Investment Analysis and Portfolio Management Case 2
Ada Lam is the founder and sole stockholder of AL Gifts, Co. Ltd., Ada is a recent divorcee and realizes that her finances may need to be revised now that her divorce has been settled. Her former husband, Kelvin, is the father of her two children and the major stockholder of GOOD Manufacturing, Co. Ltd., GOOD Manufacturing has been in business 15 years, is financially stable, and currently has a book value in excess of $380M. Kelvin has agreed to pay for 50% of their children’s education.
案例r投资管理案例r投资管理
Personal Information
Name
Age
Health
Occupation
Ada Lam
39
Good
President – AL Gifts, Co. Ltd.
Susan Lam
14
Excellent
Student
Candy Lam
9
Excellent
Student
Kelvin Lam
42
Excellent
President – GOOD Manufacturing, Inc.
Ada Lam
STATEMENT OF FINANCIAL POSITION
As at Aug 31, 2018
ASSETS
LIABILITIES
Cash/Cash equivalents
$ 100,000
Credit cards 1
$ 260,000
NAV of AL Gifts, Co. Ltd.
576,000
Mortgage 2
8,432,529
Residence (bought 5 yrs ago, 763 sq. ft 3-Bedroom apt)
13,800,000
Auto loan3
423,137
Auto (BMW 325is, bought 1/2 year ago)
530,000
TOTAL LIABILITIES
$ 9,115,666
NET WORTH
$ 5,890,334
TOTAL ASSETS
$15,006,000
TOTAL LIABILITIES
AND NET WORTH
$ 15,006,000
1 Variable rate, currently 35.71% APR.
2 25 years left with P-2.95% (2.05%)
3 2.5 years left with fixed flat rate at 2.15% for 3 years
Ada Lam
PROJECTED MONTHLY CASH FLOW STATEMENT
Current Monthly
CASH INFLOWS
Gross salary
$ 60,000
Child support
25,000
Total
$ 85,000
CASH OUTFLOWS
Savings and investments
$ 0
Mortgage payment (P+I)
35,948
Maintenance and repairs on the home
2,000
Textbook and miscellaneous (2 Kids)
600
Food and supplies
6,500
Utilities (Electricity, water, gas)
3,500
Transportation (gas, oil, repairs)
9,000
Car payment
14,105
Clothing
2,000
Travel and entertainment
3,500
Credit card payments
4,500
Total
$ 81,653
SURPLUS/(DEFICIT) CASH FLOW
$3,347
AL GIFTS, CO.LTD.
BALANCE SHEET
As at March 31, 2018
ASSETS1
LIABILITIES
Cash/Cash equivalents
$ 200,000
Accounts payable
$298,000
Accounts receivable
400,000
Loan2
500,000
Inventory
600,000
TOTAL LIABILITIES
$798,000
Furniture and fixtures, net of depreciation
130,000
STOCKHOLDER EQUITY
$576,000
Prepaid expenses & other
44,000
TOTAL ASSETS
$1,374,000
TOTAL LIABILITIES AND SHAREHOLDER EQUITY
$1,374,000
1 All assets are listed at fair market value (FMV)
2 $2,000 a month payable to Kelvin Lam at 4.8% interest, which is the going market rate on similar loans.
AL GIFTS, CO. LTD
PROJECTED MONTHLY INCOME STATEMENT
TOTAL SALES
$215,000
EXPENSES
Cost of goods sold
$ 75,250
Advertising and promotion
1,500
Depreciation
2,400
Interest on loan
2,000
Insurance – business
250
Rent (300 sq. ft.)
11,000
Salaries (1part time staff & herself)
68,500
Supplies and miscellaneous
3,500
Utilities
1,200
(165,600)
NET INCOME
49,400
Ms. Lam’s investment objective is to ensure financial security for herself, her business & her children. She plans to send her children to Australia for 5 years (last 2 year of high school and 3 years university) to receive western education.
