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Empirical Finance

创建日期：2024-07-20 15:23:09

所属分类：金融Finance

标签： Finance

Empirical Finance

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Empirical Finance Spring

1.(10pts) The Carey company paid Dt = 1 of dividends this year. If its dividends are expected to grow at G = 1.03 per year,

Please double check your answers.

Q1. (40pts) Gordon growth model

(10pts) The Carey company paid Dt= 1 of dividends this year. If its dividends are expected to grow at G = 1.03 per year, what is the dividends for the Carey company five years from now, that is, Dt+5?
(10pts) From our lecture slide, we can express price as

for some large k. The Gordon growth model assumes (i) Dt+1 = G × Dt and (ii)

Rt = R. Express

according to the Gordon growth model.

(10pts)The current price of Carey stock is $25 per If its current dividend is $1 per share and investors’ required rate of gross return is 1.1, what is the growth rate of dividends for Carey stock based on the Gordon growth model?
(10pts)A company with Dt = 1 and R = 1.2 grows at G = 1.06 for the first 5 years and drops to zero (meaning Gj = 1) thereafter (we use Gj to indicate its the new growth rate). What should its current price be according to the Gordon growth model?

Q2. (30pts) Portfolio choice

Suppose that the S&P 500 index has mean of E(rM ) = 0.16 and standard deviation of

σ(rM ) = 0.10. The risk-free rate is rf = 0.08.

(10pts)What is the expected return and standard deviation of a portfolio that is totally invested in the risk-free rate?
(10pts) What is the expected return and standard deviation of a portfolio that has weight ω = 0.5 on the risk-free rate and 1 − ω = 0.5 in the S&P 500index?
(10pts) What are the weights on a portfolio, ω for investing in the risk-free rateand 1 − ω for investing in the S&P 500 index, that produce a standard deviation that is 0.04? What is the expected return on that portfolio?

Q3. (20pts) Read Fama and French (2004) carefully and summarize the paper in one page (at least four paragraphs).

Q4. (80pts) Portfolio choice (coding exercise)

Download “stocks.xlsx.” You will find 3 stock prices (labeled “market, A, B”) and 3 factors (labeled “riskfree, smb, hml”) in the range of 2011:M12 to 2021:M2.

(20pts) Let the log return for stock i be ri,tat time t. Provide the sample mean and standard deviation for rM,t, rA,t, rB,t where 2012:M1 ≤ t ≤ 2021:M2. For convenience, “M” refers to “market.”
(20pts) Estimate the CAPM equation and report the estimated β and R2from the regression. Here the estimation sample ranges from 2012:M1 to 2021:M2. Note that you are estimating the CAPM equation for A and B stocks separately (so, twice in total).
Similarly estimate the Fama-French 3 factor model for A and B stocks. Here the estimation sample ranges from 2012:M1 to2021:M2.

(a)(20pts) Compare the estimates of βwith those from the CAPM equation.

(b)(20pts)Based on the coefficient estimates for “smb” and “hml” factors, discuss the characteristics of A and B stocks.

Q5. (30pts) Investment

Suppose that the month t prices are PM = $3, 972.89, PA = $16.19, and PB = $521.66. You can spend up to $100,000 in stocks (M, A, B) after studying the historical price/return series (2012:M1-2021:M2). For this question, you may want to analyze their log return dynamics.

The minimum requirement is that you have to at least spend $10,000 on each stock. To helpyou understand the problem, suppose you buy 3 of M and 618 of A and 20 of B,

3 · PM = $11919

618 · PA = $10005

20 · PB = $10433

then the total cost of your portfolio is Pp = 3 · PM + 618 · PA + 20 · PB = $32357. Here, I am rounding up the decimal points for ease of illustration. Note that you can buy more asyou still have $67643 remaining. Now, suppose that the month t + 1 prices are PMj , PAj , and PBj , respectively. You are going to calculate the one-month holding period return of your portfolio

Ppj = 3 · PMj+ 618 · PAj+ 20 · PBj

where the holding period return is defined as

Explain how much you would buy each of M , A, and B. Your answer should be based on your analysis of HPR from the historical data. Thus, what only matters is HP R, that is, what’s your monthly return on investment, not about Pp or Ppj .

