ࡱ> M g9bjbj== .`WWg5lt:=??????$ Xcc<x<<<=<=<<} #kbt0,66<Dmitriy Barskiy Anatoly Shkolnikov Sylwia Koc 10 out of 10; excellent The risk of Staples Inc. stock  INCLUDEPICTURE "https://chart.bigcharts.com/custom/etrade-com/chart.asp?symb=SPLS&time=13&freq=3&type=64&compidx=aaaaa:0&uf=2048&ma=2&maval=200&lf=268435456&style=216&size=1" \* MERGEFORMATINET  Represented above is a plot of Staples Inc. monthly stock prices for the last ten years and the earnings trends. The stock does not pay out dividends. The stock prices and earnings have been on the strong upward trend during the period until 1999, when they began decline with the market. SPLS ReturnsDJI ReturnsMean0.00083Mean0.000504Standard Error0.001433Standard Error0.000435Median-0.00161Median0.000579Mode0Mode#N/AStandard Deviation0.039452Standard Deviation0.011971Sample Variance0.001556Sample Variance0.000143Kurtosis1.533502Kurtosis2.441366Skewness0.227068Skewness-0.26988Range0.325086Range0.113471Minimum-0.17815Minimum-0.06366Maximum0.146939Maximum0.049806Sum0.628835Sum0.382075Count758Count758 The standard deviation of daily returns for the period 12/29/97 to 12/29/00 is 3.9%, a significantly larger number then the standard deviation of daily returns on Dow Jones Industrial index, which stands at only 1.2% (Excel Sheet 1). This indicates that the returns of Staples are much more volatile than the returns on the DJI. We would expect the difference also to be significant for NYSE Composite and the Willshire 5000. In order to analyze the risk and return for Staples. Inc stock, we ran the regression analysis in Excel and constructed the regression plots using Telerate. However, the results between the two methods do not always match since Telerate may not be using simple regression formulas for Beta Errors may have introduced into Telerate results since the graph shows that the regression was based on significantly lower number of days or significantly higher number of months than specified in the formula. Therefore, we will use the coefficient values calculated in Excel for the purposes of the discussion, while using the Telerate regression plots for visual analysis. Regression diagnostics: a) Slope of the regression. The slope of the regression of Staples daily return on three indices is the stocks Beta a measure of the riskiness of the stock relative to the market. Staples Beta (on 29 Dec 1997 29 Dec 2000 daily DJI) = 1.28 Staples Beta (on 29 Dec 1997 29 Dec 2000 daily NYA) = 1.62 Staples Beta (on 29 Dec 1997 29 Dec 2000 daily TMW) = 1.32 The betas based on the tree indices differ significantly. However, they all agree that the returns on Staples stock fluctuate more than the market in response to market moves, therefore presenting more risk. The Dow Jones is composed of 30 blue chip companies, while NYSE Composite consists of about 3000 companies and Wilshire 5000 consists of 5000 companies. However, there is no predictable pattern depending on the size of the index, as the mid-sized index in this case took the highest Beta value. However, it is possible to conclude that the Beta based on Wilshire 5000 index represents the Beta better than other indices because the true Beta must be calculated using regression on all possible assets, and 5000 is the highest number available in this case. Therefore, we can conclude that the Beta of Staples is about 1.32. b) The intercept of the regression The intercept of the regression enables us to compare the companys actual performance with its expected performance Rf (1 B) during the specified period. The intercept of the regression of Staples on Wilshire 5000 is 0.000219, which is the actual average daily performance on Staples stock. The expected performance, with a 0.01667% daily Rf rate (average of T-bills) in the period from 1997 to 2000, is Rf (1 B) = 0.01667 (1 1.32) = 0.01667 (-0.32) = -0.0053344 Staples performed 0.000219 (-0.0053344) = 0.0055534% better than expected on a daily basis from 1997 to 2000. Annualized Excess Return = (1 + 0.0055534)365 1 = 6.55% The better-than expected return in the past does not guarantee similar performance in the future. Furthermore, it is not possible to conclude from the above analysis whether the excess returns can be attributed to the performance of the entire sector, or to the firm-specific actions other firms in the industry would have to be analyzed for this comparison. Having this knowledge would have enabled us to