An Estimation of Systematic Risk This is a financial report on the estimation of risk for Walt Disney CO. (D’S) and Energy Transfer Equity LP (ETE). This report is done on the basis of the Normality Assumption suggesting that there is a constant variance and that the two variables tested are related – there error terms = O. There is also the assumption that the distribution of error term is normal between both variables. Contents Statement of Hypothesis 2 Specification of the Mathematical Model of the Theory 3 Specification of the Statistical or Economic Model 5 Obtaining Data 6
Estimation of the Parameters of the Econometric Model 7 Hypothesis Testing 8 Forecasting, Prediction and Advice 1 1 Hypothesis: The expectation of each security is that its systematic risk will tend to mirror the market more closely and take certain values closer to 1 then its stated beta. I expect Walt Disney (D’S) to take up a beta less than its stated value of 1. 2, and arbitrarily be 1. 15, . 05 less, and I expect Energy Transfer Equity LP (ETE) to take up a beta greater than its stated value of . 82, and arbitrarily be . 87, . 05 greater.
My hypothesized numbers are closer to 1 to represent the basis of my hypothesis that he true is closer to 1 . I’m suggesting this theory because securities want to appear more attractive to investors and not mirror the market too closely. Securities will exaggerate their betas in order to appear more dispersed from the market. It is important for investors to have the most accurate data possible as to make the proper assumptions about their investments. This will become better represented in the return analysis and CAPM models of each stock supported by the benchmark of the S 500.
A formula representation of the hypothesis should look like: HO: P2 1. 15 (D’S) HI: *1. 15 (D’S) HO: = . 87 (ETE) HI: . 87 (ETE) The data from these SRF will suggest that the stated values of DIS and ETE beta will be closer than they are represented on common business sites such as Yahoo Finance and MSN Money. It will be apparent Walt Disney and Energy Transfer Equity should still be highly considered as potential options in portfolios. With a more accurate measure of each stocks it will provide the investor with better information to assess the amount of risk the investor is willing to take on based off the returns of each security.
Specification of the Mathematical Model of the Theory Independent Variable, X = S 500 Dependent variables, Y, Yl = D’S, Y2 = ETE Using the two-variable linear regression model we can calculate the SRF and draw inferences about our PRF. The market or S&P 500 will have a benchmark of 1 as that is the stated basis for testing the f the market. Yi will be the daily returns of the securities over the last five years dating from March 25th, 2008 to March 25th, 2013. These five years will be the basis for all data collection.
A mathematical It is estimated from the SRF A mathematical representation of the SRF for DIS and ETE is as follows: 9i = DAI + The mathematical model for the SRF of the data states that the parameters are DAI which is the risk free rate or rf, and OA2 which is the slope or of the security. The y- intercept, or DAI will be represented as O because it’s already factored into our expected return (ER) of the securities and subtracted from it. Using the Capital Asset Pricing Model or CAPM we can further discuss the relationship between the independent and dependent variables.
A graphical representation of the CAPM is as follows: ERi is known as the expected return of the securities, and is known as the systematic risk or the return of the market. The relationship between the dependent and independent variables in our hypothesis is a positive one because the assumption as stated in the hypothesis is that the betas of DIS and ETE are positive values, so regardless of actual value, they move in a positive manner with the market. DAI is assumed to be O in this graphical representation as stated prior as it is subtracted from our expected returns of each security.
A mathematical representation of the CAPM model is as follows: (ERi – rf) = (ERm – rf) ERm is the expected return of the market, calculated by averaging the yield of the S 500 for the last five years. The risk-free rate is estimated from the five year average return of 3-month Treasury bills. Specification of the Statistical or Economic Model A mathematical representation of the error term is as follows: Ui = Yi – E (y/xi) In this equation, Ui is known as the error term of a given variable, in our case the minus the mean return of the given security, E (y/xi).
The error term in this hypothesis represents the variation of returns in our securities that cannot be explained by the market. In other words, it’s our inability to model all the movements f the dependent variable. There are other variables other than the S&P 500 that effect the return of DIS and ETE. Geographical, political, and other economic factors all affect the return of a security in some way. Increasing the sample size of our SRF further eliminates the error term, but it’s impossible to completely eliminate the error term due to the immeasurable connectivity of all variables.
Obtaining Data Data is necessary in order to help explain the basis of our hypothesis. It is essential that the collection of data be done in the most intentional and accurate way according to your hypothesis. Data for testing was obtained through Yahoo Finance. Data for Walt Disney Inc. , Energy Transfer Equity LLP, and the S 500 was collected from a five year daily period from March 25th, 2008, to March 25th, 2013. Data selection was intentionally selected to avoid the majority of the great recession and the years before.
To increase the accuracy and reduce the error term of our returns, daily returns were preferred over weekly or monthly. Data collected was the % changes in each the price of each variable. With this data a simple mathematical equation was performed to adjust the % changes into returns. The mathematical equation is as follows: Y2 represents the % change in a securities price the day after Yl . Using SAS Web Editor to run tests on the data collected further interpretations of the two parameters, Pl and P2 can be concluded.
