Question

Given below is hypothetical data on two stocks on the LUSE and the market data (All Lusaka Share Index). The market data already includes dividends paid during the year.

 

Stock 1                                  Stock 2                                  Market Index

Year   Stock Price  Dividend       Stock Price  Dividend       (Includes Dividends)

2013:  K25.88           K1.73              K73.13           K4.50              17,495.97

2012:  22.13              1.59                78.45              4.35                13,178.55

2011:  24.75              1.50                73.13              4.13                13,019.97

2010:  16.13              1.43                85.88              3.75                9,651.05

2009:  17.06              1.35                90.00              3.38                8,403.42

2008:  11.44              1.28                83.63              3.00                7,058.96

 

Required:

 

 

      i.        Prepare a table presenting the Returns on the three securities for each year (Years, as Rows; Security Names as Columns).

     ii.        Determine and explain the following for each security by referring to part (i) above:

o   The appropriate Annual Average Return

o   The Total risk exposure

o   The Downside deviation (Semi deviation)

o   The relationship between Stock 1 and the market, as well as Stock 2 and the market.

Answer 1

The stock price of the year 2008 will be the opening price for the year whereas the price of the year 2009 will be the closing price for the year 2008. As we don't have the 2014 price, so the dividend received in year 2013 is not taken into consideration.

А B D E F G H 2 3 4 5 6 Opening Stock Price Closing Stock Price Dividend Recived Return = { Closing Price - Opening Price + Dividend} / Opening Price 22.15 25.88 1.59 24.02% 24.75 22.15 1.5 -4.44% 16.13 24.75 1.43 62.31% 17.06 16.13 1.35 2.46% 11.44 17.06 1.28 60.31% 7 8 9 10 Stock 1 Year 2012-2013 2012-2011 2011-2010 2010-2009 2009-2008 Stock 2 Year 2012-2013 2012-2011 2011-2010 2010-2009 2009-2008 Stock 3 Year 11 12 13 Opening Stock Price Closing Stock Price Dividend Recived Return = { Closing Price - Opening Price + Dividend} / Opening Price 78.45 73.13 4.35 - 1.24% 73.13 78.45 4.13 12.92% 85.88 73.13 3.75 -10.48% 90 85.88 3.38 -0.82% 83.63 90 3 11.20% 14 15 16 17 18 19 20 2012-2013 2012-2011 2011-2010 Opening Stock Price Closing Stock Price Dividend Recived Return = { Closing Price - Opening Price + Dividend} / Opening Price 13178.55 17495.97 32.76% 13019.97 13178.55 1.22% 9651.05 13019.97 34.91% 8403.42 9651.05 14.85% 7058.96 8403.42 19.05% 21 22 2010-2009 23 2009-2008 24

The average return = {Sum of all returns/Number of Yeras}

Here we have return for 5 years.

А B с D E F G H 2 3 Stock 1 4 Year 5 2012-2013 6 Opening Stock Price Closing Stock Price Dividend Recived Return Average Return = (Sum of all return/Number of years) 22.15 25.88 1.59 24.02% 28.93% 24.75 22.15 1.5 -4.44% 16.13 24.75 1.43 62.31% 17.06 16.13 1.35 2.46% 11.44 17.06 1.28 60.31% 7 2012-2011 2011-2010 2010-2009 2009-2008 Stock 2 Year 8 9 10 11 12 13 14 Opening Stock Price Closing Stock Price Dividend Recived Return Average Return =(Sum of all return/Number of years) 78.45 73.13 4.35 -1.24% 2.32% 73.13 78.45 4.13 12.92% 85.88 73.13 3.75 -10.48% 90 85.88 3.38 -0.82% 83.63 90 3 11.20% 15 16 17 2012-2013 2012-2011 2011-2010 2010-2009 2009-2008 Stock 3 Year 2012-2013 2012-2011 2011-2010 2010-2009 18 19 20 Opening Stock Price Closing Stock Price Dividend Recived Return Average Return = (Sum of all return/Number of years) 13178.55 17495.97 32.76% 20.56% 13019.97 13178.55 1.22% 9651.05 13019.97 34.91% 8403.42 9651.05 14.85% 7058.96 8403.42 19.05% 21 22 23 2009-2008 24

The total risk exposure is the standard deviation of a stock which is calculated from the above data.

