Accounting assignment help on: Stock movement of traded companies

1. The index A in this case is the S& P 1500 which takes into consideration stock movement of 1500 actively traded companies.  Index B in this case is the S & P 500 which takes into consideration only 500 stocks which have usually the highest volumes and turnover. All the 500 stocks included in S & P 500 are also included in the S & P 1500.The sample frequency has been chosen as weekly as it adequately captures the various movements on a broad scale and thus presents a realistic view of the market and the general macroeconomic environment in a dynamic market scenario as was prevalent during this period (Graham, Dodd & Cottle, 1988). Normally the movement of the index on a weekly basis may be subdues but due to the crisis even in a week, significant volatility was observed.

The summary of certain descriptive statistics of S & P 500 is shown in the table below.

F8urther, the summary of certain descriptive statistics of S & P 1500 is shown in the table below.

CommentFrom the above descriptive statistics, it is clear that the macro environment of US was highly dynamic during the given period as there is high degree of fluctuation in both the index values which is clear from the high value of standard deviation and also the range of both the indices.  Also it is clear from the movement of the indices that the latter half of 2008 and first half of 2009 was extremely difficult for the market due to the global financial crisis. It is during this time that the both the indices in consideration touched their bottom (Graham, Dodd & Cottle, 1988).  However since August 2009, some stability and recovery was seen primarily due to the huge stimulus packages doled out by the government so as to bailout the economy. Due to global financial crisis, there was a significant decrease in the disposable income coupled with severe liquidity crunch due to which there was a global decrease in consumption due to which prices of various goods and commodities plummeted. This led to decrease in manufacturing, decrease in trade and increased unemployment to all times high further worsening the overall economy (Klein & Lammartino, 2009).

Under such circumstances, the investors liquidated their assets at ridiculously low prices as well due to which there was high volatility in the market. This is clear from the fact that during Sep 2008 – Oct 2008, the S & P 500 index declined by nearly 30%. Hence the individual assets and portfolios both were at high risk since this fall was due to the systemic failure of the overall economy and hence was not limited to a particular sector due to which diversification also did not help much (Klein & Lammartino, 2009).

2. In the given case, the six discrete weightings of the various portfolios is as shown in the table below.

To calculate the risk and standard deviation on the given portfolios, the following formulae have been used.

Return on the portfolio = r_Aw_A + r_Bw_B

Where r_A is the annual historical return on index A

r_B  is the annual historical return on index B

w_A is the weight of index A in the portfolio

w_B is the weight of index B in the portfolio

Risk on the portfolio = (σ_A² + w_B²σ_B² + 2 w_A w_B σ_A σ_B ρ )

Where σ_A is the standard deviation of the returns on index/stock A

σ_B is the standard deviation of the returns on index/stock B

ρ is the correlation coefficient between the returns on stock/index A and stock/index B

Using the above mentioned formula, the risk and return for the various above mentioned portfolios have been summarized in the table shown below.

The risk return plot for the above mentioned portfolios is presented below.

From the above it may be inferred that portfolio A is the dominant portfolio as it offers the highest return from the given choices of portfolios and has the least amount of standard deviation which effectively denotes the risk of the portfolio. Hence A has the highest amount of return on per unit risk on a comparative basis and hence can be termed as the dominant portfolio (Bacon, 2008).

3. For the given question, a portfolio has been formed with 20% weightage to INDEX A (S&P 1500) and 80% weightage to INDEX B (S&P 500). Further an amount of $ 100 million is invested in the given portfolio and its movements have been tracked during the period from January 1, 2007 to January 1, 2010.  The movement of this portfolio based on the weekly returns has been tracked over the given period. Based on these movements, the return during the period from January 1, 2007 to January 1, 2010 comes out to be -18.87% i.e. the value of the portfolio as on January 3, 2010 would have remained only $ 81.13 million. The corresponding standard deviation for the portfolio works out to be 17.877.

Further to calculate 1 day VAR at 95% confidence level, the VAR for one year would be calculated which would be multiplied by square root of 250 to arrive at the required number.4. The correlation coefficient between the two indices for the period January 1, 2007 to January 1, 2010 has been calculated using the CORREL function in excel.

The working is shown in the attached excel sheet. The value of the correlation coefficient for the above mentioned period is 0.999827. Hence we can conclude there is a very high degree of correlation between the movements of the two indices over the given period (Latane, Tuttle & Jones, 1975).

5. The correlation coefficient between the two indices for the period January 1, 2007 to January 1, 2009 is 0.999718 while the corresponding value during the period January 1, 2007 to January 1, 2009 is 0.999448. The difference in the value of the correlation coefficient for the two above mentioned period can be explained on the basis of the composition of the two indices. The composition of the S&P 500 and S&P 1500 are captured in the pie charts shown below.

S&P 1500 break up (INDEX A)

S&P 500 break up (INDEX B)From the above breakup it is apparent that there are differences between the composition of both the indices especially with respect to the percentage allocation of financials and healthcare. Hence during the period leading to the recession (January 1, 2007 to September 1, 2008), nearly all the sectors were performing well due to a robust economy due to which a higher degree of correlation has been witnessed between the two indices. However from the beginning of recession from Oct 2008 to Dec 2009, the economic scenario was very harsh due to the global economic crisis (Bacon, 2008). During this era there was a severe liquidity crunch and erosion of asset value, due to which the financial sector was severely hit. Even though, gradually the impact of the recession was also extended to other sectors, however still the worst impacted was the financial sector. Since S&P 500 has a much higher percentage composition of financials in comparison to S&P 1500, (Graham, Dodd & Cottle, 1988) the drop witnessed in the index values were greater for S&P 500. Further even when in the midst of the crisis, when the Federal government announced bailout packages to dole the economy out, there was some relief in the stock markets, however still the financial sector was primarily laggard in terms of recovery. Due to this, the correlation values for the period of recession i.e. January 1, 2009 to January 1, 2010 has a lower degree of correlation between the two indices. However it must be understood that the difference in relatively very small due to a small difference in the composition of the indices. Infact S&P 500 has a percentage weightage of about 88% in the S&P 1500 due to which the movements are relatively small. Also it is evident that since the downfall was global and structural in nature, all the sectors were adversely impacted with albeit small differences (Latane, Tuttle & Jones, 1975).

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