Financial Econometrics - Homework 2
Instructor: Dr. Nguyen Phuong Anh
1 Group Members
- Nguyen Minh Quan - MAMAIU19036
- Lam Hue Dung - MAMAIU18060
- Le Nguyen Dang Khoa - MAMAIU19008
For further discussion, please contact us via email: quannguyenuw@gmail.com.
2 Libraries
library(readxl)
library(rio)
library(psych)
library(graphics)
library(car)3 UKHP
url = 'https://raw.githubusercontent.com/QuanNguyenIU/Res_Med_Fin/main/UKHP.xls'
UKHP = rio::import(file = url)
head(UKHP, 6)## Month Average House Price
## 1 1991-01-01 53051.72
## 2 1991-02-01 53496.80
## 3 1991-03-01 52892.86
## 4 1991-04-01 53677.44
## 5 1991-05-01 54385.73
## 6 1991-06-01 55107.38summary(UKHP)## Month Average House Price
## Min. :1991-01-01 00:00:00 Min. : 49602
## 1st Qu.:1997-10-16 12:00:00 1st Qu.: 61654
## Median :2004-08-01 00:00:00 Median :150946
## Mean :2004-07-31 17:54:29 Mean :124660
## 3rd Qu.:2011-05-16 12:00:00 3rd Qu.:169239
## Max. :2018-03-01 00:00:00 Max. :211756describe(UKHP$'Average House Price')## vars n mean sd median trimmed mad min max
## X1 1 327 124660.5 56387.17 150946.1 123820 68175.33 49601.66 211755.9
## range skew kurtosis se
## X1 162154.3 -0.11 -1.59 3118.22names(UKHP)[2] = 'hp'
UKHP$dhp = c(NA, 100 * diff(UKHP$hp) / UKHP$hp[1:nrow(UKHP) - 1])par(cex.axis = 1.5, cex.lab = 1.5, lwd = 2)
plot(UKHP$Month, UKHP$hp, type = 'l',
xlab = 'Date', ylab = 'House Price')
hist(UKHP$dhp)
4 SandPhedge
url = 'https://raw.githubusercontent.com/QuanNguyenIU/Res_Med_Fin/main/SandPhedge.xls'
SandPhedge = rio::import(file = url)
head(SandPhedge, 6)## Date Spot Futures
## 1 1997-09-01 947.28 954.50
## 2 1997-10-01 914.62 924.00
## 3 1997-11-01 955.40 955.00
## 4 1997-12-01 970.43 979.25
## 5 1998-01-01 980.28 987.75
## 6 1998-02-01 1049.34 1050.50SandPhedge$rspot = c(NA, 100 * diff(log(SandPhedge$Spot)))
SandPhedge$rfutures = c(NA, 100 * diff(log(SandPhedge$Futures)))
summary(SandPhedge[c('rspot', 'rfutures')])## rspot rfutures
## Min. :-18.5636 Min. :-18.9447
## 1st Qu.: -1.8314 1st Qu.: -1.9314
## Median : 0.9185 Median : 0.9976
## Mean : 0.4168 Mean : 0.4140
## 3rd Qu.: 3.2765 3rd Qu.: 3.1336
## Max. : 10.2307 Max. : 10.3872
## NA's :1 NA's :1describe(SandPhedge[c('rspot', 'rfutures')])## vars n mean sd median trimmed mad min max range skew
## rspot 1 246 0.42 4.33 0.92 0.7 3.85 -18.56 10.23 28.79 -0.84
## rfutures 2 246 0.41 4.42 1.00 0.7 3.90 -18.94 10.39 29.33 -0.88
## kurtosis se
## rspot 1.73 0.28
## rfutures 2.02 0.28plot(SandPhedge$rfutures, SandPhedge$rspot, pch = 19)
lm_returns = lm(rspot ~ rfutures, data = SandPhedge)
summary(lm_returns)##
## Call:
## lm(formula = rspot ~ rfutures, data = SandPhedge)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.45284 -0.16401 0.00236 0.23692 2.33789
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.013077 0.029473 0.444 0.658
## rfutures 0.975077 0.006654 146.543 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4602 on 244 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.9888, Adjusted R-squared: 0.9887
## F-statistic: 2.147e+04 on 1 and 244 DF, p-value: < 2.2e-16linearHypothesis(lm_returns, c('rfutures = 1'))## Linear hypothesis test
##
## Hypothesis:
## rfutures = 1
##
## Model 1: restricted model
## Model 2: rspot ~ rfutures
##
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 245 54.656
## 2 244 51.684 1 2.9718 14.03 0.0002246 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1plot(SandPhedge$Futures, SandPhedge$Spot, pch = 19)
lm_prices = lm(Spot ~ Futures, data = SandPhedge)
summary(lm_prices)##
## Call:
## lm(formula = Spot ~ Futures, data = SandPhedge)
##
## Residuals:
## Min 1Q Median 3Q Max
## -64.576 -1.996 1.436 4.309 16.612
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.8378335 1.4889725 -1.906 0.0578 .