calculate Jensens alpha by subtracting annualized excess industry returns from the firms annualized excess returns. What you have computed is already Jensens alpha. However, you are right in that you could have conducted attribution analysis, and broken up the excess return into its different components. The intercepts obtained from regressing Staples on Dow Jones Industrial and NYSE Composite closely agree with the above results: the intercepts are 0.000183 and 0.000157 respectively. c) R squared of the regression R squared of the regression (Wilshire 5000) = 0.183388. This statistic suggests that 18.34% of the variance (risk) in Staples returns can be attributed to market variance, while 80.64% of variance can be attributed to firm-specific components of risk. The firm-specific risk for Staples is higher than similar risk of an average company listed on NYSE (which was approximately 25% in 1998). Since, according to CAPM, firm-specific risk is not rewarded, Staples may be a good investment for a very well diversified individual. R squared of the daily regressions for Dow Jones Industrial and NYSE Composite are 0.151514 and 0.199343 correspondingly. d) Standard Error of Beta Estimation The standard error of beta estimation for Wilshire 5000 is 0.035675, implying that the true beta could range from 1.280353 to 1.351703 with 67% confidence (1 error away) 1.244678 to 1.387378 with 95% confidence (2 errors away) These wide estimates suggest that the measurements of Beta are very imprecise and should be considered inaccurate in any decision-making process. Youre too conservative! Your estimates are pretty precise considering the nature of the exercise you are engaged in! Comparison of regressions using monthly returns: E-trade quotes the Beta of Staples as 1.02. Interestingly, the regression of Staples monthly returns (from 12/98 to 01/00) on Wilshire 5000 exactly matches the value stated by E-trade. This demonstrates three important principles of Beta: 1) Beta should be estimated using regression against a well-diversified portfolio, such as Wilshire, which has 5000 stocks in it. 2) More recent period range provides more accurate Beta estimate because firms are dynamic, and as they change, their Bata changes as well. Therefore, the most accurate Beta estimates can be obtained from the most recent sets of data rather than historical averages that give equal weight to the long-gone past. However, using the recent data may come at a cost: there may simply be not enough recent data, which increases the standard error of beta calculation. 3) Choosing longer intervals (such as months vs. days) can decrease noise created by many short-period outlier observations as a result of significant firm-specific events that occur during the period. Noise can also be created by stocks that are not trading, which biases Beta toward 1. However, the cost of using longer intervals is significantly fewer recent observations that could be used in a regression. Based on these principles, we can compare regression results for daily returns (Dec 97 Dec 00) with monthly returns (Jan 98 Dec 00). &DJIDaily Beta is 1.28 while the monthly Beta is only 0.44. The large discrepancy exists because the Dow Jones Industrial index has only 30 stocks (not very well diversified) and is not weighed fairly, which means that it does not provide a reliable estimate for Beta. As we would expect in this case, since the index does not represent the market accurately, R squared for the monthly returns is extremely low only 3.37% of variance in Staples returns is explained by monthly returns on Dow Jones Industrial. Other indices monthly returns explain the Staples variance much better, with Wilshire having the highest R squared, as expected. However, because of many observations, the R squared for daily returns is high compared to the monthly returns it stands at 15.15%. However, it is still lower than the other R sq. calculated for other indices using daily returns. The graphs show that the daily results suffer more from noise created by many readings and outliers.NYADaily Beta is 1.68 while the monthly Beta is 0.73. This index better represents the market than DJI, but the discrepancy is wide because the standard error is very high at 0.12 and 0.44 respectively. As expected, the R sq. is higher than for DJI at 0.20 for daily and 0.08 for monthly returns.TMWDaily Beta is 1.31 while the monthly Beta is 1.02. At this point, we can see a pattern: daily Betas are significantly higher than the monthly Betas. This can be explained by a fact that during a short period, such as day, the stock can undergo big price swings in response to market moves, while in the long term (such as month), it stabilizes and the Beta value decreases. The standard error is also high at 0.10 for daily and 0.35 for monthly. The R sq. takes the highest values for TMW because this index is the best measure of the market.  