点;

    • 第三产业增加值142918亿元,增长8.9%;第三产业增加值比重为42.6%,上升0.8个百分点。

  • 2009年世界总人口为67.8亿,中国人口占世界比例为21%。


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2009年中国统计数据

  • 基础工业数据:    

    • 粗钢产量:5.68亿吨,占世界份额的46.6%,超过第2-20名的总和;钢材产量:6.96亿吨;

    • 水泥产量:16.3亿吨,超过世界份额的50%;

    • 电解铝产量:1285万吨,达到世界份额的60%;

    • 精炼铜产量;413万吨,达到世界份额的25%;进口430万吨,消费铜超过800万吨,达到世界精铜产量的50%;

    • 煤炭产量:30.50亿吨,占世界份额的45%;

    • 原油产量:1.89亿吨;进口2.04亿吨,消费量占世界的11%;

    • 乙烯产量:1066万吨,世界第二,消费2200万吨;

    • 化肥产量:6600万吨,占世界份额的35%;

    • 塑料产量:4479.3万吨;


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2009年中国统计数据

  • 基础设施数据:

    • 新增装机容量8970万千瓦,总装机容量达到8.6亿千瓦(美国为10亿千瓦);

    • 新建高速公路4719公里,总里程达到6.5万公里(美国9万公里),09年新开工1.6万公里;

    • 新增公路通车里程9.8万公里(含高速),农村公路新改建里程38.1万公里;

    • 铁路投产新线5557公里,其中客运专线2319公里;投产复线4129公里;营业总里程达8.6万公里(仅次于美国);09年新开工1.2万公里;


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2009年中国统计数据

  • 工业产品数据:

    • 汽车产量1379万辆,占世界份额的25%,世界第一;

    • 造船完工量4243万载重吨,占世界份额的34.8%;新接订单2600万载重吨,占世界份额的61.6%;手持订单18817万载重吨,占世界份额的38.5%;

    • 微机产量1.82亿台,占世界份额的60%;

    • 彩电产量9899万台,占世界份额的48%;

    • 冰箱产量5930万台,占世界份额的60%;

    • 空调产量8078万台,占世界份额的70%;

    • 洗衣机产量4935万台,占世界份额的40%;

    • 微波炉产量6038万台,占世界份额的70%;

    • 手机产量6.19亿部,占世界份额的50%;


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2009年中国统计数据

  • 轻工产品:

    • 纱产量2393.5万吨,占世界份额的46%;

    • 布产量740亿米;

    • 化纤产量2730万吨,占世界份额的57%;

  • 其他:

    • 黄金产量:313.98吨,世界第一;

    • 玻璃产量:5.8亿重量箱,占世界份额的50%;


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2009年中国统计数据

  • 农业数据(中国的膳食比例应该是世界上最合理的)

    • 粮食产量5.31亿吨,占世界份额的24%;

    • 肉类产量7642万吨,占世界份额的28%;

    • 禽蛋产量2741万吨,占世界份额的45%;

    • 牛奶产量3518万吨,仅占世界份额的5%;

    • 水产品产量5120万吨,占世界份额的40%;

    • 蔬菜产量5.7亿吨, 占世界份额的50%;

    • 水果产量1.95亿吨,占世界份额的18%;

    • 油料产量3100万吨,占世界份额的7.5%(中国是世界上最大的大豆进口国);

    • 白糖产量1200万吨, 占世界份额的7%


2010 1 2

中美日德2010年1、2月汽车销量


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2009年中国统计数据

  • 发展潜力

    • 现在国内人均钢材消费量400多公斤峰值:美国,711公斤;日本,802公斤

    • 现在国内人均铜消费量6公斤峰值:日本,12公斤

    • 国内水泥消费人均:1300公斤峰值:日本,1000公斤;美国,1000公斤


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资本估价模型

  • 基本方法

    • 资产负债表估价法

    • 红利贴现法

    • 市盈率方法

  • 评估增长率和增长机会


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资产负债表估价法

  • 清算价值(净资产)

