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1. Returns and Risk

Estimate and compare the returns and variability (i.e. annual standard deviation over the past five years) of Reynolds and Hasbro with that of the S&P 500 Index. Which stock appears to be riskiest?

S&P:

Monthly average return=0.57%

Annual return= 6.89%

Annual SD= 12.477% (monthly SD 3.60* 3.46 (square of 12))

Reynolds:

Monthly average return= 1.87%

Annual return= 1.87% * 12= 22.50%

Annual SD: 32.446% (monthly SD 9.37* 3.46 (square of 12))

Hasbro:

Monthly average return= 1.18%

Annual return= 1.18% * 14.21%

Annual SD= 28.114% (monthly SD 8.12* 3.46 (square of 12))

Conclusion: Correlation between high risk and high return. Reynolds is the riskier stock with an annual SD of 32.41% over 5 years, compared to Hasbro’s 28.08%. Reynolds annual return over the 5 year period of 22.50% is also higher than Hasbro’s return of 14.21%.

2. Portfolio Risk

Suppose Sharpe’s position had been 99 percent of equity funds invested in the

S&P 500 and either one percent in Reynolds over one percent in Hasbro. Estimate the resulting portfolio position. How does each stock affect the variability of the equity investment? How does this relate to your answer in question 1 above?

ER of .99 S&P + .01 Reynolds

Annual: 7.0481%

SD of Reynolds in Portfolio

Monthly: 3.5933%

Annual: 12.4476%

ER of .99 S&P + .01 Hasbro

Annual: 6.9651%

SD Hasbro in Portfolio

Monthly: 3.6174%

Annual: 12.5310%

Results: Although Reynolds was shown to be an overall riskier stock in question 1, its lower standard deviation illustrates that it is less correlated than Hasbro to the S&P 500, thereby decreasing the variability of the portfolio, which makes it less risky in comparison to Hasbro.

3. Regression Analysis to Calculate Beta

Perform a regression of each stocks’ monthly returns on the Index returns to compute a “beta”

...FINA 5210: Investment Analysis (Prof. Abhiroop Mukherjee) Alex Sharpe’s Portfolio Discussion Guidelines 1. Download the raw data file from the LMES website under folder Cases Alex Sharpe’s Portfolio. Estimate and compare the average returns and variability of Reynolds and Hasbro. Which stock appears to be the riskiest by itself? Computing the average returns and standard deviations of Reynolds and Hasbro gives us the results shown in the table below. If the stocks are judged just by themselves, Reynolds has a higher standard deviation than Hasbro (9.37>8.12), hence it is more risky. Question: Can we also consider the sharpe-ratio? This would show some kind of risk adjusted-return! | REYNOLDS | HASBRO | Mean | 1.87% | 1.18% | Stdev | 9.37% | 8.12% | 2. Suppose Sharpe’s position had been 99% of equity funds invested in the Vanguard 500 Index and either 1% in Reynolds or 1% in Hasbro. Estimate the average return and volatility of the resulting portfolio. How does each stock affect the variability of the equity investment? How does this compare to your answer in question 1? For both portfolio a and b, the average return increases compared to holding 100% of V500. The average return on portfolio a is higher than that of portfolio b (0.587>0.580). For portfolio a, the volatility of the portfolio decreases, whereas the volatility of Portfolio b increases. It is interesting to note that although Reynolds has a much higher standard deviation...

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...Executive Summary Our team concludes that risk and return are strongly correlated. A higher risk usually yields a higher return. Our team observed that within Alex Sharpe’s portfolio, the Reynolds’ fund holds the highest risk (highest standard deviation of 32.45%), as well as the highest return (16.27% in comparison to Hasbro’s return of 11.31%). Although a lower standard deviation (lower risk) is ideal for an investment portfolio, the Reynolds’ fund yields a higher return for the higher associated risk. Furthermore, our team’s data illustrated that the mix of S&P with Reynolds has a higher return and lower standard deviation than the S&P alone. In addition, if Sharpe invests in Reynolds and Hasbro equally, at for instance, one percent, the average return for Reynolds is significantly higher (at 7.08%) than the average return for Hasbro (at 6.97%). Computing the Sharpe ratio for each of the portfolios, the one with 1% Reynolds is the highest at. Given this analysis, our team feels that Alex Sharpe should consider investing more in the Reynolds fund than in Hasbro fund. Stock Analysis 1. Returns and Risk Estimate and compare the returns and variability (i.e., annual standard deviation over the past five years) of Reynolds and Hasbro with that of the S&P 500 Index. Which stock appears to be riskiest? | S&P500 | Reynolds | Hasbro | Arithmetic Return | 6.89% | 22.50% | 14.21% | Std Dev | 12.48% | 32.45% | 28.11% | Reynolds has the highest risk...

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...within Alex Sharpe’s portfolio, the Reynolds’ fund holds the highest risk (highest standard deviation of 32.45%), as well as the highest return (16.27% in comparison to Hasbro’s return of 11.31%). Although a lower standard deviation (lower risk) is ideal for an investment portfolio, the Reynolds’ fund yields a higher return for the higher associated risk. Furthermore, our team’s data illustrated that the mix of S&P with Reynolds has a higher return and lower standard deviation than the S&P alone. In addition, if Sharpe invests in Reynolds and Hasbro equally, at for instance, one percent, the average return for Reynolds is significantly higher (at 7.08%) than the average return for Hasbro (at 6.97%). Computing the Sharpe ratio for each of the portfolios, the one with 1% Reynolds is the highest at. Given this analysis, our team feels that Alex Sharpe should consider investing more in the Reynolds fund than in Hasbro fund. Stock Analysis 1. Returns and Risk Estimate and compare the returns and variability (i.e., annual standard deviation over the past five years) of Reynolds and Hasbro with that of the S&P 500 Index. Which stock appears to be riskiest? | S&P500 | Reynolds | Hasbro | Arithmetic Return | 6.89% | 22.50% | 14.21% | Std Dev | 12.48% | 32.45% | 28.11% | Reynolds has the highest risk (measured by Std Dev) and highest return. The standard deviation for Reynolds is 32.45% over 5 years. The arithmetic return is 22.5% over the same period. 2. Portfolio Risk ...

