证券投资学第2章

s 34.293
Example: Risky Investments with Risk-Free Investment
Risky Inv.
W1 = 150 Profit = 50
100
1-p = .4
Risk Free T-bills
W2 = 80 Profit = -20 Profit = 5

How much extra return do we need to be compensated for the additional risk?


most people would prefer the sure $15,000: both choices offer an expected reward of $15,000 but one of them also has risk, which we dislike if the sure thing reward was only $10,000, you might choose the lottery instead
证券投资的收益和风险

问题


你投资在哪种证券 有哪些风险 如何度量风险 如果该股票下一年的预期价格为10元，你是 否会投资该股票 投资者如何决策
证券投资风险

风险的来源

经营风险(Business risk) 财务风险(Financial risk) 流动风险(Liquidity risk) 违约风险(Default risk) 利率风险 通货膨胀风险 国家经济状况

最大、最小值之差 频率分布

作业：计算我国股市的回报率和风险

目的：使得我们对各种可能投资的表现有一个合理 的预期。 要求：

把股票分成大、中、小三个板快分别计算回报率和风险 按照样本均值、最大和最小值、分布频率分别计算回报率

VaR (Value at Risk)

the expected maximum loss (or worst loss) over a target horizon within a given confidence interval

多期回报率和复利

例子：一种股票现价为46元，假设一年后价 格为50元，两年后价格为56元；在第一年中 红利为1.5元，第二年中红利为2元，假设每 次分红都在年末进行，求这种股票在这两年 中的持有期收益率HPR，以及以复利计算时 的每年持有期收益率HPR。

假设红利支付后马上投资
几何平均与算术平均
Risk Premium = 17


The question of whether a given risk premium provides adequate compensation for the investment’s risk is age-old. One of central concerns of finance theory is the measurement of risk and the determination of the risk premiums that investors can expect of risky assets in wellfunction capital markets.


We should stress that variability of HPR in the past can be an unreliable guide to risk, at least in the case of the risk-free asset. For risk-free asset, the variance is zero, but the sample variance is not zero. This reflects variation over time in expected returns rather than fluctuations of actual returns around prior expectations.

The additional average returns from stocks should reflect the greater riskiness of stocks.

Finance theory says:

Average returns over long periods of time are determined by risk
ending price
140元 110元 80元
HPR
44% 14% -16%

３. 对风险证券收益的度量

期望回报率 (expected return) 样本均值


The record of past rates of return is one possible source of information about expected return. 因为我们无法知道将来，所以用样本均值来估计期 望回报率.
state of the economy
boom normal growth recession

probability
0.25 0.50 0.25
ending price
140元 110元 80元
HPR
44% 14% -16%

４.对风险证券风险的度量


方差、标准差 样本方差


The record of past rates of return is one possible source of information about variance. 因为我们无法知道将来，所以用样本方差来 估计方差.
P(W (0) W (T ) Var ( )) 1

例子

HPR的方差 HPR的标准差

Annual rates of return, 1926-1999
Small Large Long- Interm T-bills inflati stocks stocks term ediateon bonds term bonds 18.81 13.11 5.36 5.19 3.82 3.17 39.69 20.21 8.12 6.38 3.29 4.46

系统风险与非系统风险
收益和风险的例子

一支股票，现价100元/股，预期在接下来的一 年中的红利为4元，一年后的价格预期为下表 所示，无风险利率为6%
state of the economy
boom normal growth recession

probability
0.25 0.50 0.25
W1 = 150 Profit = 50
W = 100
1-p = .4
W2 = 80 Profit = -20
E(W) = pW1 + (1-p)W2 = 6 (150) + .4(80) = 122
s2 = p[W1 - E(W)]2 + (1-p) [W2 - E(W)]2 =
.6 (150-122)2 + .4(80=122)2 = 1,176,000
Mean St. Dev
The trade-off between risk and return

一般来说，高收益伴随着高风险 The equity premium for the market of U.S. from 1926-2002 is 5.9%

Example: Risk - Uncertain Outcomes
５. 投资者的选择方式

投资者的效用函数

例子 U (WT ) exp(WT ) 最大化效用函数
5.1 风险厌恶


例子: a lottery where you will either receive $50,000 if a coin lands heads and lose $20,000 if it lands tails compare this with getting $15,000 for sure
第二章 证券投资风险和收益

回报和风险的定义 投资者制定投资目标应考虑回报和风险

投资者厌恶风险，承担风险需要补偿 不同的投资者对风险厌恶程度不一样，怎样 刻画不同投资者对收益-风险之间的权衡关 系

市场给出收益-风险之间的公平关系-市场 定价
1. 回报率的定义

回报率是对证券表现的一种度量。
2. 证券投资的风险

风险是指未来的不确定性 没有风险就没有股市

2001年下半年以来的中国股市 2001年9.11 1987年10月19日，被称为“黑色星期一” DJIA 下跌了22.6%(508点）
近八年中国股市
10000
15000
20000
25000
30000
35000
40000

（1）30天到期、现在年收益率为6%的货币 市场基金 （2）一年定期存款，利率为7.5% （3）10年期长期国债，每年收益为9% （4）一种股票，现价10元/股，下一年的预 期股价为11.2元/股，且估计红利为0.2元 （5）一人向你借钱，期限一年，利率15% (6）以8.4元人民币兑1美元买外汇

Risk averse
U X1 (1 ) X 2 U X1 (1 )U X 2

Stock offer higher average returns than bonds because:

People are risk averse: to be willing to hold a risky security they must receive higher expected return as a reward for doing so.

2 55 Gross Return= 1.14 50

净回报率
dt 1 Pt 1 rt 1 1 Pt
d t 1 Pt 1 Pt Pt Pt

净回报率=收入收益+资本利得

HPR provides a useful device for simplifying the complex reality of investment analysis. Although no panacea, it allows an analyst to focus on the most relevant horizon in a given situation and offers a good measure of performance over such a period.
NASDAQ指数曾高达5100多点，2002/10/2不到1200！
微软为绩优股，但股价已较2000年高位下跌约六成！
LUCENT 2002/10/2股价仅$0.75，不及1999年高位的1%！！
证券投资的风险

例子：下一年你有5000块钱用于投资， 投资一年，有六种投资机会供选择：


45000
5000
Jan-85 Ja来自百度文库-86 Jan-87 Jan-88 Jan-89 Jan-90 Jan-91 Jan-92 Jan-93 Jan-94 Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02
0
NIKKI 225 Index

实现回报率 (realized return) 风险酬金(risk premium)与超额回报率(excess return)
例子：风险酬金(risk premium)与超额 回报率(excess return)

一支股票，现价100元/股，预期在接下来的一 年中的红利为4元，一年后的价格预期为下表 所示，无风险利率为6%

总回报率(持有期收益率HPR(holding period return))
d t 1 Pt 1 Rt 1 Pt

假设红利在持有期末支付

Example: buy share at $50, at end of year it is worth $55 and pays $2 dividend