Stock Price Fluctuations

STOCK PRICE FLUCTUATIONS

Principles of Financial Management

1. On your web browser, go to http://finance.yahoo.com/.  In the upper part of the page and left of center, you will see a search box just to the right of the Yahoo logo.  In the box, type in the name of a company of interest to you. When the ticker symbol (an abbreviation of usually 3 or 4 letters and the name appear, click on it.   In the middle of my screen, Yahoo displays some current information about trading for each company.  On the left side of the page, Yahoo lists the pages that are available on each stock.  This list will be the same for nearly every stock.  The availability of information on the individual pages will differ across stocks.  

The Walt Disney Company (DIS)

101.94 [pic 1]0.21(0.21%) 3:35PM EST - Nasdaq Real Time Price

2. Click on Historical Prices.  From this page, you can select a date range and the frequency of prices (daily, weekly, or monthly).  Use this to download monthly prices for your firm from December 2004 to December 2014 into an Excel spreadsheet. This should give you 121 prices. Save the date and adjusted closing price.  You can eliminate or hide the other variables.  Sort the data in Excel so that it is arranged from oldest to most recent (note Yahoo gives the data sorted newest to oldest). The adjusted closing price adjusts in the event of stock splits (or reverse splits) and assumes reinvestment of dividends. Using the adjusted closing price calculate the monthly return for each firm as

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Where the subscript t refers to a given month and the subscript t-1 refers to the prior month. This will give you one fewer returns than the number of prices that you downloaded.  You will not have a return for December 2004. Compute the median, arithmetic average, and standard deviation of monthly returns using the Excel functions =median(range), =average(range), and =stdev(range). Median, average, and standard deviation are statistics that describe the entire sequence of returns.  In each case, the range is the group of cells in the column with the sequence of monthly returns from January 2005 to the present.  You should have one value of each statistic that describes your historical return data. Note that the 3 statistics describe the observed values for the variable “monthly return”.  The statistics are not variables.

Next, compute a cumulative return from the December 2004 price to the price at each subsequent date.  To do so, set the cumulative return for December 2004 equal to 1.0.  Then compute a cumulative return for January 2005 and beyond as either of the following

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Where ACPt is the adjusted closing price in each month and ACPbeg is the closing price for December 2004 (this price doesn’t change), or        

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After entering either of these equations, drag the equation down the page. This will give you cumulative returns from December 2004 (=1.0) through the present. Insert a chart using the line graph option with Cumulative Ret as the vertical axis and date as the horizontal axis. Place the chart below the data.  This chart gives you a standardized view of the stock’s performance for the last 10 years. Also compute a geometric average return as

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The geometric average takes your final cumulative return (for December 2014) and uses an exponent which is one divided by the number of returns in your sequence and, finally subtracts one. Since you are using a month as the unit of time over which you are measuring returns, your median, arithmetic average, and geometric average will all be on a “per month” basis.

Write an analysis of your stock. Include the following information in your analysis. What do the median and the two averages tell you about returns on your stock over this time period?  How representative do you think the median and averages are as measures of return are for longer time periods?  Explain your answer. What do you think of the standard deviation as a description of risk or volatility for your stock over this time period?  How representative do you think this standard deviation is as a measure of volatility for longer time periods?  Explain your answer.

The median, avg, std dev, Geo avg, min and max of DISNEY (DIS) monthly returns are given below:

Median                1.75%

Average        1.34%

Stdev                6.24%        

GEOAvg        1.14%

Min                -18.94%

Max                20.56%

Though the average 1.34% is positive but it is lower than median 1.75% which speaks some averages returns are lower 50% of quartile.  However the mean returns are not necessarily indicative of future returns.

The geometric mean is a compound return and it provides the cumulative effect of a series of returns. It provides ability of an asset to generate earnings (or losses) that are then reinvested and generate their own earnings.  As the returns in a series of numbers become more dispersed from the average, the GEOAvg return declines. As the DIS monthly chart speak the volatility of returns, there is more drop in the GEOAvg return. The GEOAvg here 1.14% which is true avg monthly return.

The standard deviation is 6.24% which is more than average returns. As the spread high it speak returns are quite volatile (some months are positive and some negative). The monthly return chart of DIS clearly speaks volatility. Hence the standard deviation does the volatility for longer time periods

Using monthly and cumulative returns for your company, describe the pattern of returns across time.  Why do you think you observe this pattern? How do price, monthly return, and cumulative return relate to each other? When are the highs and lows for each for your company? Do they occur at the same points in time or at different points for price, monthly return, and cumulative return?  Why or why not?  You may locate highs and lows visually from your graphs or use the Excel functions =max(range) and =min(range) to assist you.

The pattern indicates linearly growing returns though there was slightly a dip in 2008. The cumulative return and ACP does follow closely. Currently DIS stock price is at high and low occurred in back in 2008.The Low and High of Cumulative returns does match with ACP. But High of monthly return does not match with them, though the Low of monthly return does match with ACP and Cumulative return. The reason being volatility quite High in 2008 and 20011

3. Return to the first page of Yahoo Finance.  Across the top of the page, you should see info for several stock indices.  Click on the symbol for the S&P 500.  Click on “historical prices” and download data for the same period as step 3. Be sure to sort the index data so that it is also arranged from oldest to most recent.  After sorting, copy the adjusted closing values for the index into your spreadsheet.  

(a) Calculate monthly returns and cumulative returns for the S&P index as you did above for your stock. Also compute the median monthly return, arithmetic and geometric average monthly returns, and standard deviation of monthly returns for the S&P index. Compare these 4 values for the index to the values you calculated for your firm. Does this change your view of the typical return and risk level of your stock?  Why or why not? Also compute the correlation of monthly returns between your stock and the S&P index using the Excel function =correl(range for variable 1, range for variable 2).  What does this correlation tell you about the volatility of your stock?