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...SOLUTIONS TO EXERCISES AND CASES For FINANCIAL STATEMENT ANALYSIS AND SECURITY VALUATION Stephen H. Penman Fifth Edition CHAPTER ONE Introduction to Investing and Valuation Exercises Drill Exercises E1.1. Calculating Enterprise Value This exercise tests the understanding of the basic value relation: Enterprise Value = Value of Debt + Value of Equity Enterprise Value = $600 + $1,200 million = $1,800 million (Enterprise value is also referred to as the value of the firm, and sometimes as the value of the operations.) E1.2. Calculating Value Per Share Rearranging the value relations, Equity Value = Enterprise Value – Value of Debt Equity Value = $2,700 - $900 million = $1,800 Value per share on 900 million shares = $1,800/900 = $2.00 E1.3 Buy or Sell? Value = $850 + $675 = $1,525 million Value per share = $1,525/25 = $61 Market price = $45 Therefore, BUY! Applications E1.4. Finding Information on the Internet: Dell Inc., General Motors, and Ford This is an exercise in discovery. The links on the book’s web site will help with the search. E1.5. Enterprise Market Value: General Mills and Hewlett-Packard a) General Mills | | | |Market value of the equity = $36.50 ( 644.8 million shares = ...

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...Alex Sharpe’s Portfolio 1. Returns and Risk Estimate and compare the returns and variability (i.e. annual standard deviation over the past five years) of Reynolds and Hasbro with that of the S&P 500 Index. Which stock appears to be riskiest? S&P 500 Annualized Expected Return: 6.8920% S&P 500 SD (Annualized): 12.477% Reynolds Annualized Expected Return: 22.4980% Reynolds SD (Annualized): 32.446% Hasbro Annualized Expected Return: 14.2060% Hasbro SD (Annualized): 28.114% Reynolds appears to be the riskiest stock since it has the highest standard deviation. The fact that Reynolds also has the highest annualized expected return supports this calculation since risk and return should be directly correlated. 2. Portfolio Risk Suppose Sharpe’s position had been 99 percent of equity funds invested in the S&P 500 and either one per cent in Reynolds over one percent in Hasbro. Estimate the resulting portfolio position. How does each stock affect the variability of the equity investment? How does this relate to your answer in question 1 above? Portfolio Return of S&P 500 and Reynolds (annualized): 7.0481% Portfolio Return of S&P 500 and Hasbro (annualized): 6.9651% Standard Deviation of S&P 500: 12.477% Standard Deviation of S&P 500 and Reynolds: 12.3638% Standard Deviation of S&P 500 and Hasbro: 12.3699% Although Reynolds was a riskier stock overall than Hasbro (as determined in question 1), due to the fact that Reynolds is less correlated to S&P...

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...Context: Alex Sharpe currently invests her children’s educational savings in Vanguard 500 Index Fund, which tracks the performance of S&P 500 and is passively managed. However, she is now considering switching her investment strategy to a more active one to achieve better outcomes. Hasbro, a toy manufacturer, and Reynolds, a tobacco firm, have come into Sharpe’s sight and she wants to choose one of them and invest a small proportion of equity funds in it. In order to select a more appropriate investment target, the following issues should be taken into consideration by Sharpe: 1) What are the risk-return characteristics of each stock 2) What are the impacts of either stock to the overall risk-return profiles of the equity portfolio Analysis: 1. Suppose Sharpe's position had been 99 percent of equity funds invested in the S&P500 and either one percent in Reynolds or one percent in Hasbro. Estimate the resulting portfolio position. How does each stock affect the variability of the equity investment? Which stock appears to be the riskiest? Let A (and B) be the portfolio with 99% of S&P 500 and 1% of Reynolds (and 1% Hasbro). | S&P 500 | Reynolds | Hasbro | Portfolio A | Portfolio B | Mean Return | 0.5743% | 1.8748% | 1.1838% | 0.5873% | 0.5804% | Std Dev | 3.6017% | 9.3665% | 8.1158% | 3.5933% | 3.6174% | According to our calculation, Portfolio A is a better choice with higher expected return (0.5873%) and lower standard deviation (3.5933%)...

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...Case Study Assignment: Alex Sharpe's Portfolio 1. Estimate and compare the returns and variability (i.e. annual standard deviation over the past five years) of Reynolds and Hasbro with that of the S&P 500 Index. Which stock appears to be riskiest? | S&P 500 | REYNOLDS | HASBRO | Annualized Expected Return | 6.892% | 22.498% | 14.206% | Annualized Standard Deviation | 12.477% | 32.446% | 28.114% | Reynolds seems riskier than Hasbro due to its higher percentage of standard deviation. 2. Suppose Sharpe’s position had been 99% of equity funds invested in the S&P 500 and either 1% in Reynolds or one per cent in Hasbro. Estimate the resulting portfolio position. How does each stock affect the variability of the equity investment? How does this relate to your answer in question 1 above? * - Scenario 1: = SP500 (99%) * Reynolds (1%) * = (.99) x (.689) + (.01) x (.2249) * = 0.06823 + 0.00224 = 0.07047 * = 7.05% * Standard Deviation = 12.3638% * * * - Scenario 2: = HASBRO (1%) SP500 (99%) = (.01) x (.1421) + (.99) (.689) ...

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