Transcript 金融市场学

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
P
c
c
c




1  r  1  r 2
r
 贴现债券
P
FV
1  r T
到期收益率
 简易贷款
 年金
 附息债券
 贴现债券
c1
c2
cT  F
P


2
1  Y  1  Y 
1  Y T
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
 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
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
 US Treasury Bills (T-Bills)
 Certificates of Deposit (CD)
 Commercial paper (CP)
 Bankers’ acceptances
 Eurodollars
 Repos and Reverses
 Federal Funds
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
 $10,000 par T-bill at $9,600 with 182 DTM.
 $400(360/182) = $791.21
thus 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
 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 It may not be withdrawn upon demand.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
 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
 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
 Dollar denominated time deposits in foreign banks.
 Most are for large amounts and with maturity of less
than 6 months.
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
 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 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
 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
 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
 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.
Rate
Mo/Yr
Bid
Asked Chg.
83/4
Aug 00n 105:16 105:18
+8
Ask Yld
7.55
Rate coupon payment 83/4% of $1,000;
paid semiannually; $43.75 per bond each 6 mo.
Maturity = August 2000
n = 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)
 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
 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
 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).
债券条款
 信用
 赎回条款
 转换条款
 回售条款
 浮动利率
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
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）
违约风险保护
 偿债基金
 未来债务
 红利限制
 抵押
债券定价（Bond Pricing）
ParValue
T
C
t
PB  

T
t
(1 r )
t 1 (1 r )
T
PB
Ct
T
R
=
=
=
=
债券价格
利息
付息次数
要求收益率
10年期，面值1000, 8%息票率，半
年付息一次
40
1000
PB  

20
t
(10.03)
t 1 (1 0.03)
20
PB
Ct
P
T
r
=
=
=
=
=
$1,148.77
40
1000
20 periods
3%
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
价格和要求收益率
Price
Yield
10 年期，面值1000，息票率 = 7%，
当前价格= $950
35
1000
950  

T
t
(1 r )
t 1 (1 r )
20
则，收益率r = 3.8635%
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 %
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
持有期收益
HPR 


I   P0  PI  
I = 利息
P1 = 卖出价格
P0 = 买入价格
P0
Example
息票率= 8%
期限 =10年
要求收益率 = 8%
P0
= $1000
由于要求收益率降到 7%
P1
=
$1068.55
HPR =
HPR =
[40 + ( 1068.55 - 1000)] / 1000
10.85% (半年)
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
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
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
久期的计算


wt  CF t (1  y ) Price
t
T
D   t wt
t 1
CFt CashFlow for period t
一个例子
8%
Bond
Time
years
Payment
PV of CF
(10%)
Weight
C1 X
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
久期与价格之间的关系
P
  Dr 
P
r  =连续复利
P
r
 D
P
1 r
r =年复利
修正久期D* = D / (1+y)
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 5 The duration of a level perpetuity is equal to:
(1  y)
y
 Rule 6 The duration of a level annuity is equal to:
1 y
T

y
(1  y ) T  1
 Rule 7 The duration for a corporate bond is equal to:
1  y (1  y )  T (c  y )

y
c[(1  y ) T  1]  y
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
久期和凸性
Price
Pricing Error
from convexity
Duration
Yield
凸性修正
1
Convexity 
2
P  (1  y )
 CFt

2

 (1  y )t (t  t )
t 1 

n
Correction for Convexity:
P
2
1
  D  y  [Conveixity (y ) ]
2
P
Active Bond Management:
Swapping Strategies
 Substitution swap
 Intermarket swap
 Rate anticipation swap
 Pure yield pickup
 Tax swap
Yield Curve Ride
Yield to
Maturity %
1.5
1.25
.75
Maturity
3 mon
6 mon
9 mon
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
金融市场学
股票
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
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
关键经济变量
 Gross domestic product
 Unemployment rates
 Interest rates & inflation
 Consumer sentiment
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
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
经济周期
 经济周期
 波峰
 波谷
 行业与经济周期
 敏感
 不敏感
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
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
行业生命周期
Stage
Sales Growth
Start-up
Consolidation
Maturity
Relative Decline
Rapid & Increasing
Stable
Slowing
Minimal or Negative
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
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%。
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；
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；
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%；
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%；
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%
中美日德2010年1、2月汽车销量
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
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
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
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
红利贴现法的基本原理