  • 重置成本

  • 托宾Q

    • 托宾Q=市值/重置成本


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内在价值和市场价格

  • 内在价值

  • 市场价格

  • 交易信号

    • IV > MP Buy

    • IV < MP Sell or Short Sell

    • IV = MP Hold or Fairly Priced

    • 爆仓


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红利贴现法的基本原理

V0 = Value of Stock

Dt = Dividend

k = required return


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无增长模型

Stocks that have earnings and dividends that are expected to remain constant

Preferred Stock


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无增长模型的举例

E1 = D1 = $5.00

k = 0.15

V0 = $5.00 / 0.15 = $33.33


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稳定增长模型

g = constant perpetual growth rate


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稳定增长模型的举例

E1 = $5.00b = 40% k = 15%

(1-b) = 60%D1 = $3.00 g = 8%

V0 = 3.00 / (.15 - .08) = $42.86


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估计红利增长率

g = growth rate in dividends

ROE = Return on Equity for the firm

b = plowback or retention percentage rate

(1- dividend payout percentage rate)


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特定持有期模型

PN = the expected sales price for the stock at time N

N = the specified number of years the stock is expected to be held


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两分定价:增长和无增长成分

PVGO = Present Value of Growth Opportunities

E1 = Earnings Per Share for period 1


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两分定价举例

ROE = 20% d = 60% b = 40%

E1 = $5.00 D1 = $3.00 k = 15%

g = .20 x .40 = .08 or 8%


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两分定价举例

Vo = value with growth

NGVo = no growth component value

PVGO = Present Value of Growth Opportunities


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市盈率

  • 决定市盈率的两个因素

    • 要求收益率

    • 红利预期增长

  • 应用

    • 相对定价

    • 行业分析中的广泛应用


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市盈率:无预期增长

  • E1 - expected earnings for next year

    • E1 is equal to D1 under no growth

  • k - required rate of return


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市盈率:稳定增长

b = retention ratio

ROE = Return on Equity


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市盈率:无增长例子

E0 = $2.50 g = 0 k = 12.5%

P0 = D/k = $2.50/.125 = $20.00

PE = 1/k = 1/.125 = 8


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市盈率:有增长例子

b = 60% ROE = 15% (1-b) = 40%

E1 = $2.50 (1 + (.6)(.15)) = $2.73

D1 = $2.73 (1-.6) = $1.09

k = 12.5% g = 9%

P0 = 1.09/(.125-.09) = $31.14

PE = 31.14/2.73 = 11.4

PE = (1 - .60) / (.125 - .09) = 11.4


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市盈率分析中的误区

  • 使用会计数据

  • 收益随经济周期波动


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通货膨胀

  • 影响

    • 历史成本低估了经济成本

    • 实证研究表明高通货膨胀通常带来低的实际收益

  • 可能的原因

    • Shocks cause expectation of lower earnings by market participants

    • Returns are viewed as being riskier with higher rates of inflation

    • Real dividends are lower because of taxes


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金融市场学

资产组合


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风险与风险厌恶

  • 风险与风险厌恶

    • 单一前景的风险

    • 风险、投机与赌博

    • 风险厌恶与效用


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风险与风险厌恶

  • 无差异曲线特征

    • 斜率为正

    • 下凸

    • 同一投资者有无限多条

    • 不能相交

  • 资产组合风险

    • 资产风险与资产组合风险

    • 资产组合中的数学


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一个例子

  • 无风险收益5%


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风险与风险厌恶

  • 概率分布的描述

    • 一阶矩

    • 二阶矩

    • 高阶矩

  • 正态分布和对数正态分布

  • 风险厌恶与预期效应


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风险与无风险资产的配置

  • 将风险资产看作一个整体

  • 无风险资产——短期国债

  • 一种风险资产与一种无风险资产

    • 资产配置线

    • 酬报与波动性比率

  • 风险忍让与资产配置

  • 消极策略——资本市场线


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最优风险资产组合

  • 分散化与资产组合风险

  • 两种风险资产的资产组合

  • 资产在风险与无风险之间的配置

  • Markowitz资产组合选择模型

  • 具有无风险资产限制的最优资产组合


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资本资产定价模型

  • 股票需求与价格均衡

    • 积极投资基金对股票的需求

    • 被动投资(指数)基金对股票的需求

    • 价格均衡


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资本资产定价模型

  • 为什么所有投资者都持有市场资产组合?

  • 消极策略有效吗?

