class: title-slide, center, middle # Methods of Empirical Finance ## Seminar (UE) ### Christoph Huber ### University of Innsbruck #### Master in Banking and Finance ### Winter term 2019/20 (this version: 2019-12-03) --- class: center, middle, inverse # Regression Analysis ### Methods of Empirical Finance --- <footer></footer> # Regression Analysis ### A simple (univariate) linear regression model .center[ `\(y_i = \alpha + \beta\;x_i + \varepsilon_i\)` ] .smaller[ with `\(i \in \left[ 1, 2, . . . , n \right]\)` referring to the `\(i\)`th observation `\(\alpha ...\)` intercept (often denoted `\(\beta_0\)`) `\(\beta ...\)` slope coefficient `\(\varepsilon ...\)` a random disturbance term ] --- <footer></footer> # Regression Analysis ### Example: Download stock price data ```r library(tidyverse) library(tidyquant) sp500 <- tq_get("^GSPC") # download S&P500 prices nflx <- tq_get("NFLX") # download Netflix (NFLX) prices msft <- tq_get("MSFT") # download Microsoft (MSFT) prices ``` <br> .smaller[ Stata: `getsymbols` command (install using `ssc install getsymbols`) ] --- <footer></footer> # Regression Analysis ### Example: MSFT prices
--- <footer></footer> # Regression Analysis ### Example: Plot price development .pull-left[ ```r plot(sp500$date, sp500$close, type = "l") ``` <img 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" width="576" /> ] .pull-right[ ```r plot(sp500$date, sp500$close, type = "l") ``` <img src="data:image/png;base64,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" width="576" /> ] --- <footer></footer> # Regression Analysis ### Example: Plot price development (`ggplot2`) .pull-left[ ```r sp500 %>% ggplot(aes(x = date, y = close)) + geom_line() + theme_tq() ``` <img src="data:image/png;base64,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" width="576" /> ] .pull-right[ ```r msft %>% ggplot(aes(x = date, y = close)) + geom_line() + theme_tq() ``` <img src="data:image/png;base64,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" width="576" /> ] --- <footer></footer> # Regression Analysis ### Example: Correlation of Returns .center[ <img src="data:image/png;base64,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" width="576" /> ] --- <footer></footer> # Regression Analysis ### Example: Estimating portfolio characteristics using OLS CAPM: .center[ `\(E(R_i) - R_f = \beta_i(E(R_M) - R_f)\)` ] This implies the following linear model: .center[ `\(E(R_i) = \alpha_i + \beta_i E(R_M),\)` ] where `\(\alpha_i \neq 0\)` unless `\(\beta_i = 1\)`. We can then express the single index model in the form .center[ `\(R_{it} = \alpha_i + \beta_i X_t + \varepsilon_{it},\;\;\;\;\;\; \varepsilon_{it} \sim i.i.d.(0, \sigma_i^2).\)` ] --- <footer></footer> # Regression Analysis ### Example: Estimating portfolio characteristics using OLS ```r msft_weekly <- msft %>% tq_transmute( adjusted, periodReturn, period ="weekly", col_rename = "msft.weekly" ) sp500_weekly <- sp500 %>% tq_transmute( adjusted, periodReturn, period="weekly", col_rename = "sp500.weekly" ) weekly_combined <- left_join(msft_weekly, sp500_weekly, by = "date") ``` --- <footer></footer> # Regression Analysis ### Example: Estimating portfolio characteristics using OLS .smaller[ ```r msft_ols <- lm(msft.weekly ~ sp500.weekly, data = weekly_combined) summary(msft_ols) ``` ``` ## ## Call: ## lm(formula = msft.weekly ~ sp500.weekly, data = weekly_combined) ## ## Residuals: ## Min 1Q Median 3Q Max ## -0.128693 -0.010955 -0.000378 0.011463 0.131208 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 0.002231 0.001025 2.176 0.03 * ## sp500.weekly 0.953651 0.047945 19.890 <2e-16 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 0.02435 on 569 degrees of freedom ## Multiple R-squared: 0.4101, Adjusted R-squared: 0.4091 ## F-statistic: 395.6 on 1 and 569 DF, p-value: < 2.2e-16 ``` ] --- <footer></footer> # Regression Analysis ### Example: Estimating portfolio characteristics using OLS ```r weekly_combined %>% tq_performance(Ra = msft.weekly, Rb = sp500.weekly, performance_fun = table.CAPM) ``` ``` ## # A tibble: 1 x 12 ## ActivePremium Alpha AnnualizedAlpha Beta `Beta-` `Beta+` Correlation ## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> ## 1 0.112 0.0022 0.123 0.954 1.05 0.826 0.640 ## # ... with 5 more variables: `Correlationp-value` <dbl>, ## # InformationRatio <dbl>, `R-squared` <dbl>, TrackingError <dbl>, ## # TreynorRatio <dbl> ``` --- <footer></footer> # Regression Analysis ### A multivariate regression model .center[ `\(y_i = \beta_1\;x_{i,1} + \beta_2\;x_{i,2} + ... + \beta_k\; x_{i,k} + \varepsilon_i, \hspace{1em} i = 1, ... n\)` ] -- <br> ### Vector notation .center[ `\(y_i = \mathbf{x}_i'\;\beta + \varepsilon_i, \hspace{1em} i = 1, ... n \hspace{2em}\)` `\(\rightarrow\)` `\(\mathbf{x}_i = \begin{bmatrix}x_{i,1} \\ x_{i,2} \\ \vdots \\ x_{i,k}\end{bmatrix}\)` includes `\(k \geq 1\)` variable(s) ] -- ### Matrix notation .center[ `\(\textbf{y} = \mathbf{X}\boldsymbol{\beta} + \boldsymbol{\varepsilon} \hspace{2em}\)` with `\(\mathbf{X} = \begin{vmatrix}x_{1,1} & x_{1,2} & ... & x_{1,k} \\ x_{2,1} & x_{2,2} & ... & x_{2,k} \\ \vdots & \vdots & \ddots & \vdots \\ x_{n,1} & x_{n,2} & ... & x_{n,k}\end{vmatrix}\)`, `\(\boldsymbol{\beta} = \begin{bmatrix}\beta_1 \\ \beta_2 \\ \vdots \\ \beta_k \end{bmatrix}\)`, and `\(\mathbf{y} = \begin{bmatrix}y_1 \\ y_2 \\ \vdots \\ y_n \end{bmatrix}\)` ] --- <footer></footer> # Regression Analysis ### Assumptions of the linear regression model <br> .smaller[ __1.__ the residuals have zero mean: `\(E(\varepsilon_i) = 0\)` __2.__ the variance of the residuals is constant and finite for all values of `\(x_i\)`: `\(\text{Var}(\varepsilon_i) = \sigma^2 < \infty\)` __3.__ the residuals are linearly independent of each other: `\(\text{Cov}(\varepsilon_i, \varepsilon_j) = 0\)` __4.__ the residuals are linearly independent of the corresponding `\(x\)` variates: `\(\text{Cov}(\varepsilon_i, x_i) = 0\)` __5.__ the residuals are normally distributed with zero mean and constant variance `\(\sigma^2\)`: `\(\varepsilon_i \sim N(0, \sigma^2)\)` ] --- <footer></footer> # Regression Analysis ### Example .small[ ```r data$PCT_CHANGE <- data$CHG_NET_YTD/(data$PX_LAST-data$CHG_NET_YTD) reg <- lm(PCT_CHANGE ~ PE_RATIO + PCT_WOMEN_ON_BOARD + BOARD_AVERAGE_TENURE + BOARD_AVERAGE_AGE + AVERAGE_BOD_TOTAL_COMPENSATION, data = data) summary(reg) ``` ``` ## ## Call: ## lm(formula = PCT_CHANGE ~ PE_RATIO + PCT_WOMEN_ON_BOARD + BOARD_AVERAGE_TENURE + ## BOARD_AVERAGE_AGE + AVERAGE_BOD_TOTAL_COMPENSATION, data = data) ## ## Residuals: ## Min 1Q Median 3Q Max ## -0.74114 -0.14035 0.00104 0.13755 0.86784 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 3.615e-01 2.208e-01 1.637 0.10229 ## PE_RATIO 8.474e-04 2.862e-04 2.960 0.00323 ** ## PCT_WOMEN_ON_BOARD -2.845e-03 1.231e-03 -2.310 0.02130 * ## BOARD_AVERAGE_TENURE -3.332e-04 3.675e-03 -0.091 0.92779 ## BOARD_AVERAGE_AGE -1.205e-03 3.601e-03 -0.335 0.73796 ## AVERAGE_BOD_TOTAL_COMPENSATION -1.859e-09 3.542e-08 -0.053 0.95815 ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 0.2338 on 469 degrees of freedom ## (30 observations deleted due to missingness) ## Multiple R-squared: 0.02927, Adjusted R-squared: 0.01892 ## F-statistic: 2.829 on 5 and 469 DF, p-value: 0.01575 ``` ] --- <footer></footer> # Regression Analysis .smaller[ ### Regression Diagnostics ```r par(mfrow=c(1,4)) plot(reg) ``` <img 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width="1008" /> ] --- <footer></footer> # Regression Analysis ### Heteroskedasticity .smaller[ Breusch Pagan Test ```r library(lmtest, lib.loc = "I:/R/library") bptest(reg) ``` ``` ## ## studentized Breusch-Pagan test ## ## data: reg ## BP = 33.823, df = 5, p-value = 2.583e-06 ``` We can reject the null hypothesis that the variance of the residuals is constant `\(\rightarrow\)` heteroskedasticity ] --- <footer></footer> # Regression Analysis ### Heteroskedasticity .smaller[ Non-adjusted standard errors ```r coeftest(reg) ``` ``` ## ## t test of coefficients: ## ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 3.6151e-01 2.2083e-01 1.6371 0.10229 ## PE_RATIO 8.4737e-04 2.8625e-04 2.9603 0.00323 ** ## PCT_WOMEN_ON_BOARD -2.8450e-03 1.2313e-03 -2.3105 0.02130 * ## BOARD_AVERAGE_TENURE -3.3325e-04 3.6754e-03 -0.0907 0.92779 ## BOARD_AVERAGE_AGE -1.2055e-03 3.6011e-03 -0.3348 0.73796 ## AVERAGE_BOD_TOTAL_COMPENSATION -1.8594e-09 3.5416e-08 -0.0525 0.95815 ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ``` ] --- <footer></footer> # Regression Analysis ### Heteroskedasticity .smaller[ Heteroskedasticity-consistent standard errors ```r library(sandwich) coeftest(reg, vcov. = vcovHC(reg, "HC0")) ``` ``` ## ## t test of coefficients: ## ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 3.6151e-01 2.4987e-01 1.4468 0.14862 ## PE_RATIO 8.4737e-04 5.5162e-04 1.5361 0.12518 ## PCT_WOMEN_ON_BOARD -2.8450e-03 1.4126e-03 -2.0140 0.04458 * ## BOARD_AVERAGE_TENURE -3.3325e-04 3.5304e-03 -0.0944 0.92484 ## BOARD_AVERAGE_AGE -1.2055e-03 3.8963e-03 -0.3094 0.75717 ## AVERAGE_BOD_TOTAL_COMPENSATION -1.8594e-09 1.6788e-08 -0.1108 0.91186 ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ``` ] --- <footer></footer> # Regression Analysis ### Multicollinearity .smaller[ Variance inflation factors ```r library(car, lib.loc = "I:/R/library") vif(reg) ``` ``` ## PE_RATIO PCT_WOMEN_ON_BOARD ## 1.012047 1.027449 ## BOARD_AVERAGE_TENURE BOARD_AVERAGE_AGE ## 1.256336 1.249016 ## AVERAGE_BOD_TOTAL_COMPENSATION ## 1.003105 ``` Interpretation: The square root of the variance inflation factor indicates how much larger the standard error increases compared to if that variable had 0 correlation to other predictor variables in the model. ```r vif(reg)^(1/2) ``` ``` ## PE_RATIO PCT_WOMEN_ON_BOARD ## 1.006005 1.013631 ## BOARD_AVERAGE_TENURE BOARD_AVERAGE_AGE ## 1.120864 1.117594 ## AVERAGE_BOD_TOTAL_COMPENSATION ## 1.001551 ``` ]