Dt
Vo  
t
t  1 (1  k )
V0 = Value of Stock
Dt = Dividend
k = required return
无增长模型
D
Vo 
k
Stocks that have earnings and dividends that are
expected to remain constant
Preferred Stock
无增长模型的举例
D
Vo 
k
E1 = D1 = $5.00
k = .15
V0 = $5.00 / .15 = $33.33
稳定增长模型
Do (1  g )
Vo 
kg
g = constant perpetual growth rate
稳定增长模型的举例
Do (1  g )
Vo 
kg
E1 = $5.00 b = 40%
k = 15%
(1-b) = 60% D1 = $3.00 g = 8%
V0 = 3.00 / (.15 - .08) = $42.86
估计红利增长率
g  ROE  b
g = growth rate in dividends
ROE = Return on Equity for the firm
b = plowback or retention percentage rate
(1- dividend payout percentage rate)
特定持有期模型
P
D
D
D

... 
V 
(1 k ) (1 k ) (1 k )
1
0
N
2
1
2
N
N
PN = the expected sales price for the stock at time
N
N = the specified number of years the stock is
expected to be held
两分定价:增长和无增长成分
E1
Vo 
 PVGO
k
Do (1  g )
E1
PVGO 

(k  g)
k
PVGO = Present Value of Growth
Opportunities
E1 = Earnings Per Share for period 1
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%
两分定价举例
3
Vo 
 $42.86
(.15.08)
5
NGVo 
 $33.33
.15
PVGO  $42.86  $33.33  $9.52
Vo = value with growth
NGVo = no growth component value
PVGO = Present Value of Growth Opportunities
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
市盈率：无预期增长
E1
P0 
k
P0
1

E1
k
 E1 - expected earnings for next year
 E1 is equal to D1 under no growth
 k - required rate of return
市盈率：稳定增长
D1
E 1(1  b)
P0 

k  g k  (b  ROE )
P0
1 b

E 1 k  (b  ROE )
b = retention ratio
ROE = Return on Equity
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
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
市盈率分析中的误区
 使用会计数据
 收益随经济周期波动
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
金融市场学
资产组合
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
1
U  E (r )  A 2
2
U  E(r )  0.005A 2
均值
2
1
0
 2
1
0


标准方差
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
一个例子
 无风险收益5%
概率
公司A收益率
公司B收益率
正常年份
牛市
熊市
0.5
0.3
25%
10%
1%
-5%
异常
年份
0.2
-25%
35%
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
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
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
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
A股票
B股票
每股价格
39元
39元
流通股数
500万股
400万股
每年每股红利预期
6.4元
3.8元
要求收益率
16%
10%
40%
20%
市值
年末每股价格预期
资本收益率
红利率
年度总预期收益率
收益率标准差
相关系数
0.2
无风险收益率
5%
A股票
B股票
每股价格
39元
39元
流通股数
500万股
400万股
市值
195百万元
156百万元
每年每股红利预期
6.4元
3.8元
要求收益率
16%
10%
年末每股价格预期
40
38
资本收益率
2.56%
-2.56%
红利率
16.41%
9.74%
年度总预期收益率
18.87%
7.18%
收益率标准差
40%
20%
相关系数
0.2
无风险收益率
5%
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)
 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
 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
 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)
E(rM)
M
rf
m
CML
Slope and Market Risk Premium
M
rf
E(rM) - rf
=
=
=
Market portfolio
Risk free rate
Market risk premium
E(rM) - rf
=
Market price of risk

=
Slope of the CAPM
2
M
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
M
= 1.0
SML Relationships
 = [COV(ri,rm)] / m2
Slope SML = E(rm) - rf
= market risk premium
SML = rf + [E(rm) - rf]
Betai
= [Cov (ri,rm)] / m2
Betam
= m2 / m2 = 1
Sample Calculations for SML
E(rm) - rf = .08
rf = .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
ß
y
1.0
ß
m
1.25
ß
x
Disequilibrium Example
E(r)
SML
15%
Rm=11%
rf=3%
ß
1.0
1.25
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
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
 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