  • 市场资产组合的风险溢价

  • 单个证券的期望收益

  • 证券市场线


Capital asset pricing model capm

Capital Asset Pricing Model (CAPM)

  • Equilibrium model that underlies all modern financial theory

  • Derived using principles of diversification with simplified assumptions

  • Markowitz, Sharpe, Lintner and Mossin are researchers credited with its development


Assumptions

Assumptions

  • Individual investors are price takers

  • Single-period investment horizon

  • Investments are limited to traded financial assets

  • No taxes, and transaction costs

  • Information is costless and available to all investors

  • Investors are rational mean-variance optimizers

  • Homogeneous expectations


Resulting equilibrium conditions

Resulting Equilibrium Conditions

  • All investors will hold the same portfolio for risky assets – market portfolio

  • Market portfolio contains all securities and the proportion of each security is its market value as a percentage of total market value

  • Risk premium on the market depends on the average risk aversion of all market participants

  • Risk premium on an individual security is a function of its covariance with the market


Capital market line

E(r)

CML

M

E(rM)

rf

m

Capital Market Line


Slope and market risk premium

Slope and Market Risk Premium

M=Market portfoliorf=Risk free rateE(rM) - rf=Market risk premiumE(rM) - rf=Market price of risk

=Slope of the CAPM

2

M


Expected return and risk on individual securities

Expected Return and Risk on Individual Securities

  • The risk premium on individual securities is a function of the individual security’s contribution to the risk of the market portfolio

  • Individual security’s risk premium is a function of the covariance of returns with the assets that make up the market portfolio


Security market line

E(r)

SML

E(rM)

rf

ß

ß

= 1.0

M

Security Market Line


Sml relationships

SML Relationships

= [COV(ri,rm)] / m2

Slope SML = E(rm) - rf

= market risk premium

SML= rf + [E(rm) - rf]

Betai = [Cov (ri,rm)] / sm2

Betam = sm2 / sm2 = 1


Sample calculations for sml

Sample Calculations for SML

E(rm) - rf = .08rf = .03

x = 1.25

E(rx) = .03 + 1.25(.08) = .13 or 13%

y = .6

E(ry) = .03 + .6(.08) = .078 or 7.8%


Graph of sample calculations

E(r)

SML

Rx=13%

.08

Rm=11%

Ry=7.8%

3%

ß

.6

1.0

1.25

ß

ß

ß

y

m

x

Graph of Sample Calculations


Disequilibrium example

E(r)

SML

15%

Rm=11%

rf=3%

ß

1.25

1.0

Disequilibrium Example


Disequilibrium example1

Disequilibrium Example

  • Suppose a security with a  of 1.25 is offering expected return of 15%

  • According to SML, it should be 13%

  • Underpriced: offering too high of a rate of return for its level of risk


5178024

CAPM模型的扩展形式

  • 零贝塔模型

  • 生命周期与CAPM模型

  • CAPM模型与流动性


Black s zero beta model

Black’s Zero Beta Model

  • Absence of a risk-free asset

  • Combinations of portfolios on the efficient frontier are efficient

  • All frontier portfolios have companion portfolios that are uncorrelated

  • Returns on individual assets can be expressed as linear combinations of efficient portfolios


Efficient portfolios and zero companions

E(r)

Q

P

E[rz (Q)]

Z(Q)

Z(P)

E[rz (P)]

s

Efficient Portfolios and Zero Companions


Zero beta market model

Zero Beta Market Model

CAPM with E(rz (m)) replacing rf


Capm liquidity

CAPM & Liquidity

  • Liquidity

  • Illiquidity Premium

  • Research supports a premium for illiquidity

    • Amihud and Mendelson


Capm with a liquidity premium

CAPM with a Liquidity Premium

f (ci) = liquidity premium for security i

f (ci) increases at a decreasing rate


Illiquidity and average returns

Illiquidity and Average Returns

Average monthly return(%)

Bid-ask spread (%)


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单指数证券市场

  • 系统风险与公司特有风险

  • 指数模型的估计

  • 指数模型与分散化


Single index model

Single Index Model

  • Reduces the number of inputs for diversification

  • Easier for security analysts to specialize

    ri = E(Ri) + ßiF + e

    ßi = index of a securities’ particular return to the factor

    F= some macro factor; in this case F is unanticipated movement; F is commonly related to security returns

