Obtain the summary statistics for your sample and briefly discuss the risk and average return relationship in each stock. Which stock (Google or Yahoo) is relatively riskier than the other?
Answer:
In order to determine the parameters of sample from population, the imperative model is Central limit theorem. There are three main aspects of Central limit theorem that are highlighted below:
- If the sample size is equal to or greater than 30 then it can be assumed that the data is normally distributed.
- The mean of sample would be assumed to be same as the mean of population.
- The below highlighted expression would be used to compute the standard deviation of sample from the standard deviation of population.
The above understanding would be applied to the given data set (population) in order to compute the sample parameters.
Probability
Probability of getting a return value of at least 4%
Probability
Probability of getting negative returns values
Case 1: For Google Returns
Case 2: For Yahoo Returns
From z table:
Hypothesis testing has to be applied in order to ascertain if for the given period the two stocks have similar average returns or not.
H0: The two given stocks i.e. Google (Stock1) and Yahoo (Stock2) have average monthly returns that are not statistically different from each other
H1: The two given stocks i.e. Google (Stock1) and Yahoo (Stock2) have average monthly returns that are statistically different from each other
Critical Value Method
If computed t statistic does not lie within the critical interval, then proceed to null hypothesis rejection. For the given test, two tail critical value ranges from -1.98 to 1.98. However, the computed t value (-0.83) lies in this interval which implies that there should not be null hypothesis rejection.
The stock of choice based on risk return characteristic has emerged to be Yahoo. Thus, the relevant excess returns computation is indicated
The estimated CAPM model representation is highlighted below
Excess stock returns = 1.91 + 1.64*Excess Returns on S&P 500
R2
The slope also called as beta has a 95% confidence interval as highlighted in the above regression output (1.06, 2.23).
The testing of hypothesis in the given case needs to be performed using
H0: Yahoo has a beta which does not significantly deviates from 1 and thereby is a neutral stock.
H1: Yahoo has a beta which does significantly deviates from 1 and thereby is not a neutral stock.
Relevant slope for testing of hypothesis is (1.06, 2.23).
It is apparent that 1 does not belong to the above stated confidence interval and thereby rejection of null hypothesis is facilitated yielding that alternative hypothesis is true.
Interpretation
S&P 500 – The index tends to have an upside movement whereby the index is witnessing steady gains without much sideways movement. The index in a time period of around 4.5 years tends to deliver a return of around 50%.
Yahoo Stock – The stock does not show a particular trend but has periods where certain trends are noticeable. For instance, from February 2012 till the end of 2013, the stock has witnessed significant gains in excess of 150%. However, this rally was halted when the stock correct during the initial half of 2014 but again stated the upward movement to reach the peak valuation at 2014 end. The stock paired some gains in 2015 when there was correction but improvement in stock price was evident in 2016.
Google Stock –
The stock showed a spectacular run during February 2012 till March 2014 as it gained almost 100%. The declining price noticed in April 2014 is on account of splitting of the stock which resulted in the stock price becoming half overnight. However, even after the split the stock has again come back on the growth trajectory as the stock has gained in value especially in 2016.
b) With relation to the summary statistics obtained, the primary objective is to compare the risk and returns of the two stocks for the given time period. The mean returns are indicative of the average monthly returns while the standard deviation is indicative of the underlying risk of the stock. With regards to returns clearly Yahoo is the outperformer as it boasts of higher returns. Further, in terms of risk also, Google has a higher value of standard deviation which implies that higher risk is associated with the Google stock in comparison with Yahoo.
As the null hypothesis got rejected, thus the non-normal nature of the various stock and index distributions is confirmed with 95% confidence.
In order to ascertain if the returns of the given two stocks i.e. Yahoo and Google is the same or not hypothesis testing was deployed using the given sample data. But as the standard deviation for the two stocks tend to be different, hence their risks cannot be deemed as equal. Since the Google stock is more risky, hence a rational investor would choose Yahoo over Google.
The excess return expected on the stock has come out to be 1.91% as represented by the slope of the line indicative of the CAPM model. Hence, it would be fair to assume that positive abnormal returns may result from Yahoo stock even after adjusting for the difference in risk between the stock and index.
The slope of the CAPM model is known as beta and has been derived as 1.64 categorizing Yahoo as an aggressive stock. Essentially, this would imply that change in value of market by 1% would bring about same direction change of 1.64% in the Yahoo stock.
The coefficient of determination has been highlighted in the excel output as 0.3808. This clearly reflects that market only is partially successful in driving the stock price of Yahoo as it can account for only 38.08% changes in the stock price. This may be because the beta is not a good measure of risk and does not accurately capture the various associated risks with the Yahoo stock.
We can conclude with a confidence of 95% that the beta of Yahoo common stock would be lying in the interval between 1.06 and 2.23. The stock is clearly aggressive as the mean has to lie in the interval and this interval has all values greater than 1.
Through the hypothesis testing process, it has been derived that there is a rejection of null hypothesis culminating into the realisation that Yahoo is not a neutral stock. Further, considering the confidence interval, it is highly likely (95% confidence) that it is an aggressive stock.