## Futures 1.0016065 0.0009993 1002.331 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.908 on 245 degrees of freedom
## Multiple R-squared: 0.9998, Adjusted R-squared: 0.9998
## F-statistic: 1.005e+06 on 1 and 245 DF, p-value: < 2.2e-16linearHypothesis(lm_prices, c('Futures = 1'))## Linear hypothesis test
##
## Hypothesis:
## Futures = 1
##
## Model 1: restricted model
## Model 2: Spot ~ Futures
##
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 246 11816
## 2 245 11693 1 123.35 2.5846 0.10925 CAPM
url = 'https://raw.githubusercontent.com/QuanNguyenIU/Res_Med_Fin/main/capm.xls'
capm = rio::import(file = url)
head(capm, 6)## Date SANDP FORD GE MICROSOFT ORACLE USTB3M
## 1 2002-01-01 1130.20 15.30 37.15 31.855 17.26 1.68
## 2 2002-02-01 1106.73 14.88 38.50 29.170 16.62 1.76
## 3 2002-03-01 1147.39 16.49 37.40 30.155 12.80 1.83
## 4 2002-04-01 1076.92 16.00 31.55 26.130 10.04 1.75
## 5 2002-05-01 1067.14 17.65 31.14 25.455 7.92 1.76
## 6 2002-06-01 989.82 16.00 29.05 27.350 9.47 1.73capm$rsandp = c(NA, 100 * diff(log(capm$SANDP)))
capm$rford = c(NA, 100 * diff(log(capm$FORD)))
capm$rge = c(NA, 100 * diff(log(capm$GE)))
capm$rmsoft = c(NA, 100 * diff(log(capm$MICROSOFT)))
capm$roracle = c(NA, 100 * diff(log(capm$ORACLE)))
capm$USTB3M = capm$USTB3M/12
capm$ersandp = capm$rsandp - capm$USTB3M
capm$erford = capm$rford - capm$USTB3M
capm$erge = capm$rge - capm$USTB3M
capm$ermsoft = capm$rmsoft - capm$USTB3M
capm$eroracle = capm$roracle - capm$USTB3Mpar(cex.axis = 1.5, cex.lab = 1.5, lwd = 2)
plot(capm$Date, capm$ersandp, type = 'l',
col = 'red', ylim = c(-100, 100))
lines(capm$Date, capm$erford, lwd = 1)
legend('topright', c('SP500', 'Ford'), col = c('red', 'black'),
lty = 1, cex = 1.5)
lm_capm = lm(erford ~ ersandp, data = capm)
summary(lm_capm)##
## Call:
## lm(formula = erford ~ ersandp, data = capm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -50.727 -5.027 -1.080 3.482 65.145
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.9560 0.7931 -1.205 0.23
## ersandp 1.8898 0.1916 9.862 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10.98 on 191 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.3374, Adjusted R-squared: 0.3339
## F-statistic: 97.26 on 1 and 191 DF, p-value: < 2.2e-16alpha = lm_capm$coefficients[1]
beta = lm_capm$coefficients[2]
plot(capm$ersandp, capm$erford, pch = 19)
lines(capm$ersandp, alpha + beta * capm$ersandp, lwd = 1, col = 'red')
linearHypothesis(lm_capm, c('ersandp = 1'))## Linear hypothesis test
##
## Hypothesis:
## ersandp = 1
##
## Model 1: restricted model
## Model 2: erford ~ ersandp
##
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 192 25618
## 2 191 23020 1 2598.5 21.56 6.365e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1