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ECON0001 ECONOMICS OF FINANCIAL MARKETS
创建日期：2024-07-09 17:53:59
所属分类：经济Economics
标签： ECON0001
ECONOMICS OF FINANCIAL MARKETS

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DEPARTMENT OF ECONOMICS


ECON0001

ECONOMICS OF FINANCIAL MARKETS

Formative assessment n.1 on the first part of the unit

Section A: investment under risk or uncertainty (30 marks)

1.  [Total  9 points] Consider the decision problem of investing an amount of wealth W = $1000000 into a risky asset with return

and into a risk-less asset with risk-free interest rate r = 5%. You are a risk averse investor with a CRRA utility function

where ρ = 0.5, and WT  is the amount of wealth at the end of the investment.

(a)  Find the optimal allocation in risky and risk-less assets as a function of the probability p and the initial amount of wealth W invested.  How does it depend on p?  Comment on your result.

(b)  Compute the optimal allocation for a probability p = 50% and for p = 51%. What is the optimal allocation for p = 1?  Comment.

(c) What is the lower bound of the probability p for investing a positive share  into the risky asset? Answer with and without using the utility function, and  comment. What is this lower bound of probability for a risk neutral investor? (d) Find the lower bound of the probability p for starting to borrow money at the risk-less interest rate and invest an amount larger than W in the risky asset.

2.  [Total 7 points] Consider an asset with a risky rate of return over a time period T expressed by

The investment of an amount of wealth W returns WT  at the end of the period T, and investors have utility function U(WT ) = ln(WT ).

(a) Why this asset and this utility imply a positive risk premium?

(b) Find the Certainty Equivalent of the investment for such utility as a function of the probability p of the higher return value and the invested wealth W. How does it depend on p?  Comment on your results.

(c)  Compute Certainty Equivalent and Risk Premium for a probability p = 50%.

(d) What is the risk premium for p = 0 and for p = 1?  Comment on your results.

(e) How does the risk premium depend on the probability p?  Proof that the risk premium is anon-monotonic function of the probability p.

3.  [Total 8 points] An investor with utility function

faces the decision problem of allocating her wealth x in the following assets:  a risky asset that gives a return of 20% or a loss of -5% with equal probability, and a risk-less asset with interest rate equal to 5%.

(a) How does her relative risk aversion depend on wealth x, if σ = 10-6 $-1 ?  If her wealth increases from £1 Mln to £10 Mln, how does relative risk aversion changes? And absolute risk aversion?

(b)  Find the optimal investment in risky and risk-less asset as a function of σ and as a function of wealth x, and comment.

(c)  Study the optimal allocation for σ  !  1 and σ  !  0.  What is the condi- tion on σ for investing 100% in the risk-less asset?  Justify your answer both conceptually and mathematically.

(d) If she invests a total wealth of £1 Mln, what is the condition on risk aversion σ for the optimal allocation to be 100% invested in the risky asset?  Comment on your answer.

(e)  Evaluate the marginal effect of σ on the optimal share of investment in the risky asset.

