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# COMPARISON ON STOCK RETURNS, CAPITAL ASSET PRICING MODEL AND HYPOTHESIS TESTING

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EXECUTIVE SUMMARY

Comparison of stock returns, including dividends, stock price on two or more different investments over a given time frame. The report focuses on comparing International Business Machines (IBM) stock price, General Electric (G E) co stock price, Interest rate on 10 year US Treasury note and S&P 500 price index. The performance data reflects on past results, however this results doesn’t guarantee positive future outcomes.

The calculated required rate of return for any risky asset is the Capital Asset Pricing Model (CAPM). The required rate of return is the increase in value of the outcome you should have expected based on the relative risk level of the asset. Helps an investor understand what price should pay for a particular stock. For example, if stock A is more of a risk than stock B, the value of stock A should be lower than that of stock B to compensate investor’s decision for taking up a higher risk [ CITATION Aha81 l 1033 ].

Hypothesis testing involves identifying the null hypothesis and the alternative hypothesis. In this scenario testing the difference of the two standard deviation. Two equal variance will satisfy the equation, concluding as accepting or rejecting the null hypothesis which states that both standard deviations are equal [ CITATION Bai88 l 1033 ].

TABLE OF CONTENT

1. INTRODUCTION.

2. METHODS AND ANALYSIS.

3. DESCRIPTIVE ANALYSIS.

4. COMPARISON OF STOCK RETURNS.

5. HYPOTHESIS TESTING.

6. CAPITAL ASSET PRICING MODEL (CAPM).

REFERENCES.

APPENDICES.

INTRODUCTION

Research carried out on data analysis of various stock prices in a certain market portfolio. Market portfolio investments that are found in the stock market. Each investment weighted in proportion to its current stock price in the market Help investors to understand which stock will have better performance overtime. Descriptive analysis conducted on International Business Machines (IBM), General Electric co., and S&P 500 price index and interest rate on 10 year US Treasury note [ CITATION Bai88 l 1033 ].

Compare risk –return relationships between the two stocks. Risk and return relationship states that the higher the expected return for an investment the higher the risk. By accepting more risk doesn’t mean that there will be a guarantee that returns will be significantly higher.

Riskier investments suggest a greater chance that you could make losses your money. Before purchase of stock investors should evaluate risks.

Technical analysis on line charts on the closing price of different stocks during the period January 2011 –December 2015.The line is constructed by joining the stock prices over a given range for a period of time. Line charts don’t provide information on individual points such as high, low and opening prices. Closing price is considered the most important stock data [ CITATION Bau00 l 1033 ].

METHODS AND ANALYSIS.

LINE CHARTS

These are the stock charts used in study of chart patterns in technical analysis.

Line chart is a style of chart that connects a series of past stock prices in a single unbroken line within a specified time period. This line charts S&P 500 price index, International Business Machines (IBM) stock price, General Electric co. stock price. Typically, the y-axis represents the price of the stock and x-axis represents the time frame.

Line chart 1. International Business Machine Co. Stock price.

The above chart can give the investor a good understanding of where the assets of International Business Machines co. stock price have moved over specified time frame. Using the closing price being the most important prices in the stock data. Stock price of IBM co. was highest at a value of 213.3003 series “close” point “3/1/2013”. From the start January 2011 significant value of stock has been on the increase with slight high and low changes.

Lowest point recorded on the stock price series “close” point “12/1/2015” value: 137.619. Highest recordings were between 2013 and 2014.

Line chart 2. On S&P 500 price index.

S&P 500 price index line chart analysis uses stock prices points to draw trend to interpret stock price movement. Trend lines connect the high and lows in the past stock price and try predict what the stock price might do in the future. S&P 500price index have a relative upward slope known as ascending trend lines. This means that the stock price is outperforming the S&P price index, the stock price is rising, while the S&P 500 index is falling.

Line chart 3 General Electric co. (GE)

General Electric co stock price have an upward sloping movement from series “close” point “9/1/2011” value: 15.22 as the lowest data point stock price. A relative increase in the stock price throughout series “close” point 12/1/2015 value 31.15. General Electric has an ascending trend line.

