本次英国代写主要为金融经济学相关的限时测试
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
厌恶（ARA）和相对风险厌恶（RRA）。 （5分）
b）计算并解释对数的ARA和RRA值
效用函数�（�）=log𝑎�，其中a是一个正参数，x
> 0。注意x可以理解为与每个可能的结果相关联
给定选择，或者给定每种可能的财富水平
选择的结果。 （5分）
建议答案：
a）绝对风险规避的Arrow-Pratt系数（ARA，2-
三维）描述效用函数的局部曲率。给定一个
单调递增效用函数（表示不满意的代理
假设），度量的负值对应于风险-
寻求行为和积极的价值观，以规避风险。
ARA系数越大，规避风险越大（或风险越小）
爱）一个人处于x的水平。
相对风险规避的Arrow-Pratt系数（RRA，2
维度）是另一种描述本地风险规避的方法
个人对比例风险的态度。
不断增加/减少/不断增加的RRA意味着财富增加
个人愿意冒险承担的财富比例
随财富增加而保持不变/增加/减少。
��𝐴（�）= −�𝑢′′
（�）
𝑢’（�）
b）ARA = 1 / x。这意味着任何遵循这种实用程序的人
功能显示规避风险的行为。但是，作为x（财富）
增加，风险规避变得越来越小。
RRA = 1。这意味着任何人的财富比例
遵循这种类型的效用功能愿意冒着风险
随着财富的增加而保持不变。
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-
免费资产。使用框架回答问题的以下部分
CAPM。
a）解释市场投资组合的定义并计算
在此市场投资组合中的两只股票的权重
假设的市场。 （4分）
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？
投资组合和股票B？ （4分）
c）在图中说明您对a）-b）部分的答案。 （2分）
建议答案：
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
切线组合M（即所有证券均按比例包括在内
他们的市场价值），那么M中每项风险资产的权重就是
资产市值占总市值的份额；这
投资组合M完全分散，仅包含系统风险
（=市场投资组合）。由于我们这里只有两个风险资产，
它们的权重为w1 = 800 * 5 /（800 * 5 + 100 * 60）= 40％
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
股票B的beta = 2/3或大约0.67
c）使用SML线进行说明。
预期收益率
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)
Suggested answer:
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)
Suggested answer:
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