Read the following information regarding Alex Sharpe’s investment strategy and answer the following Questions

On Friday, January 26, 2020, Alex Sharpe sat in her home office and pondered her investment strategy. During her MBA program, Sharpe had learned that in an efficient market, investors should buy and hold the ‘market portfolio’ because no other portfolio can offer the same expected return at a lower risk. Since the Standard & Poor’s (S&P) 500 was the most commonly used benchmark for the overall U.S. stock market, Sharpe had invested her children’s educational savings in the Vanguard 500 Index Fund, a no-load mutual fund constructed to track the performance of the S&P 500.

The S&P 500 index consists of 500 stocks chosen for market size, liquidity and industry grouping, among other factors. This index is meant to reflect the risk/return characteristics of large-cap stocks. The S&P 500 is a market value-weighted index, i.e., each stock’s weight in the index is proportionate to its market value. There were a number of financial products available to investors that are based on the S&P 500, including Vanguard’s. Investors chose these index funds in order to provide themselves with a broad market exposure without buying 500 different.

Indexing represents a form of passive fund management that offers a low management expense ratio and has historically outperformed most actively managed mutual funds. Vanguard is one of the world’s largest equity and fixed income managers, and had been credited with the popularization of index funds and with the driving down of costs across the mutual fund industry. Vanguard is unique in that it is owned by the funds themselves, which better aligns management’s interests with those of their shareholders. In contrast, other mutual funds have to balance the goals of providing a profit for their outside owners with that of providing the most cost-effective funds for their shareholders.

In order to achieve higher returns, Sharpe had been considering changing her passive investment strategy to one that was more active. She wanted to begin conservatively by adding carefully chosen stocks to her current equity portfolio. Based on recent analyst forecasts, Ms. Sharpe had narrowed her search to the following two companies:

Hasbro (NYSE: HAS) was an American toy and game company that was the second-largest toy maker in the world, next to Mattel. Industry sources expected Hasbro to introduce several innovative toys linked to summer 2007 blockbusters, such as Spider Man 3 and The Fantastic Four: Rise of the Silver Surfer. Additionally, Hasbro’s full-length, live-action movie based on the company’s enormously popular TRANSFORMERS and produced by Tom DeSanto (X-Men and X2: X-Men United) were scheduled to open in summer 2007.

R.J. Reynolds Tobacco Company (RJR) was the second-largest tobacco firm in the world, with a share of approximately 30 per cent of the U.S. cigarette market. R.J. Reynolds was a wholly owned subsidiary of Reynolds American Inc. (NYSE: RAI). The company faced some unique challenges; for example, most consumer-product companies did not have to spend millions of dollars annually on advertising aimed at discouraging use of their product for consumers under the age of 18. R.J. Reynolds had been subject to significant litigation for many decades, but the company had a strong track record in defending tobacco- related cases in court and assured its shareholders that it would continue to take appropriate steps to maintain a successful litigation record.

RISK AND RETURN

The last five years’ worth of monthly returns for the Vanguard 500 Index Fund, Hasbro and R.J. Reynolds are provided in Exhibit 1. In addition to comparing the returns on the individual components of her portfolio, Sharpe also wanted to fully compare the risk profiles of the two companies to that of the Vanguard Fund. She wanted to ensure that the expected return of her new portfolio would provide adequate compensation for taking on any new risky assets.

Exhibit 1 INVESTMENT RETURN DATA

Date

S&P 500

REYNOLDS

HASBRO

Jan-02

-1.70%

6.13%

1.66%

Feb-02

-2.31%

9.87%

-13.27%

Mar-02

4.37%

-1.37%

10.55%

Apr-02

-5.06%

6.87%

1.01%

May-02

-1.19%

2.17%

-4.26%

Jun-02

-7.15%

-23.97%

-11.37%

Jul-02

-8.23%

1.64%

-9.66%

Aug-02

0.64%

7.71%

7.35%

Sep-02

-10.14%

-31.48%

-15.36%

Oct-02

7.35%

0.57%

-8.18%

Nov-02

5.96%

-4.81%

25.44%

Dec-02

-5.50%

9.09%

-9.91%

Jan-03

-2.46%

0.59%

3.90%

Feb-03

-1.72%

-5.78%

0.92%

Mar-03

0.89%

-19.17%

14.70%

Apr-03

8.12%

-12.68%

15.19%

May-03

6.18%

21.02%

0.06%

Jun-03

1.48%

9.15%

9.24%

Jul-03

2.18%

-4.54%

7.78%

Aug-03

2.34%

-3.86%

-1.86%

Sep-03

-1.06%

15.78%

0.97%

Oct-03

5.89%

21.47%

16.70%

Nov-03

1.51%

14.93%

1.42%

Dec-03

4.39%

5.34%

-3.75%

Jan-04

2.20%

1.56%

-7.19%

Feb-04

1.40%

4.52%

10.73%

Mar-04

-1.20%

-1.99%

-0.55%

Apr-04

-2.56%

7.06%

-13.15%

May-04

1.24%

-13.23%

4.08%

Jun-04

2.00%

20.27%

-3.36%

Jul-04

-3.88%

6.45%

-4.37%

Aug-04

0.11%

4.93%

1.98%

Sep-04

1.91%

-9.88%

1.46%

Oct-04

1.66%

1.21%

-5.90%

Nov-04

4.43%

9.83%

7.57%

Dec-04

3.34%

3.93%

1.84%

Jan-05

-2.74%

2.32%

1.14%

Feb-05

2.09%

1.90%

7.76%

Mar-05

-1.86%

-1.66%

-3.17%

Apr-05

-2.66%

-3.25%

-7.48%

May-05

3.59%

6.34%

6.66%

Jun-05

0.99%

-4.96%

3.02%

Jul-05

4.22%

5.72%

5.53%

Aug-05

-0.78%

0.76%

-5.65%

Sep-05

0.93%

-1.10%

-5.07%

Oct-05

-2.19%

2.38%

-4.12%

Nov-05

3.82%

4.73%

8.39%

Dec-05

0.19%

7.09%

-1.18%

Jan-06

3.90%

6.08%

5.05%

Feb-06

-0.36%

4.96%

-4.29%

Mar-06

1.76%

-0.61%

3.99%

Apr-06

1.15%

3.93%

-6.59%

May-06

-3.30%

0.26%

-5.94%

Jun-06

-0.19%

4.88%

-2.32%

Jul-06

-0.28%

9.96%

3.26%

Aug-06

2.30%

2.65%

8.56%

Sep-06

1.81%

-4.76%

12.07%

Oct-06

3.60%

1.92%

13.93%

Nov-06

2.13%

1.71%

3.20%

Dec-06

0.91%

1.91%

1.87%

Required:

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?

2. Suppose Sharpe’s position had been 99 per cent of equity funds invested in the S&P 500 and either one per cent 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?

3. Perform a regression of each stock’s monthly returns on the Index returns to compute a “beta” for each stock. How does this relate to your answer in question 2 above?

4. How might the expected return of each stock relate to its riskiness?

5. In what stock(s) (if any) should Sharpe invest?