    Assumption: a broad market index like the S&P500 is the common factor


Single index model1

(ri - rf)= i + ßi(rm - rf)+ ei

Single Index Model

Risk Prem

Market Risk Prem

or Index Risk Prem



= the stock’s expected return if the

market’s excess return is zero

i

(rm - rf)= 0

ßi(rm - rf)= the component of return due to

movements in the market index

ei = firm specific component, not due to market

movements


Risk premium format

Let: Ri = (ri - rf)

Risk premium

format

Rm = (rm - rf)

Ri = i + ßi(Rm)+ ei

Risk Premium Format


Security characteristic line

Excess Returns (i)

SCL

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Excess returns

on market index

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.

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Ri =  i + ßiRm + ei

Security Characteristic Line


Using the text example

Using the Text Example

Excess

GM Ret.

Excess

Mkt. Ret.

Jan.

Feb.

.

.

Dec

Mean

Std Dev

5.41

-3.44

.

.

2.43

-.60

4.97

7.24

.93

.

.

3.90

1.75

3.32


Regression results

Regression Results

rGM - rf = + ß(rm - rf)

ß

Estimated coefficient

Std error of estimate

Variance of residuals = 12.601

Std dev of residuals = 3.550

R-SQR = 0.575

-2.590

(1.547)

1.1357

(0.309)


Components of risk

Components of Risk

  • Market or systematic risk: risk related to the macro economic factor or market index

  • Unsystematic or firm specific risk: risk not related to the macro factor or market index

  • Total risk = Systematic + Unsystematic


Measuring components of risk

Measuring Components of Risk

i2 = i2m2 + 2(ei)

where;

i2 = total variance

i2m2 = systematic variance

2(ei) = unsystematic variance


Examining percentage of variance

Examining Percentage of Variance

Total Risk = Systematic Risk + Unsystematic Risk

Systematic Risk/Total Risk = 2

ßi2 m2/ 2 = 2

i2m2/i2m2 + 2(ei) = 2


Index model and diversification

Index Model and Diversification


Risk reduction with diversification

Risk Reduction with Diversification

St. Deviation

Unique Risk

s2(eP)=s2(e) / n

bP2sM2

Market Risk

Number of Securities


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CAPM模型与指数模型

  • 实际收益与期望收益

  • 指数模型与已实现收益

  • 指数模型与期望收益的贝塔关系

  • 指数模型的行业版本


Industry prediction of beta

Industry Prediction of Beta

  • Merrill Lynch Example

    • Use returns not risk premiums

    • a has a different interpretation

    • a = a + rf (1-b)

  • Forecasting beta as a function of past beta

  • Forecasting beta as a function of firm size, growth, leverage etc.


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多因素模型

  • 经验基础

  • 理论基础

  • 经验模型与ICAPM


Multifactor models

Multifactor Models

  • Use factors in addition to market return

    • Examples include industrial production, expected inflation etc.

    • Estimate a beta for each factor using multiple regression

  • Fama and French

    • Returns a function of size and book-to-market value as well as market returns


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套利定价理论

  • 套利机会与利润

  • 充分分散的投资组合

  • 证券市场线

  • 单个资产与套利定价理论

  • 套利定价理论与CAPM模型

  • 多因素套利定价理论


Arbitrage pricing theory

Arbitrage Pricing Theory

  • Arbitrage - arises if an investor can construct a zero investment portfolio with a sure profit

  • Since no investment is required, an investor can create large positions to secure large levels of profit

  • In efficient markets, profitable arbitrage opportunities will quickly disappear


Arbitrage example from text

Arbitrage Example from Text

Current ExpectedStandard

Stock Price$ Return% Dev.%

A 10 25.0 29.58

B 10 20.0 33.91

C 10 32.5 48.15

D 10 22.5 8.58


Arbitrage portfolio

Arbitrage Portfolio

Mean S.D.Correlation

Portfolio

A,B,C25.836.400.94

D22.258.58


Arbitrage action and returns

E. Ret.

* P

* D

St.Dev.