The SAS coding for each plot is as proc plot; plot DIS*SP500; plot ETE*SP500; proc reg; model ETE=SP500; model DIS=SP500; See attached PDF for visual results of SAS tests. Interpretation of Parameters The parameter estimates for the SAS tests are as follows: For ETE, using a regression analysis, SAS concluded that Pl = . 00052687 which is ssumed to be O. SAS estimated the beta as OA2 = . 80867 which is about . 01 lower than what Yahoo Finance and MSN Money had calculated it to be, which was . 82. The standard error for ETE, SE (OA2) = . 02931. r2 was found for our ETE return model to be . 773. The value of r2 of . 3773 means that about 37. 73% of the variation in the daily return of ETE is explained by the markets daily return. For D’S, using a regression analysis, SAS concluded that Pl = . 00041319 which, again, is assumed to be O. The SAS calculated the beta for DIS as OA2 = 1. 09786 which was about . 1 lower han what Yahoo Finance and MSN Money had calculated it to be, which was 1. 2. The standard error for D’S, SE (OA2) = . 02036. r2 was found for our DIS return model as . 6983. The value of r2 of . 6983 means that about 69. 3% of the variation in the daily return of DIS is explained by the markets daily return. The intercept for each regression analysis is interpreted as O because the risk-free rate is already factored into the return of the securities. Using the estimates from the parameters of the regression analysis one can test the statistical significance of their hypothesis. Running a test of significance test will show the range in which the true beta is found. Running a t-test one will be able to see if the stated betas of DIS and ETE are statistically significant than the actual beta.
The hypothesized betas for the securities are as follows: HO: P2 = 1. 15 (D’S) The estimated betas for the securities are as follows: = 1 . 09786 (D’S) = . 80867 (ETE) The estimated standard errors of each security are as follows: SE (OA2) = . 02036 (D’S) SE (QQ) = . 02931 (ETE) Region of Acceptance Testing The formula for calculating the region of acceptance for our HO is as follows: Pr [P2 – an SE (OA2) + tan SE (OA2)] = 1 -a D’S: ??2=1. 15 tan = 1. 962 SE (OA2) = . 02036 pr [1. 11 ETE: = . 87 SE (OA2) = . 02931 pr [ . 812 . 28] = 95% level of significance These equations show the range in which the true value of the beta for each security is found. We are 95% confident that the true is found within these values. Notice how both levels of significance tend to stretch towards 1. The stated for DIS was 1. 2, and . 82 for ETE. The HO for both securities is located within this level of significance, which is a good indicator in support of my hypothesis. T-testing The formula for calculating the t-value of each security is as follows: t = (OA2 – HO: ??2)/ SE On the basis oft for Walt Disney we see that t = (1. 09786 – 1. 15)/ . 2036 which equals -2. 5609 which is significant at a = 5% if you compare the t-value. Taking the absolute value of the calculated t-value we can make a comparison The t-value calculated: tal 2 = t. 025 = 1. 962
Again, given the confidence coefficient of 95%, in the long run 95 out of 100 case intervals will contain the true beta of Energy Transfer Equity LLP. F-value When testing the overall significance of the model one can analyze the f-value for each security. The estimated f-values for each security are as follows: F-value ETE = 761. 03 The calculated f-value formula is as follows: (ESS/(k- 1 K is equal to the #of independent variables which is 2. N is the sample size. (2-1)/ (1256-2) & 1/ 1254 Using the F table and that data above the calculated f-value on a =5% interval is 3. 84. Since 3. 84
My hypothesis essentially suggested that the betas of each security would tend to mirror the market more closely than their stated beta, testing rejected that theory. My arbitrary guess was that each security would be . 05 closer to 1 than its stated beta. Data suggested that the beta for ETE was actually farther away from 1, the opposite of my hypothesis, and while data for DIS suggested a beta closer to 1, it wasn’t statistically significant nough to fail to reject my hypothesis.
However analysis on the level of significance for each security suggested that the true beta was indeed closer to 1, again, Just not statistically significant enough. Forecasting and Prediction: Based off of the estimated parameters from hypothesis testing we can suggest that Walt Disney will produce roughly a 10% – 20% higher swing in volatility related to the market. With greater systematic risk in this security one can predict higher returns as well. Forecasting the return for DIS based the estimated parameters consists of oughly a 10% – 20% higher return than the market.
Forecasting for Energy Transfer Equity LP based off of the estimated parameters suggests that returns will be slightly less volatile than reported from MSN Money and Yahoo Finance. With an estimated beta of . 80867, and a stated beta from financial states at . 82, ETE looks to be generating revenues at about 20% less than the market. Both of these predictions are under the assumption that the percentage of risk for each security directly correlated to the percentage of return for that security. Investment Advice: Financially speaking, DIS is going to provide higher returns for a portfolio than ETE, but at a greater risk.
In terms of investing, security selection boils down the type of investor, and how risk averse they are. It’s important to diversify a portfolio which is why I’d definitely suggest including these two security’s together, to avoid taking on unnecessary risk. As I stated in my hypothesis mirroring the market is generally something avoided in investing, however in light of the recent positivity of the market and what many consider a bull market, mirroring the market could actually be a very safe and profitable decision.