Ms. Lam wants to pay off the $500,000 loan borrowed from Kelvin (her ex-husband) and be able to save enough funding (approx. $1.5M) to expand her business. She finally would like to retire when she turns 65 years old.案例r语言作业 EF 5070: FinancialEconometrics
Problem Set 4: Mock FinalExam
Section A (40%)
Attempt ALL questions from this Section
EF 5070: FinancialEconometrics
Problem Set 4: Mock FinalExam
Due Dec 14th, 2018
Section A (40%)
Attempt ALL questions from this Section
1. (20 pts) Answer briefly the following questions
a) How to understand volatility? How to understand uncertain and risk?
b) Describe one test statistics that can be used to evaluate model adequacy and explain how it works using plain words.
c) Provide two reasons for the observed significant first order autocorrelation of high frequency data.
2. (20 pts) Suppose that simple return of a monthly stock index follows an AR dynamics,
image.png
a) What is the mean of the simple return of this monthly stock?
b) What is the variance of the simple return of this monthly stock?
c) Consider the forecast origin h = 100 with
image.png
. Compute the 1-step-ahead forecast of the simple return at the forecast origin h = 100 and the variance of your forecast error.
d) Compute 2-step-ahead forecast at the forecast origin h=100.
e) Provide two features of AR models.
Section B (60%)
Attempt ALL questions from this Section
1. (30 pts) Consider the daily returns of Apple (AAPL) stock from October 1st, 2009 to September 30, 2017. Let Pt denote daily closing prices. We denote rt as the percentage log returns of daily Apply stock.
a) Provide two reasons why we prefer log returns over price levels in regression analysis.
b) Based on R output Q(b), can you ensure stationarity of the return series? Provide your reasoning.
c) From the R output in appendix Q3 (c), we fit a Gaussian AR (1) model to the rt series. Do you find strong evidence on the predictability ability that lagged returns exhibit on current returns at 5% significance level? Form your hypothesis, write down the test statistics, asymptotic distribution of your test statistics, rejection rule and conclusion.
d) Now, we want to fit an MA model to the rt series. From the R output in appendix Q3 (d) and Figure Q3-1 below, what is the best MA(q) model? Why? Write down the fitted MA(q) model.
案例r语言作业案例r语言作业
a) From the Figure Q3-2 below, do you think we should model volatility processes? Why? Now, we fit an GARCH model to the rt series. Please explain why GARCH models can capture the well-known volatility clustering effect.
案例r语言作业.png
Figure Q3-2
b) Now, we will fit a GARCH(1,1) model to the return series. From R output in appendix Q3 (e)-(f), please write down the fitted model and its equivalent ARMA representation. Is the GARCH(1,1) model estimated in f) adequate?
c) From the R output in appendix Q3 (e)-(f), do you observe significant impact that historical conditional volatility may exhibit on current conditional volatility? Write down your hypothesis, test statistics, rejection rule and conclusion. Does your model satisfy stationary conditions?
1. (30 pts) We will investigate the role nonlinearity plays in our regression analysis.
a) Now, we consider another simple nonlinear model that allows us to examine asymmetric pattern in constant effect as follows,
image.png
From the R output in appendix Q4 (a), write down the fitted model of (Q4-1) and provide interpretations for x .
a) Do you find statistically significant evidence for asymmetry in the constant effect at 10% level? Form your hypothesis, write down the test statistics, rejection rule and conclusion.
b) Do you find statistically significant evidence for the predictability ability that lagged one period return exhibit on current return at 5% level? Form your hypothesis, write down the test statistics, rejection rule and conclusion.
Now, we consider a two-stage Markovian chain Regime-switching model for the market model.
image.png
a) From the R output in appendix Q4 (d)-(f), write down the fitted model.
b) Compute the unconditional volatility of the model in stage 1 and state 2. Which regime has higher uncertainty?
c) From the R output in appendix Q4 (d)-(f), compute the expected duration for stage 1 and stage 2 respectively.