E (ri )  E (rQ )  E (rP )  E (rQ )

Cov(ri , rP )  Cov(rP , rQ )
 P2  Cov(rP , rQ )
Efficient Portfolios and Zero
Companions
E(r)
Q
P
E[rz (Q)]
E[rz (P)]
Z(Q)
Z(P)

Zero Beta Market Model

E (ri )  E (rZ ( M ) )  E (rM )  E (rZ ( M ) )

Cov(ri , rM )
CAPM with E(rz (m)) replacing rf
 M2
CAPM & Liquidity
 Liquidity
 Illiquidity Premium
 Research supports a premium for illiquidity
 Amihud and Mendelson
CAPM with a Liquidity Premium


E (ri )  rf   i E (ri )  rf  f (ci )
f (ci) = liquidity premium for security i
f (ci) increases at a decreasing rate
Illiquidity and Average Returns
Average monthly return(%)
Bid-ask spread (%)
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
 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 Model
(ri - rf) =
Risk Prem

i
 i + ßi(rm - rf) + ei
Market Risk Prem
or Index Risk Prem
= the stock’s expected return if the
market’s excess return is zero
(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)
Rm = (rm - rf)
Ri =
Risk premium
format
i + ßi(Rm) + ei
Security Characteristic Line
Excess Returns (i)
SCL
.
.
.
.
.
.
. . .
.
.
.
.
.
.
.
.
.
.
.
. .
.
.
Excess returns
.
.
.
on market index
.
.
.
.
.
.
.
.
.
. . . .
.
.
.
.
. . . . . R =.  + ß R + e
i
i
i m
i
Using the Text Example
Jan.
Feb.
.
.
Dec
Mean
Std Dev
Excess
GM Ret.
5.41
-3.44
.
.
2.43
-.60
4.97
Excess
Mkt. Ret.
7.24
.93
.
.
3.90
1.75
3.32
Regression Results
rGM - rf =  + ß(rm - rf)
ß
Estimated coefficient
-2.590
Std error of estimate
(1.547)
Variance of residuals = 12.601
Std dev of residuals = 3.550
R-SQR = 0.575
1.1357
(0.309)
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
i2 = i2 m2 + 2(ei)
where;
i2 = total variance
i2 m2 = systematic variance
2(ei) = unsystematic 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
RP   P   P  eP
N
P  1N  P
i 1
N
 P  1 N  P
i 1
eP  1
N
N
e
i 1
P
2
 P   P2 M
  2 (eP )
Risk Reduction with
Diversification
St. Deviation
Unique Risk
2(eP)=2(e) / n
P2M2
Market Risk
Number of
Securities
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
 Merrill Lynch Example
 Use returns not risk premiums
 has a different interpretation
  = + rf (1-)
 Forecasting beta as a function of past beta
 Forecasting beta as a function of firm size, growth,
leverage etc.
多因素模型
 经验基础
 理论基础
 经验模型与ICAPM
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
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 - 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
Current
Expected
Stock Price$ Return%
A
10
25.0
B
10
20.0
C
10
32.5
D
10
22.5
Standard
Dev.%
29.58
33.91
48.15
8.58
Arbitrage Portfolio
Mean
Portfolio
A,B,C 25.83
D
S.D.
6.40
22.25
Correlation
0.94
8.58
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
APT & Well-Diversified Portfolios
rP = E (rP) + PF + 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
Disequilibrium Example
E(r)%
10
7
6
A
D
C
Risk Free 4
.5
1.0
Beta for F
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
E(r)%
M
[E(rM) - rf]
Market Risk Premium
Risk Free
1.0
Beta (Market Index)
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
金融市场学——期权
攀 登
二OO六年春季
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
 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 - 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
 Stock Options
 Index Options
 Futures Options
 Foreign Currency Options
 Interest Rate Options
Payoffs and Profits on Options at
Expiration - Calls
Notation
Stock Price = ST Exercise Price = X
Payoff to Call Holder
(ST - X) if ST >X
0
if ST < X
Profit to Call Holder
Payoff - Purchase Price
Payoffs and Profits on Options at
Expiration - Calls
Payoff to Call Writer
- (ST - X) if ST >X
0
if ST < X
Profit to Call Writer
Payoff + Premium
Payoff Profiles for Calls
Payoff
Call Holder
0
Call Writer
Stock Price
Payoffs and Profits at
Expiration - Puts
Payoffs to Put Holder
0
if ST > X
(X - ST) if ST < X
