#### Statistics and Quantitative Methods for Finance

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follow the instructions in the word and the excel

small RESEARCH PROJECT: BUS_633 “Statistics and Quantitative Methods for Finance”, October-November 2015 – NBAD_MFIN

Theme: Critical Thinking and Quantitative Reasoning applied in the study of a security

As a financial analyst or investors’ advisor you selected a stock from a capital market and you have to explain to your client why to buy or not this particular security, based on the expected returns and the risk of the security. Several questions then may arise in the mind of the client:

Why this particular stock?

What are the expected return and risk characteristics of this security?

Given the cost of money in the economy is currently 1.85% what is the excess return of the stock?

What are the above characteristics as compared as with the market index?

What is the sensitivity of this stock in market’s changes (that is the beta factor of the stock)?

How large is the company’s risk (or specific risk of the stock)?

What is the percentage of returns’ changes due to the market movements?

… and many other questions that will be deployed in the course of Modern Portfolio Management (or Investments).

In order to be as accurate as possible your analysis should include several steps in two Parts.

PART (A)

Thus, the first step is to have a graphical representation of the stock price and see if this is a stable process or not. For example, to identify trends or periods of tranquility, structural breaks, trend reversals etc. To complete your “discussion” with the graph (remember that sometimes “a picture paints a thousand words”) you may plot a moving average (or two, one short and one long), and apply the crossover Rule for buy and sell signals. At least you will get an information of the current position of the security’s price in comparison with its moving average.

The second step is to perform some calculation in order to approximate the distributional properties of the returns (Attention! All your calculations hereafter are based on returns series; not the raw data. WHY?).

The third step is to infer if these characteristics- calculated in step 2- are stable over time. An idea is to divide your sample in to sub-samples and perform the same calculations and comments (i) for the whole period, (ii) for the first sub-period, (iii) for the third sub-period. Usually, we divide in two parts our time series. The ideal would be if the division of the whole period is not arbitrary but based on some event (political elections, some major regulatory event, war, structural change, a monetary action from the central bank (of the country or the Fed from USA or the European Central Bank … it depends of the event and the purpose of the study) … etc) or other criteria (mathematical or econometric such as restrictions on the parameters’ value etc).

This part is useful and meaningful if you perform hypothesis testing. For example, you might like to test if the mean returns over the two sub-periods are the same. That means to test if their difference is statistically significant or not. The same question you may ask for the risk (standard deviation) of the security or its volatility (variance). {Hint: Make sure that you understand the slight difference between risk and volatility; visit: http://www.nasdaq.com/investing/risk/volatility.aspx }.

Then, you must have some comparative results. This means that once you have the distributional characteristics for your security you need to compare them with the characteristics of the market as a whole (or of the industry index or an international index or a benchmark or …. depending on the purpose of the study). Then, first you need the characteristics of the joint distribution that is the covariance, and the correlation coefficients. {Hint: in this address, as above, http://www.nasdaq.com/investing/risk/volatility.aspx push “next” and you will find simple cases with interpretation for those two coefficients, and much more …}.

For that purpose you select the market index, calculate the returns, and all other measures as above. Then you calculate the correlation and the covariance with you stock. (Hint: For this step and all the calculations in Section (II) below, use only weekly returns).

PART (B)

In this part you consider the CAPM model, and you regress the (weekly) returns of the security to the (weekly) returns of the Index. You estimate the slope coefficient. You perform a hypothesis testing to infer the statistical significance of the estimated value, and the overall fit of the regression line.

NOW in practice

Section (I)

(i). Select a stock (maximum 5 years historical daily closing prices)

(ii). Calculate logarithmic returns for daily, weekly and monthly time periods

(iii). Calculate the mean, variance, standard deviation, coefficient of variation for daily, weekly and monthly returns

(iv). Present graphs for price and returns.

(v). Calculate the moving average (m.a.) of 21 periods and the moving average 65 periods (approximately monthly m.a. and quarterly m.a.; in other words the short and the long moving average).

Here is an example { http://www.investopedia.com/university/technical/techanalysis9.asp}:

Comments_Section (I):

(a). Comment on the graph of prices (are there trends? Upward or downward? Which period(s)? Do you know if any significant event was present in these periods? Any significant event on the break of the trend (the change from upward to downward an d vice versa?)… etc. As for returns you can choose daily OR weekly. (Hint: Choose the one you can have more comments).

(b). Comment on the returns (choose daily or weekly) graph (are there clusters? That is a tendency that high returns are followed by high returns and, low returns are followed by low returns? Is the range of returns stable? Small? Large? For all the 5 years period? Some particular period? Is there any correspondence with the price graph? What is the implication for the risk of the chosen security?).

(c). Comment on your findings in Part (I)-point (iii).

Section (II)

Divide your original time period in two (maximum 3 if there is a reason for that) sub-periods.

Repeat all the calculations as in Part (I)

Comments_Section (II):

(a). Comment on the graph of prices (are there trends? Upward or downward? Which period(s)? Do you know if any significant event was present in these periods? Any significant event on the break of the trend (the change from upward to downward an d vice versa?)… etc. As for returns you can choose daily OR weekly. (Hint: Choose the one you can have more comments).

(b). Comment on the returns (choose daily or weekly) graph (are there clusters? That is a tendency that high returns are followed by high returns and, low returns are followed by low returns? Is the range of returns stable? Small? Large? For all the 5 years period? Some particular period? Is there any correspondence with the price graph? What is the implication for the risk of the chosen security?).

(c). Comment on your findings in Part (II).

Section (III)

You conduct the “risk analysis” estimating the CAPM model.

Comments_Section (III):

(a). Estimate the regression coefficients, a and b. Test their statistical significance.

(b). Perform the analysis of variance (ANOVA).

(c). Explain the findings.

SUMMARY REPORT

You should report on your client an executive summary. This summary should contain:

Present a graph of the stock price along with one or two moving averages (if possible). Comment on the relative position of the current price of the stock. The same for the market index.

The statistical characteristics of you stock and the Market (the Index)

The comparison of two. Here you can report the Sharpe ratio both for the stock and the index and comment about their adjusted risk. You can use a table to present all the characteristics.

The beta coefficient and its statistical validity. Comment on the riskiness of your stock.

Conclusion: Buy- Sell or Hold the asset? And why (in two-three lines)?

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TECHNICAL: EXCEL for the Regression (CAPM)

Suppose A (A1:A200) the returns of the stock and B (B1:B200) the returns of the index. Select DATA then DATA ANALYSIS (if you do not have, go: FILE, OPTIONS (left and down), ADD INS (on the left column) and choose ANALYSIS TOOLPAK. Restart Excel and that’s all!). Now you have DATA ANALYSIS. Then REGRESSION, y: you insert the returns of the stock, that is A1:A200, and x: you insert the returns of the index (B1:B200). In this dialog box you check the box LINE FIT PLOT (in the RESIDUALS).