Appendix 1:
R Output Appendix
> library(quantmod)
> library(tseries)
> library(TSA)
> getSymbols(‘AAPL’,from=’2009-10-01′,to=’2017-09-30′)
[1] “AAPL”
> head(AAPL)
AAPL.Open AAPL.High AAPL.Low AAPL.Close AAPL.Volume AAPL.Adjusted
2009-10-01 29.538 29.676 28.797 25.83714 131177900 23.16128
2009-10-02 28.910 29.632 28.900 26.41429 138327000 23.67865
2009-10-05 29.673 29.778 29.366 26.57429 105783300 23.82208
2009-10-06 29.919 30.280 29.848 27.14428 151271400 24.33305
2009-10-07 30.240 30.366 30.124 27.17857 116417000 24.36378
2009-10-08 30.384 30.510 30.102 27.03857 109552800 24.23828
> tail(AAPL)
AAPL.Open AAPL.High AAPL.Low AAPL.Close AAPL.Volume AAPL.Adjusted
2017-09-22 152.085 152.817 151.101 151.89 46645400 151.3459
2017-09-25 150.529 152.376 149.696 150.55 44387300 150.0107
2017-09-26 152.326 154.473 152.235 153.14 36660000 152.5914
2017-09-27 154.353 155.276 154.092 154.23 25504200 153.6776
2017-09-28 154.443 154.835 153.249 153.28 22005500 152.7310
2017-09-29 153.761 154.684 152.546 154.12 26299800 153.5679
> AAPLP=as.numeric(AAPL$AAPL.Close)
>
> #Form percentage log returns
> lnrt=diff(log(AAPLP))*100
> head(lnrt)
[1] 2.2091892 0.6039056 2.1222470 0.1262342 -0.5164430 0.6320077
>
##Q3(b)
> #(b)
> Box.test(lnrt)
Box-Pierce test
data: lnrt
X-squared = 1.307, df = 1, p-value = 0.2529
> adf.test(lnrt,k=20)
Augmented Dickey-Fuller Test
data: lnrt
Dickey-Fuller = -9.2706, Lag order = 20, p-value = 0.01 alternative hypothesis: stationary
##Q3(c)##
> #(c)
> mc=arima(lnrt,order=c(1,0,0))
> mc
Coefficients:
ar1 intercept 0.0255 0.0888
s.e. 0.0223 0.0368
##Q3 (d)
> md=arima(lnrt,order=c(0,0,1))
> md
Coefficients:
ma1 intercept 0.0255 0.0887
s.e. 0.0223 0.0368
#Q3 (e)-(f)
> library(‘fGarch’)
> mf=garchFit(~garch(1,1),data=lnrt,trace=F)
> summary(mf)
Std. Errors:
based on Hessian Error Analysis:
Standardised Residuals Tests:
Statistic p-Value
Jarque-Bera Test R Chi^2 1344.524 0
Shapiro-Wilk Test R W 0.9621468 0
Ljung-Box Test R Q(10) 11.66765 0.3079153
Ljung-Box Test R Q(15) 16.84009 0.3285136
Ljung-Box Test R Q(20) 20.52761 0.4253902
Ljung-Box Test R^2 Q(10) 4.954776 0.8941784
Ljung-Box Test R^2 Q(15) 9.191117 0.8673143
Ljung-Box Test R^2 Q(20) 12.17481 0.9099277
LM Arch Test R TR^2 6.862016 0.8665957
##Q4## ##Q4(a)-(c)##
> y=lnrt[2:T]
> x=lnrt[1:(T-1)]
> idx=c(1:(T-1))[x<0]
> nsp=rep(0,(T-1))
> nsp[idx]=x[idx]
> c1=rep(0,(T-1))
> c1[idx]=1
> xx=cbind(y,x,c1,nsp)
>
> mda=lm(y~c1+x)
> summary(mda) Coefficients:
##Q4(d)-(f)##
> mod<-lm(lnrt ~ 1)
> msm_intercept <- msmFit(mod, k=2, sw=c(T,T,T), p=1)
> summary(msm_intercept) Markov Switching Model
Coefficients:
Regime 1
———
Estimate Std. Error t value Pr(>|t|)
(Intercept)(S) 0.1540 0.0386
lnrt_1(S) 0.0182 0.0328
Residual standard error: 1.063557
—
Regime 2
———
Estimate Std. Error t value Pr(>|t|) (Intercept)(S) -0.0786 0.1169
lnrt_1(S) 0.0205 0.0478
Residual standard error: 2.468642
Transition probabilities:
Regime 1 Regime 2
Regime 1 0.91144868 0.2150418
Re