Each bar on the histogram chart represents stocks traded during that month. Bar length indicates a stocks high-low price range. Of course the top bar corresponds to the highest price paid for the stock during that month, lowest price paid corresponds bottom of the bar i.e. the vertical x-axis.

DESCRIPTIVE STATISTICS.

Return Distribution 1

 180.1252 Standard Error 2.414436 Standard Deviation 18.70214 Sample Variance Kurtosis -0.44496 Skewness -0.46693 75.68001 10807.51 Frequency 0

Return Distribution 2.

 166.3803 Standard Error 4.025384 Standard Deviation 31.18049 Sample Variance 972.2231 Kurtosis -1.57185 Skewness 0.050536 Frequency

Return Distribution 3.

 Standard Error 0.470496 Standard Deviation 3.644447 Sample Variance Kurtosis -0.60778 Skewness -0.18898

Frequency

0

0

0

Conclusion: based on the computed statistics IBM is relatively riskier than General Electric co., this happens so a there is a wider margin on the standard deviation and variance on IBM compared to GE.

HYPOTHESIS TESTING.

Risk-return relationship states that the higher the expected return for an investment the higher the risk. By accepting more risk doesn’t mean that there will be a guarantee that you will receive higher returns. Riskier investment suggests[ CITATION Bea95 l 1033 ] a greater chance that you could make loss on your money.

Key investments risks, returns are not assured/guarantee General Electric co stock price have from the past performed well over the long term. You are not assured of making money on a stock at any given period of time.GE co. standard deviation from its average price to its high-low prices of \$ 23.115 is 3.644, lower margins result high historic volatility.

GE co stock price at mean of \$23.115 has a relative high frequency of above 24 with \$30 having a frequency of 23 volatility is measured largest loss recorded that month. Invest in a diversified portfolio. Choosing type of industries, companies or the same industry might have a fall while companies from different industries might be gaining. E.g. agricultural companies might be doing well than technological companies.

To perform a t-test, follow these steps:

1. Compute f-test to determine if the variance of the two variables are equal.

2. T-test two sample assuming unequal variance

Variance close 1 =168.54

Standard deviation close1 =12.98

Variance close 2=4.7766

Standard deviation close 2=2.185

Conclusion: we do a two tailed test, if t-test ˂t critical two tailed or t stat ˃t critical two tail, we reject the null hypothesis. Observed difference between the sample standard deviation (2-12) is not convincing to say that the average stock price between close 1 and close 2 differ significantly.

CAPITAL ASSET PRICING MODEL.

Capital asset pricing model required to[ CITATION Bea95 l 1033 ] compute the required rate of return for any risky asset. The increase in value expected based on the inherent risk level of the asset.

Use CAPM to decide the preferred stock.

The CAPM formula is

R a=r f + B a (r n-r n, t)

Where r r, t=rate of return for a risk free security

Rm= the broad markets expected rate of return

B=beta of the asset

On computation you should demand the following rate of return on investments.

1. + [0.75*(0.10-0.03)] =0.0825=8.25%

The inputs r f, r m and Ba are determined by the investor and are open to interpretation. CAPM helpful in determining the fair price of an investment. Calculate the risky assets rate of return used to discount the investments to their current values thus computing the investments fair value.

## Works Cited

.Smith, B. M. a. C., 1995. Financial architecture. leverage,maturity and priority., 8(4), pp. 4-17.

Bailey.W, 1988. Canada dual class shares. further evidence on the market value of cash dividends, 43(5), pp. 1143-1160.

Barclay, M. C. S. a. R. W., 1995. The determinants of corporate leverage and Dividend policies. Applied corporate finance, 8(4), pp. 4-19.

G.Palmer, B. W. a., 1995. Risk management:problems and solutions. 1 ed. new york: McGraw Hill.

Quandt, B. W. a. R., 2000. Invetsments and decision rates under capital rationing. A programming approach,Economic journal, 75(4), pp. 317-329.

Swary, A. J. a. I., 1981. Quartely dividends and earnings announcment and Stockholders Returns.. An empirical analysis, 36(journal of finance), pp. 1-12.