Note: I am asking you to use your imagination + data analysis skill you’ve learned so far in class.

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1300A ENGG 1300 OLET1139 STAT 3503 STAT 206 FEM11149 ELEN 4720 COMP20003 SOLA1070 CS574 C11CS LINB29H3 MAST90083 ECON7200 STAT 610 LINB29 DSM-5 COMP3161 EEEN40010 MATH 4431 K353 STA 3386 IERG4300 COMS W4167 ENG5298 AMME 2302 CS3910 COMPSCI 320 STATS 369 GR5242 COSC 328 CSCI435 MGTS1301 INFS2200 COMP3900 CIS 375 Module AE03 COMP3121 CS260 HAM503 MGMT5050 INT3075 COSC 285 GEOL0029 GEGE2X01 STAT1201 MATH1061 MMF1941H STAT 5060 CS 520 COMP 4320 MSIN0104 000T FINS3648 ECMT2160 ECON4003 Phys 129L CSE 142 CS 3130 MGEB01 EECS 340 Finance (20443/20444) ECMM149 COMP5310 EEEN60180 CSC 111 AT2 CSCI 4430 STAB57 MA/CSC 427 MATH322 D100 CSCI544 CITS3004 CI6227 CSE 565 APCO 1P01 852L1 ELEC S411F COMP3207 STATS330 ECON7530 FIT5149 CSI4104 CMPT 371 COMP201 SEHS4696 FI4003 MATH6182 CG1 WS MATH401 MGT 205 QTM 110 COMP 0137 MACE12201 FIT5210 ECE 544 BISM7206 HUDM 6055 ECON3203 STATS 210 MSCI 570 MATH6173 COMPSCI4039 Accounting COM3503 AOE2024 ECON213 PSYC10004 Control Data 100/200A PHIL2617 PHYS3116 MIE250 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ATMS 201 COMP3425 MATH7861 SOLA2060 MA 325 7CCEMCTH ECON 432 INFT2051 SOLA 2060 ECOS2002 Stats141XP BIOA02H3 S2022 MA4601 K5 COMP5329 EG 284 IB3A70 WECO1020 COMP3027 Energy ACS61011 MAST20026 STAT 533 MATA31 ENVS257 BEM2031 EC 486 COMP0172 CS3214 EECE5644 IB2B20 COSC2536 COSC1147 COMP6214 5CCM242A COMP0130 AMME2000 MTMG50: EG238 ACF6006 QBUS2810 COSC2391 ECON7560 MATH377 STA305 CS 486 COMP1117B EL648 ELEC3909 ECON 241 COMP 4901W BUSI4428 ENEN20002 ENGN4524 ELEC3115 CSC 413 PSYC 100B ECON1002 MATH256 ANSC20005 MTHS2008 MATH40082 COSC 2406 FIT3174 STA 238 CMT202 Differential Equations MTHM017 GARCH 101 MATH2069 CSC336S ACSC12 ETF2121 CEME 2001 DB B474F ARHT1001 EECS 3311 3220 STATS 786 CS 484 COMP20008 MATH4091 ECE 455 CSCI 204 BUS B200F BA 875 BU5562 COSC 1147 X11 GEOG 101 IMM250F CSE 584A MATH38172 LAB 4 ELEC5882M FINS5523 EE 430 COMP 465 6CCS3PRE 7CCSMNSE FINANCE ACMB02H3 ENGG2112 ELEC5616 SCM B371 CHEM3120 CS22 ECMT2130 MAST30011 ADSPBF706 CENG0013 ACCOUNTING BUSS1040 CHEM 181 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