Short 3 shares of D and buy 1 of A, B & C to form P

You earn a higher rate on the investment than you pay on the short sale

Arbitrage Action and Returns


Apt well diversified portfolios

APT & Well-Diversified Portfolios

rP = E (rP) + bPF + eP

F = some factor

For a well-diversified portfolio

eP approaches zero

Similar to CAPM


Portfolio individual security comparison

E(r)%

E(r)%

F

F

Portfolio

Individual Security

Portfolio &Individual Security Comparison


Disequilibrium example2

Disequilibrium Example

E(r)%

10

A

D

7

6

C

Risk Free 4

Beta for F

.5

1.0


Disequilibrium example3

Disequilibrium Example

  • Short Portfolio C

  • Use funds to construct an equivalent risk higher return Portfolio D

    • D is comprised of A & Risk-Free Asset

  • Arbitrage profit of 1%


Apt with market index portfolio

APT with Market Index Portfolio

E(r)%

M

[E(rM) - rf]

Market Risk Premium

Risk Free

Beta (Market Index)

1.0


Apt and capm compared

APT and CAPM Compared

  • APT applies to well diversified portfolios and not necessarily to individual stocks

  • With APT it is possible for some individual stocks to be mispriced - not lie on the SML

  • APT is more general in that it gets to an expected return and beta relationship without the assumption of the market portfolio

  • APT can be extended to multifactor models


5178024

金融市场学——期权

攀 登

二OO六年春季


Option terminology

Option Terminology

  • Buy - Long

  • Sell - Short

  • Call

  • Put

  • Key Elements

    • Exercise or Strike Price

    • Premium or Price

    • Maturity or Expiration


Market and exercise price relationships

Market and Exercise Price Relationships

  • In the Money - exercise of the option would be profitable

  • Call: market price>exercise price

  • Put: exercise price>market price

  • Out of the Money - exercise of the option would not be profitable

  • Call: market price>exercise price

  • Put: exercise price>market price

  • At the Money - exercise price and asset price are equal


American vs european options

American vs. European Options

American - the option can be exercised at any time before expiration or maturity

European - the option can only be exercised on the expiration or maturity date


Different types of options

Different Types of Options

  • Stock Options

  • Index Options

  • Futures Options

  • Foreign Currency Options

  • Interest Rate Options


Payoffs and profits on options at expiration calls

Payoffs and Profits on Options at Expiration - Calls

Notation

Stock Price = ST Exercise Price = X

Payoff to Call Holder

(ST - X) if ST >X

0if ST < X

Profit to Call Holder

Payoff - Purchase Price


Payoffs and profits on options at expiration calls1

Payoffs and Profits on Options at Expiration - Calls

Payoff to Call Writer

- (ST - X) if ST >X

0if ST < X

Profit to Call Writer

Payoff + Premium


Payoff profiles for calls

Payoff

Call Holder

0

Call Writer

Stock Price

Payoff Profiles for Calls


Payoffs and profits at expiration puts

Payoffs and Profits at Expiration - Puts

Payoffs to Put Holder

0if ST> X

(X - ST)if ST < X

Profit to Put Holder

Payoff - Premium


Payoffs and profits at expiration puts1

Payoffs and Profits at Expiration - Puts

Payoffs to Put Writer

0if ST > X

-(X - ST)if ST < X

Profits to Put Writer

Payoff + Premium


Payoff profiles for puts

Payoffs

Put Writer

0

Put Holder

Stock Price

Payoff Profiles for Puts


Equity options leveraged equity

Equity, Options & Leveraged Equity

InvestmentStrategyInvestment

Equity onlyBuy stock @ 100100 shares$10,000

Options onlyBuy calls @ 101000 options$10,000

LeveragedBuy calls @ 10100 options $1,000

equityBuy T-bills @ 2% $9,000

Yield


Equity options leveraged equity payoffs

Equity, Options & Leveraged Equity - Payoffs

IBM Stock Price

$95$105$115

All Stock$9,500$10,500$11,500

All Options$0 $5,000$15,000

Lev Equity $9,270 $9,770$10,770


Equity options leveraged equity1

Equity, Options & Leveraged Equity

IBM Stock Price

$95$105$115

All Stock-5.0%5.0% 15%

All Options-100% -50% 50%

Lev Equity -7.3%-2.3% 7.7%


Protective put

Protective Put

Use - limit loss

Position - long the stock and long the put

PayoffST< XST > X

Stock ST ST

Put X - ST 0


Protective put profit

Protective Put Profit

Profit

Stock

Protective Put Portfolio

ST

-P


Covered call

Covered Call

Use - Some downside protection at the expense of giving up gain potential

Position - Own the stock and write a call

PayoffST< XST > X

Stock ST ST

Call 0 - ( ST - X)


