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A部分（同时回答Q1和Q2；回答Q3或Q4）50分
Q1。回答问题的以下部分。
a）简要解释绝对风险的Arrow-Pratt系数是多少

b）计算并解释对数的ARA和RRA值

> 0。注意x可以理解为与每个可能的结果相关联

a）绝对风险规避的Arrow-Pratt系数（ARA，2-

ARA系数越大，规避风险越大（或风险越小）

��𝐴（�）= −�𝑢′′
（�）
𝑢’（�）

b）ARA = 1 / x。这意味着任何遵循这种实用程序的人

RRA = 1。这意味着任何人的财富比例

Q2。假设简化的金融市场仅包含2个风险资产：
800股A股，每股售价5英镑和100股

B股票的价格为每股60磅。假设存在风险-

CAPM。
a）解释市场投资组合的定义并计算

b）如果股票A的贝塔系数为1.5，那么市场的贝塔系数是多少？

c）在图中说明您对a）-b）部分的答案。 （2分）

a）如果所有投资者在风险资产中每种风险资产的比例相同

（=市场投资组合）。由于我们这里只有两个风险资产，

w2 = 100 * 60 /（800 * 5 + 100 * 60）= 60％的市场组合
b）市场beta = w1 *股票A的beta + w2 *股票B的beta = 1
40％* 1.5 + 60％*股票B的beta = 1

c）使用SML线进行说明。

Section A (answer both Q1 and Q2; answer either Q3 or Q4) 50 marks
Q1. Answer the following parts of the question.
a) Briefly explain what Arrow-Pratt coefficients of absolute risk
aversion (ARA) and relative risk aversion (RRA) are. (5 marks)
b) Calculate and interpret the ARA and RRA values for the logarithmic
utility function �(�) = log𝑎 �, where a is a positive parameter and x
>0. Note x can be understood as each possible outcome associated
with a given choice, or the level of wealth given each possible
outcome of a choice. (5 marks)

a) Arrow-Pratt coefficient of absolute risk aversion (ARA, 2-
dimentional) describes local curvature of a utility function. Given a
monotone increasing utility function (indicating non-satiable agents
assumption), negative values of the measure correspond to risk-
seeking behaviour and positive values to risk-avoiding behaviour.
The greater the ARA coefficient, the more risk averse (or less risk
loving) an individual is at the level of x.
Arrow-Pratt coefficient of Relative risk aversion (RRA, 2-
dimensional) is another local risk aversion measure that describes
an individual’s attitude toward proportional risks.
Constant/decreasing/increasing RRA with increasing wealth means
the proportion of wealth that an individual is willing to put at risk
remains constant/increases/decreases as wealth increases.
��𝐴(�) = −�𝑢′′
(�)
𝑢′(�)

b) ARA=1/x. It means that anyone who follows this type of utility
function shows risk-avoiding behaviour. However, as x (wealth)
increases, risk aversion gets smaller and smaller.
RRA=1. It means that the proportion of wealth that anyone who
follows this type of utility function is willing to put at risk remains
constant as wealth increases.

Q2. Assume a simplified financial market consists of only 2 risky assets:
800 shares of stock A which sells for 5 pounds per share and 100 shares

of stock B which sells for 60 pounds per share. Assume there is a risk-
free asset. Answer the following parts of the question using the framework
of CAPM.
a) Explain the definition of the market portfolio and calculate the
weights on the two stocks in the market portfolio in this
hypothetical market. (4 marks)
b) If the beta of stock A is 1.5, what are the betas for the market
portfolio and the stock B? (4 marks)
c) Illustrate your answers to parts a)-b) in a diagram. (2 marks)

a) If all investors have the same proportion of each risky asset in the
tangent portfolio M (i.e. all securities are included in proportion to
their market values), then the weight of each risky asset in M is the
share of the asset’s market value of the total market value; the
portfolio M is completely diversified and include only systematic risk
(=the market portfolio). As we only have two risky assets here,
their weights are w1=800*5/(800*5+100*60)=40% and
w2=100*60/(800*5+100*60)=60% in the market portfolio
b) Market beta=w1* stock A’s beta+w2*stock B’s beta=1
40%*1.5+60%*stock B’s beta=1
stock B’s beta=2/3 or approximately 0.67
c) Illustrate using the SML line.
Expected rate of return

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