Profit to Put Holder
Payoff - Premium
Payoffs and Profits at
Expiration - Puts
Payoffs to Put Writer
0
if 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
Equity, Options &
Leveraged Equity
Investment
Strategy
Investment
Equity only
Buy stock @ 100 100 shares
$10,000
Options only
Buy calls @ 10
Leveraged
equity
Buy calls @ 10
100 options
Buy T-bills @ 2%
Yield
1000 options $10,000
$1,000
$9,000
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 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
Use - limit loss
Position - long the stock and long the put
Payoff
ST < X
ST > X
Stock
ST
ST
Put
X - ST
0
Protective Put Profit
Profit
Stock
Protective Put
Portfolio
-P
ST
Covered Call
Use - Some downside protection at the expense of
giving up gain potential
Position - Own the stock and write a call
Payoff
ST < X
ST > X
Stock
ST
ST
Call
0
- ( ST - X)
Covered Call Profit
Profit
Stock
Covered Call
Portfolio
-P
ST
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
ST < X
ST > X
0
ST - X
Payoff for
Call Owned
Payoff for
Put Written-( X -ST)
Total Payoff
ST - X
0
ST - X
Payoff of Long Call
& Short Put
Payoff
Combined =
Leveraged Equity
Long Call
Stock Price
Short Put
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
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
Position
Immediate
Cashflow
Cashflow in Six Months
ST<105
ST> 105
Buy Stock
-110
ST
ST
Borrow
X/(1+r)T = 100
+100
-105
-105
Sell Call
+17
0
Buy Put
-5
Total
2
105-ST
0
-(ST-105)
0
0
Optionlike Securities
 Callable Bonds
 Convertible Securities
 Warrants
 Collateralized Loans
Exotic Options
 Asian Options
 Barrier Options
 Lookback Options
 Currency Translated Options
 Binary Options
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
Factors Influencing Option
Values: Calls
Factor
Stock price
Exercise price
Volatility of stock price
Time to expiration
Interest rate
Dividend Rate
Effect on value
increases
decreases
increases
increases
increases
decreases
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 > S 0 - ( X + D ) / ( 1 + Rf ) T
C > S0 - PV ( X ) - PV ( D )
Allowable Range for Call
Call Value
Lower Bound
= S0 - PV (X) - PV (D)
S0
PV (X) + PV (D)
Binomial Option Pricing:
Text Example
200
100
75
C
50
Stock Price
0
Call Option Value
X = 125
Binomial Option Pricing:
Text Example
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
150
53.70
0
Payoff Structure
is exactly 2 times
the Call
Binomial Option Pricing:
Text Example
150
53.70
C
0
2C = $53.70
C = $26.85
75
0
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 Value
50
200
Call Obligation
0
-150
Net payoff
50
50
Hence 100 - 2C = 46.30 or C = 26.85
Generalizing the
Two-State Approach
Assume that we can break the year into two sixmonth 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 Approach
121
110
104.50
100
95
90.25
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 Intervals
S+++
S++
S++-
S+
S+-
S
S+-S-
S-S---
Possible Outcomes with
Three Intervals
Event
Probability
Stock Price
3 up
1/8
100 (1.05)3
=115.76
2 up 1 down
3/8
100 (1.05)2 (.97)
=106.94
1 up 2 down
3/8
100 (1.05) (.97)2
= 98.79
3 down
1/8
100 (.97)3
= 91.27
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 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
So = 100
X = 95
r = .10
T = .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
N (.43) = .6664
Table 17.2
d
N(d)
.42
.6628
.43
.6664 Interpolation
.44
.6700
Probabilities from Normal Dist.
N (.18) = .5714
Table 17.2
d
N(d)
.16
.5636
.18
.5714
.20
.5793
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
P = C + PV (X) - So
= C + Xe-rT - So
Using the example data
C = 13.70 X = 95
S = 100
r = .10
T = .25
P = 13.70 + 95 e -.10 X .25 - 100
P = 6.35
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
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
 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