Covered call profit

Profit

Stock

Covered Call Portfolio

ST

-P

Covered Call Profit


Option strategies

Option Strategies

  • Straddle (Same Exercise Price)

    • Long Call and Long Put

  • Spreads - A combination of two or more call options or put options on the same asset with differing exercise prices or times to expiration

  • Vertical or money spread

    • Same maturity

    • Different exercise price

  • Horizontal or time spread

    • Different maturity dates


Put call parity relationship

Put-Call Parity Relationship

ST< XST > X

Payoff for

Call Owned 0ST - X

Payoff for

Put Written-( X -ST) 0

Total Payoff ST - XST - X


Payoff of long call short put

Payoff

Long Call

Combined =

Leveraged Equity

Stock Price

Short Put

Payoff of Long Call & Short Put


Arbitrage put call parity

Arbitrage & Put Call Parity

  • Since the payoff on a combination of a long call and a short put are equivalent to leveraged equity, the prices must be equal.

    C - P = S0 - X / (1 + rf)T

  • If the prices are not equal arbitrage will be possible


Put call parity disequilibrium example

Put Call Parity - Disequilibrium Example

Stock Price = 110 Call Price = 17

Put Price = 5 Risk Free = 10.25%

Maturity = .5 yr X = 105

C - P > S0 - X / (1 + rf)T

17- 5 > 110 - (105/1.05)

12 > 10

Since the leveraged equity is less expensive, acquire the low cost alternative and sell the high cost alternative


Put call parity arbitrage

Put-Call Parity Arbitrage

ImmediateCashflow in Six Months

PositionCashflowST<105ST> 105

Buy Stock-110 ST ST

Borrow

X/(1+r)T = 100+100-105-105

Sell Call+17 0-(ST-105)

Buy Put -5105-ST 0

Total 2 0 0


Optionlike securities

Optionlike Securities

  • Callable Bonds

  • Convertible Securities

  • Warrants

  • Collateralized Loans


Exotic options

Exotic Options

  • Asian Options

  • Barrier Options

  • Lookback Options

  • Currency Translated Options

  • Binary Options


Option values

Option Values

  • Intrinsic value - profit that could be made if the option was immediately exercised

    • Call: stock price - exercise price

    • Put: exercise price - stock price

  • Time value - the difference between the option price and the intrinsic value


Time value of options call

Option

value

Value of Call

Intrinsic Value

Time value

X

Stock Price

Time Value of Options: Call


Factors influencing option values calls

Factors Influencing Option Values: Calls

FactorEffect on value

Stock price increases

Exercise price decreases

Volatility of stock priceincreases

Time to expirationincreases

Interest rate increases

Dividend Ratedecreases


Restrictions on option value call

Restrictions on Option Value: Call

  • Value cannot be negative

  • Value cannot exceed the stock value

  • Value of the call must be greater than the value of levered equity

    C > S0 - ( X + D ) / ( 1 + Rf )T

    C > S0 - PV ( X ) - PV ( D )


Allowable range for call

Allowable Range for Call

Call Value

Upper bound = S0

Lower Bound

= S0 - PV (X) - PV (D)

S0

PV (X) + PV (D)


Binomial option pricing text example

75

C

0

Call Option Value

X = 125

Binomial Option Pricing:Text Example

200

100

50

Stock Price


Binomial option pricing text example1

Binomial Option Pricing:Text Example

150

Alternative Portfolio

Buy 1 share of stock at $100

Borrow $46.30 (8% Rate)

Net outlay $53.70

Payoff

Value of Stock 50 200

Repay loan - 50 -50

Net Payoff 0 150

53.70

0

Payoff Structure

is exactly 2 times

the Call


Binomial option pricing text example2

75

C

0

Binomial Option Pricing:Text Example

150

53.70

0

2C = $53.70

C = $26.85


Another view of replication of payoffs and option values

Another View of Replication of Payoffs and Option Values

Alternative Portfolio - one share of stock and 2 calls written (X = 125)