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关键词一 关键词二 关键词三 关键词四 关键词五 和法规和的发更好的风格和 ECON 615 FINC 612 CSC148 COMP 639 ACCT 203 ACCT 211 PSYC 101 MTH2009 COMP52315 PSYCO 432 statistics MATH4063 11 xxx 1 MA1MSP MAST30028 MATH3888 CS341 EEE30002 ES2F5 MCD4160 CC0933 ECON 1101 MCHM3001 CHEM3118 COMMGMT 2511 COMP41280 STAT 631 24T1 IRE379 SENG365 ECON433 FIT3139 MATH4602 LING5621M FINS5516 ECON3208 MN2177 L2 SM EEET1415 Finance DS4023 COMP3004 7CCSMRTS K1S5B6 Stat230 CSCI4211 CSI2132 ECON30130 MAS6100 ENVS222 COM2107 INFO1112 STAT 4004 FIT2100 comp2022 COMP4691 Physics 307 Econ 659 probability CSCI316 fir29 CSCI203 COMP3160 COMP6714 INFO1113 Physics 7B Physics Photonics S203031 STAT2005 COMP90015 CSCI 2110 CSCC46 Information CSC477 COMP4650 Statistical COMP 346 COMP1017 ELEC340 MATH1007 Programming function STAT 244 CS 134 Java cse13s Math 108A FW20 ECON3389 CSE 130 Science 331 COMP9020 engineering COSC 445 CSE 5523 GAME2012 visualization MATH 235 Math 370 CSC343 COGS 108 EE524 COMP10200 STAT 416 3FK4 MSCI 311 ECON6113 ACC40700 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MATH 239 QF5203 INFR08010 IT114105 FIT2093 ECON3124 ECON1195 MATH 337 STAT 3006 COMP202 COMP3130 MATH3609 COMP 250 CS6140 IEEE ELE00041I FIN40090 CIV 5899 MATH3066 IGNMENT MATH 2009 STAT3405 HIST 101 MATH 3281 CEGE0042 ICT532 LAB 7 LAB 5 MCO455 CSIT214 Q4 IFB104 A1 ECO220Y5Y DA5020 CMPSC473 FIN9007 DSCI553 MSCI534 COMP3308 CSE-112 CMPT 310 EE104 F 2C P20 ALY2010 BUSM060 STA258 ECO00030M R BIOSTAT 274 COS6012-B FIT3155 CMPUT 340 EC421 INFS4205 ECOM135 NATS 1740 COMP809 MBE 6005 STA465 CSSE2310 CIVL2700 DATA4700 CMPSC 473 ISE 529 CS5044 MAST30020 COMP2207 ENGG1001 COMP0046 FIT3165 STAT GR5241 MECH0007 vATHK1001 ANALYTIC ATHK1001 MATH352001 HW3 S1 BMAN 24662 COMP 636 Stat-461 STAT 302 STAT 2132 STAR534 ENG4137 CMP3752M CS3103 BISM3222 STA 135 ME155A IIMT3601 ECON3371 ECON 3371 HW4 FINA 5840 DT211C CTEC3902 MAT005 MATH2148 S261F Econ 332 MATH3734 MIS41270 7CCMFM13 SYST 664 CIS434 CENG10014 MT4111 MT4527 ECMM424 CMT219 Math 136 MATH 3120 COMP10002 MAST20009 MATH0058 BEEM117 ISYE 6420 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MATH20602 COMP532 MAS275 COMP5318 COMP4002 FIT5086 MAST20004 FIT3152 FIT5129 CIS2380 CS521 COMP 1005 EECMS CITS5501 ECE 462 ECON 6002 ENG 4051 CSC 648 CMT654 MECHENG 713 PHYS1002 AMME 2000 FP0060 DDES3200 MECHENG 743 BINF90002 FIT2081 ISYS90081 ELECTENG 722 BUS 360 ECOS3010 BUS2810 ETF2100 ENG2048 STAT5002 COMP2017 CEME 2003 MATS3004 COMP9319 PHYS1001 COMP5349 AMME2261 COMP-381 FIT3173 COSC2757 ENG4025 QBUS2820 COMP9414 MATH2021 EOSC118 MFIN6690 PMATH 321 CSE-141L MATH575A COMPSCI5002 COMP1511 management comp2123 FINS3616 COMP 3331 COMS30034 DTSC 71 AcF 702 AcF702 DTSC71 MAT021 ELE8083 ACFI213 EG-127J 127J FIT5163 FIT2001 ELE00113M CMT310 CS 245 ENGL 1101 MTH6115 EE497 CS 325 Math 124A MTH5130 MBA502 MGT 5380 ARCH 1261 F033800 20LLP109 ELE4009 FINANCIAL COMP3331 Computer ECE4179 20T3 COMP9311 COMP9311 UNSW MFIN6210 ACCT 5930 EE590 ENG2029 ECO100 SIT315 ACCT3610 COMP3600 STK2100 FIT2004 COMP30020 ACTL1101 Stat 101B BANA 200 COSC2473 ENGG1400 AI COMP90043 MMF 1914H PHYS 127 CS584 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