Solution Code: 1AGFE
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Variables and Data Sources:
https://finance.yahoo.com/quote/SPY/
Downloading the Data
Download monthly data for S&P 500 index, International Business Machines (IBM) Stock Price, General
Electric (GE) Stock Price, and US TN (10 year) by clicking the above links and choosing Historical Data for all
variables covering the period based on the following criterion.
Task 1: Comparison of Stock Returns (50 Marks)
Perform an appropriate hypothesis test given the sample and report your findings. Which stock will you prefer and why?
1 Monthly return for August 2016 will be calculated as r2016 = 100[ln(PAugust2016)-ln(PJuly2016)] %
Task 2:
Estimation of CAPM and Hypothesis Testing
Excess return on preferred :stock rry= - Excess
return on market : =
Capital Asset Pricing Model
(See last page for more details on CAPM taken from The Basics of Financial Econometrics by Fabozzi et al. (2014))
Interpret the estimated coefficients in relation to the profitability of the Stock and its riskiness in
? 0 + ? 1 urr tM , - tf , + t t
= ? 0 + ? 1 t + t ,...,2,1, =
7. a. Estimate the CAPM and report your results.
b. Interpret the estim
c.Estimate the CAPM and report your results.
comparison with the market.
Estimating the CAPM for Mutual Funds (Fabozzi (2014), p.25)
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The stock prices for S&P has been between $105 to $160 until the Great Recession of 2008-09. The closing share prices dipped heavily to as low as $74. The share prices had earlier soared to above $150 in 2007. There has been a slight rising trend in the share prices of S&P before the Great Recession and a steep rise following it.
IBM share prices have gone through several ups and downs between 2005 and 2009. An upward trend is visible until the Great Recession which is more prominent after that.
GE share prices have been nearly constant before the Great Recession, however, its prices dipped to almost $5 during the Great Recession. A slow recovery is visible after that.
Null Hypothesis, H0: ?2IBM = ?2IBM (Claim)
Alternative Hypothesis, H1: ?2IBM ? ?2IBM
Significance level = 5% or .05
We will conduct an F-test for the equality of two variances.
Calculations:
Sample size of IBM stocks = 59
Sample size of GE stocks = 59
Numerator degrees of Freedom = 59 – 1 = 58
Denominator degrees of Freedom = 59 – 1 = 58
From the F Distribution table, for ?/2 = .025, DFN = 58, and DFD = 58, critical F = 1.546
Rejection Rule:
F test statistics > F critical
Test statistics = 1222
Variance of GE is higher than IBM, so 12=0.0101
And, 22=0.0042
So, F-test statistics = 0.01010.0042=2.3853
Result:
Since the F test statistics > F critical, we reject the null hypothesis.
Inference:
At .05 level of significance, there is enough evidence to reject the claim that both returns are equally volatile.
GE stocks appear to be more volatile than IBM as was found earlier. So, I would rather prefer IBM stocks than GE stocks.
Null Hypothesis, H0: µIBM=µGE (Claim)
Alternative Hypothesis, H1: µIBMµGE
Significance level = 5% or .05
Population standard deviation are unknown for both the samples. Samples are independent in a way that the stock prices are considered for two different stocks.
We will conduct an independent sample t-test for the equality of two means, assuming unequal variances.
Calculations:
Sample size of IBM stocks = 59
Sample size of GE stocks = 59
Average return for IBM stocks = 0.00572
Average return for GE stocks = –0.01475
Sample standard deviation for IBM stocks returns = 0.06497
Sample standard deviation for GE stocks returns = 0.10034
Result:
Since the t test statistics is not greater than the critical t of 1.9842, we fail to reject the null hypothesis.
Inference:
At .05 level of significance, there is not enough evidence to reject the claim that both the stocks offer the same population average return.
GE stocks appeared to be more volatile than IBM as was found earlier. So, I would prefer IBM stocks than GE stocks. Nothing certain can be determined from this hypothesis test for equality of means.
IBM vs the Market Rate of Return is shown in the chart below:
The market rate of return has been quite volatile over the period and so have been the IBM stock returns.
GE vs Market Rate of Return is shown in the chart below:
The market rate of return has been quite volatile over the period and so have been the GE stock returns, especially during and after the Great Depression. Market rate of return and GE returns appear to follow the same trend.
The sample covariance between IBM and GE stock returns, computed through Excel, is 0.002414 which indicates a positive relationship between the two stocks. Correlation between IBM and GE stock returns, computed through Excel, is 0.370378 which indicates a weak positive relationship between the two stocks.
TASK 2
IBM Stock Return = 0.00652-0.80889Market Return
The results were calculated by running a regression analysis over the IBM stock return and Market return using Excel, with IBM return as the dependent variable.
The intercept of the equation is .00652 which suggest that when the market return is 0%, IBM returns will be 0.65%. The slope of the equation is -0.8089 which suggest that as market return rises, the IBM stock return decreases and for every rise in market return by .01, IBM returns decreases by .81
The R2 value computed is 0.3552. This means that 35.52% of variations in the IBM stock returns is explained by the market returns.
Hypothesis Test:
Null Hypothesis, H0: ?1 ? 1
Alternative Hypothesis, H1: ?1 > 1
Standard Error = 0.0526
Degrees of Freedom = n-2=59-2=57
Significance Level = 0.05
It is a right tailed-test.
Critical t = 2.003
Rejection region:
T statistics > Critical t
Test statistics = 1-1se=-0.8089-10.0526=-34.37
Since the test statistic does not lie in the rejection region, we fail to reject the null hypothesis. There is not enough evidence to support the claim that the stock is aggressive. The slope is negative which is less than 1, so the IBM stock is defensive.
95% confidence interval for the slope coefficient is (-1.0980, -0.5198) which was computed as a part of regression analysis. The confidence interval entirely lies below 0 which suggest that the slope is significant.
The Auto Regressive Model for IBM stock price is:
IBM Stock Price, yt=5.1757+0.9539yt-1.
The auto regressive model suggests that IBM stock prices are positively related to previous year’s prices.
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