Portfolio is perfectly hedged

Stock Value50200

Call Obligation 0-150

Net payoff50 50

Hence 100 - 2C = 46.30 or C = 26.85


Generalizing the two state approach

Generalizing the Two-State Approach

Assume that we can break the year into two six-month segments

In each six-month segment the stock could increase by 10% or decrease by 5%

Assume the stock is initially selling at 100

Possible outcomes

Increase by 10% twice

Decrease by 5% twice

Increase once and decrease once (2 paths)


Generalizing the two state approach1

121

110

104.50

100

95

90.25

Generalizing the Two-State Approach


Expanding to consider three intervals

Expanding to Consider Three Intervals

  • Assume that we can break the year into three intervals

  • For each interval the stock could increase by 5% or decrease by 3%

  • Assume the stock is initially selling at 100


Expanding to consider three intervals1

S + + +

S + +

S + + -

S +

S + -

S

S + - -

S -

S - -

S - - -

Expanding to Consider Three Intervals


Possible outcomes with three intervals

Possible Outcomes with Three Intervals

EventProbabilityStock Price

3 up 1/8100 (1.05)3 =115.76

2 up 1 down 3/8100 (1.05)2 (.97)=106.94

1 up 2 down 3/8100 (1.05) (.97)2= 98.79

3 down 1/8100 (.97)3= 91.27


Black scholes option valuation

Black-Scholes Option Valuation

Co = SoN(d1) - Xe-rTN(d2)

d1 = [ln(So/X) + (r + 2/2)T] / (T1/2)

d2 = d1 + (T1/2)

where

Co = Current call option value.

So = Current stock price

N(d) = probability that a random draw from a normal dist. will be less than d.


Black scholes option valuation1

Black-Scholes Option Valuation

X = Exercise price.

e = 2.71828, the base of the nat. log.

r = Risk-free interest rate (annualizes continuously compounded with the same maturity as the option)

T = time to maturity of the option in years

ln = Natural log function

Standard deviation of annualized cont. compounded rate of return on the stock


Call option example

Call Option Example

So = 100X = 95

r = .10T = .25 (quarter)

= .50

d1 = [ln(100/95) + (.10+(5 2/2))] / (5.251/2)

= .43

d2 = .43 + ((5.251/2)

= .18


Probabilities from normal dist

Probabilities from Normal Dist

N (.43) = .6664

Table 17.2

d N(d)

.42 .6628

.43.6664 Interpolation

.44.6700


Probabilities from normal dist1

Probabilities from Normal Dist.

N (.18) = .5714

Table 17.2

d N(d)

.16 .5636

.18.5714

.20.5793


Call option value

Call Option Value

Co = SoN(d1) - Xe-rTN(d2)

Co = 100 X .6664 - 95 e- .10 X .25 X .5714

Co = 13.70

Implied Volatility

Using Black-Scholes and the actual price of the option, solve for volatility.

Is the implied volatility consistent with the stock?


Put option valuation using put call parity

Put Option Valuation: Using Put-Call Parity

P = C + PV (X) - So

= C + Xe-rT - So

Using the example data

C = 13.70X = 95S = 100

r = .10T = .25

P = 13.70 + 95 e -.10 X .25 - 100

P = 6.35


Adjusting the black scholes model for dividends

Adjusting the Black-Scholes Model for Dividends

  • The call option formula applies to stocks that pay dividends

  • One approach is to replace the stock price with a dividend adjusted stock price

    • Replace S0 with S0 - PV (Dividends)


Using the black scholes formula

Using the Black-Scholes Formula

Hedging: Hedge ratio or delta

The number of stocks required to hedge against the price risk of holding one option

Call = N (d1)

Put = N (d1) - 1

Option Elasticity

Percentage change in the option’s value given a 1% change in the value of the underlying stock


Portfolio insurance protecting against declines in stock value

Portfolio Insurance - Protecting Against Declines in Stock Value

  • Buying Puts - results in downside protection with unlimited upside potential

  • Limitations

    • Tracking errors if indexes are used for the puts

    • Maturity of puts may be too short

    • Hedge ratios or deltas change as stock values change


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