SD = square root of(Sum of Square of deviation/ {Number of Years-1})

F G H J K L Stock 1 Return Average Return Deviation = Return - Avg. Return Square of Deviation Sum of Square of deviation Std Deviation = square root(Sum of Square of deviation/ Number of years) 24.02% 28.93% -4.91% 0.241% 75.699% -4.44% 38.91% -4.44% 0.198% 62.31% 62.31% 38.821% 2.46% 2.46% 0.061% 60.31% 60.31% 36.379% Stock 2 Return Average Return -1.24% 2.32% -3.55% 0.126% 4.156% 12.92% 10.19% 12.92% 1.670% -10.48% -10.48% 1.098% -0.82% -0.82% 0.007% 11.20% 11.20% 1.255% Stock 3 Return Average Return 32.76% 20.56% 12.21% 1.490% 19.521% 1.22% 22.09% 1.22% 0.015% 34.91% 34.91% 12.185% 14.85% 14.85% 2.204% 19.05% 19.05% 3.628%

Semi-deviation is used to measure the dispersion of an asset's price from an observed mean hence the negative deviations will only be considered to find the Downside deviation i.e. standard deviation of negative deviations.

The highlighted ones have a negative deviation from the mean and will be considered for downside deviation.

Downside Devaiation = square root of (sum of square of downside deviation/number of years)

Number of years for stock1 is 2 and for stock2 is 3

Stock 1 Return Average Return Deviation = Return - Avg.Return Square of Deviation Sum of Square of deviation Std Deviation = square root(Sum of Square of deviation/ Number of years) 24.02% 28.93% -4.91% 0.241% 0.439% -4.44% 4.68% -4.44% 0.198% 62.31% 62.31% 38.821% 2.46% 2.46% 0.061% 60.31% 60.31% 36.379% Stock 2 Return Average Return -1.24% 2.32% -3.55% 0.126% 1.231% 12.92% 6.41% 12.92% 1.670% -10.48% -10.48% 1.098% -0.82% -0.82% 0.007% 11.20% 11.20% 1.255%

The relationship between the stock and market is given by co-variance among their return and beta of the stock which is a proxy for market risk.

А B с D E F G H 2 3 4 5 6 7 8 9 10 Stock 1 Year 2012-2013 2012-2011 2011-2010 2010-2009 2009-2008 Stock 2 Year 2012-2013 2012-2011 2011-2010 2010-2009 2009-2008 Stock 3 Year 12 13 Stock 1 Opening Stock Price Closing Stock Price Dividend Recived Return Covariance of stock with index Beta = (covariance/variance) 22.15 25.88 1.59 24.02% 0.023 0.237 24.75 22.15 1.5 -4.44% 16.13 24.75 1.43 62.31% 17.06 16.13 1.35 2.46% 11.44 17.06 1.28 60.31% Stock 2 Opening Stock Price Closing Stock Price Dividend Recived Return 78.45 73.13 4.35 -1.24% -0.009 -0.906 73.13 78.45 4.13 12.92% 85.88 73.13 3.75 -10.48% 90 85.88 3.38 -0.82% 83.63 90 3 11.20% Stock 3 Opening Stock Price Closing Stock Price Dividend Recived Return 13178.55 17495.97 32.76% 13019.97 13178.55 1.22% 9651.05 13019.97 34.91% 8403.42 9651.05 14.85% 7058.96 8403.42 19.05% 14 15 16 17 18 19 20 2012-2013 2012-2011 2011-2010 2010-2009 21 22 23 2009-2008 24 | Chooti Chopta Shoot SL boots Thoota bot7

The stock1 has a postitve covariance with the index which means the movement is along with the index or moves in the same direction of the index.

Whereas the second stock has a negative covariance which means it moves opposite to the index movement. That means when the index is declining the stock price is appreciating.