Furthermore, we can compare regression results for monthly returns for the period Jan 95 Dec 97 with monthly returns for Jan 98 Dec 00 period. &DJIJan 95 Dec 97 Beta is 1.02 while Jan 98 Dec 00 Beta is 0.44. The standard errors in both cases are very high at 0.46 and 0.40 correspondingly. The high standard errors result from having very few observations in both cases and the Betas for two periods do not match closely because as the firm changes overtime (management, projects, etc.), its Beta changes overtime. NYAJan 95 Dec 97 Beta is 1.81 while Jan 98 Dec 00 Beta is 0.73. The standard errors are again very high because of lack of a large number of readings.TMWJan 95 Dec 97 Beta is 1.86 while Jan 98 Dec 00 Beta is 1.02. A pattern can be established: R sq. for the most recent period is much lower in every case than R sq for the prior period. This can be explained by a fact that 1) The prior period is longer and provides more data. 2) The staples stock was performing very well in the period Jan 95 Dec 97 as the economy was booming too, however, the problems that occurred in the market in 1998 and 2000 caused the stocks performance to start deviating significantly from the general market performance. We can also notice, that as we moved to the most diversified index and to the most recent time period, the calculated Beta most closely approached the real Beta (=1.02 calculated by E-trade). Dont be so quick to define the e-Trade beta as the real beta, simply because it is the most recent one! Maybe the nature of Staples changed over the time period. Did you look at the nature of their assets? What about their marketing strategy? These could have affected the beta. SPLS v. Dow Jones Industrial (Source: CNBC)  INCLUDEPICTURE "http://www.marketwatch.com/charts/big.chart?nosettings=1&sid=6001&symb=&style=1013&size=2&comp=+AAAAA~0&compidx=DJIA~1643&time=5yr&freq=1wk&bcind_comp=AAAAA~0&rand=3169" \* MERGEFORMATINET  The above diagram is a visual representation of the movements in the price of Staples stock compared to the market moves, presented by DJIA, for the past five years. According to this diagram, we would expect Staples to have Beta higher than one, as it responds strongly to the market trends. However, the correlation between the two is not very high according to the diagram. One of the reasons could be that DJIA consists of only 30 stocks and is not a very good representation of the overall market. This presentation also displays the value of diversification, presenting it as a way to escape high volatility and sharp price changes of an individual stock. SPLS v. Special Retailers Industry (Source: CNBC)  INCLUDEPICTURE "http://www.marketwatch.com/charts/big.chart?nosettings=1&sid=6001&symb=&style=1013&size=2&comp=+OTS~171577&compidx=AAAAA~0&time=5yr&freq=1wk&bcind_comp=OTS~171577&rand=5541" \* MERGEFORMATINET  The above diagram represents the comparative price movements between Staples and the Special Retailers Industry. As a member of the industry, the general price movements of the stock follow the industry price movements, as expected (high correlation). However, we would expect the Beta to be higher than one as we see that the response of Staples stock often is a larger proportion than 1:1. Beta, as a measure of risk, represents an extremely inaccurate and often subjective value, as questions arise what benchmark to use to analyze the assets returns against. Furthermore, the choice of the intervals and the period of time that should be analyzed are also extremely subjective parameters. For example, recent news on Nov 20th that Staples appointed Jevin S. Eagle as Senior VP of Strategy (Source: Business Wire) might increase the Beta of the company, as Mr. Eagle is known for taking risky new projects in an attempt to increase profits. Therefore, it would be more appropriate to use more recent data to assess the risk. 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