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A31021 Any Calculator
Creation date：2024-04-11 16:55:43
Belonging category：金融Finance
Tag A31021
A31021 Any Calculator

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A31021 Any Calculator

Department of Economics
Economics of Financial Markets
Time Allowed: 1 Hour plus 30 minutes for uploading of answers

Answer TWO questions

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A31021 Page 2 Turn Over
Answer Two Questions. Each question has 25 marks allocated. The
marks awarded for each section of a question are shown in bracket.
In order to gain full marks you must explain fully the steps you take in solving the
problems. Since this is an online exam, if you use formulae from the lectures or class
exercises, you will not get credit for stating these formulae without an explanation of
what the formulae mean and why you are using them to answer the question.

1. You observe that a consumer with a power utility function in consumption
U=400C0.5 and a subjective discount factor of value 5/6, chooses to consume
400 today and a distribution of consumption next period such that the
expected value of marginal utility is 12 and a standard deviation of marginal
utility is 0.1. There is a single financial asset with an expected net return of x
and this asset has a standard deviation of return of y and a correlation of -0.8
with the individual’s marginal utility of future consumption.

What is the relationship between x and y if the individual is maximising utility?
(10 marks)

Explain how the Consumption-based CAPM provides an understanding of the
risk of an asset and discuss how this is illustrated in terms of the relationship
between x and y
(15 marks)

2. The consumer has a utility function given by U(C)=ln(C-H) where H is the
habit level of consumption. Her subjective discount factor is given by 0.8.
There are two states of the world next period. Given contingent claim prices
the individual chooses a level of consumption 15 today and 16 in state 1 and
17 in state 2. State 1 occurs with probability 0.6.

Use this information to calculate the value of the two contingent claim prices
(7 marks).

Discuss how incorporating Habit in the utility function delivers time-varying
risk aversion (8 marks)

Discuss, briefly, how time-varying risk aversion provides an explanation for
the predictability of stock returns. (10 marks)

3. An individual with current wealth of 10 at time t, investing over a single
period, has a utility function U=100Wt+1-0.5Wt+12 where Wt+1 is wealth at t+1.
She can hold either cash which pays zero interest or a share which has a
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A31021 Page 3 Turn Over

price today of P and will have a price next period of 90 in state 1 with
probability 0.5 and 120 in state 2 with probability 0.5 (the price includes any
dividend owing).
What is the optimal portfolio for this individual to hold?
(15 marks)
Use you solution in the problem above to explain the optimal portfolio
selection when an individual’s labour income varies across the two states of
the world in the second period
(10 marks)

4. (a) Consider the share of a new company that is expected to pay no dividend
for n periods and then a dividend D* which grows at rate g after that. The
expected return on the asset is R*. Show that the price (P) of such an asset is
P=D*
(1+g)
(1+R*)
n
(R*-g)

(10 marks)

(b) Use the analysis above to consider how the share price of a company
displaying this dividend behaviour could develop a bubble. (7 marks)

(c) examine how the price equation above could be used to explain the impact
of the covid-19 pandemic on share prices (8 marks)
Case category
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CMP7000A CMP-7038B Math 263 LAW3016 CS371 STAT 334 FIN0008 ACC3004 STAT 371 ​COMP1921 MTH201 ACCT2000 UN3412 CIV6000 MATHS 3021 MATE7014 ECON1 CIBC6035 LAW121G COMM 321 CSC8204R TTM2033 CSCI 2600 MAE 115 LNG302 CENV6175W1 ECON30019 CPS2015 BST969 DDES9015 AMATH242 CS 1151 N1592 ACCT600 EG503G SMM519 EC318 Ecstatistics EEE 471 MARK2051 Topology COM00037H ACCT3000 MTHM501 EG501V COM00055H BUSN9085 GGR273 MATH 2B ITD102 MA214 ECON0060 ECE3114 ECMM447 Mechanics CCT361H5S BSAN3210 WELF2001 Fin3001 RESP5001 STA 137 Linguistics 101 CSCI368 CMPSC497 LUBS3655 OMBA 5355 BUSM2562 ​BFF5902 CYBR7001 CULT2005 ECON 7720 MTRX3760 FSE598 ​LUE1001 MGSC 7100 CS3240 COSC7500 ACCT3091 INFOGR TRAN 2080 DESIGN CIVE215001 CIVE2360 CPSC 8430 FNCE2003 Stoichiometry INFS6023 Quantitative Method Math 21D ECE5179 Design ​ECON8022 Chemical DMS 213 ADM1370 BFF5902 BFF2701 AGRI10051 AMN400 ECON7322 ​FINC5090 ​MATH1052 ​SciComp Elec4622 ​FINS5516 ENG 101 MMM143 CS431CA2 BSAN2201 EBSC7070 ES9v9-10 PLIN0009 DATA 8 MATH 101 BCPM0097 ​MAT 237 BISM2201 EEE8099 Physics 11 ECE2238B Biostat 234 ​ECON30009 INF10025 CHEM252 CCMA4008 CIVE 3007 STAT0031 ELEC ENG 3108 MGMT90140 CHEM 252 STAT3016 MMM095 ​MMGT6016 Legal STAT 311 ELEC9764 COMP 370 TCS 3053 EECS 1021 FIT1051 C/C++ EE3C COMP2003J COM398 COMP51915 Simulator FIN42330 8PRO102 PGD ELEC5160 XJCO1921 COMP5123M INFS 2042 CHE1148H ECA5313 IN3329 Microsoft Modeling B15 2TT COMP3687 COMP2432 DMS2030 KAN4TSF CFKG CSE 5322 CSE 445 STATS 3DA3 CHC5223 COMP1048 EL3105 EECS 3221 CS231 ME 4434 ITP4510 ITP4501 CSCI 5708 Controller EECE 5699 CPEN 231L CPN programs CSC8016 MATU9D2 ENGN4213 2. SVM. (10 points) Consider an SVM classifier using RBF kernel, and finish the following python code to search for the optimum kernel parameter γ. You are required to calculate the RBF function and search yourself, instead of using functions in Scikit-Learn (sklearn). def parameter search(gamma list ,Xtr,ytr,Xts,yts ,...): """ Parameters gamma list: A list of RBF kernel parameter gamma to search for Xtr: Training data, shape (ntr,nrow,ncol) ytr: Training labels, shape (ntr,) Xts: Test data, shape (nts,nrow,ncol) yts: Test labels, shape (nts,) ... Add other parameters as needed Returns: gamma optimum: The gamma with minimum error on Xts, yts """ ... return gamma optimum
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