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Chapter 3: Problem 55

Bloomberg Personal Finance (July/\mathrm{ August } 2 0 0 1 ) \text { included the following companies in its } recommended investment portfolio. For a portfolio value of \(\$ 25,000,\) the recommended dollar amounts allocated to each stock are shown. $$\begin{array}{lccc} \text { Company } & \begin{array}{c} \text { Portfolio } \\ \text { (\$) } \end{array} & \begin{array}{c} \text { Estimated Growth Rate } \\ \text { (\%) } \end{array} & \begin{array}{c} \text { Dividend Yield } \\ \text { (\%) } \end{array} \\ \text { Citigroup } & 3000 & 15 & 1.21 \\ \text { General Electric } & 5500 & 14 & 1.48 \\ \text { Kimberly-Clark } & 4200 & 12 & 1.72 \\ \text { Oracle } & 3000 & 0.00 & 0.96 \\ \text { Pharmacia } & 3000 & 20 & 2.48 \\ \text { SBC Communications } & 3800 & 12 & 0.00 \\ \text { WorldCom } & 2500 & 35 & 0.00 \\ \hline\end{array}$$ a. Using the portfolio dollar amounts as the weights, what is the weighted average estimated growth rate for the portfolio? b. What is the weighted average dividend yield for the portfolio?

Short Answer

Expert verified
a. 14.62% weighted growth rate. b. 1.1726% weighted dividend yield.

Step by step solution

01

Calculate Total Portfolio Value

First, sum the dollar amounts allocated to each company in the portfolio to verify the total value. This is given as \(25,000, but let's re-calculate to ensure accuracy.\[3000 + 5500 + 4200 + 3000 + 3000 + 3800 + 2500 = 25000\]The total portfolio value is indeed \)25,000.
02

Determine Weights for Companies

Compute the weight of each company in the portfolio. The weight is the proportion of each company's allocation in the total portfolio.For Citigroup: \[\frac{3000}{25000} = 0.12\]Similarly, calculate the weights for each of the remaining companies.
03

Calculate Weighted Growth Rates

Multiply each company's estimated growth rate by its weight, then sum these products to get the weighted average growth rate for the portfolio.\(Weighted\ growth\ rate = (0.12 \times 15) + (0.22 \times 14) + (0.168 \times 12) + (0.12 \times 0) + (0.12 \times 20) + (0.152 \times 12) + (0.1 \times 35)\)Perform the calculations for each term and sum them.
04

Compute Weighted Growth Rate

Finish the weighted growth rate calculation:\[= 1.8 + 3.08 + 2.016 + 0 + 2.4 + 1.824 + 3.5 = 14.62\]The weighted average estimated growth rate for the portfolio is 14.62%.
05

Calculate Weighted Dividend Yields

Now, multiply each company's dividend yield by its weight, then sum these products to find the weighted average dividend yield for the portfolio.\(Weighted\ dividend\ yield = (0.12 \times 1.21) + (0.22 \times 1.48) + (0.168 \times 1.72) + (0.12 \times 0.96) + (0.12 \times 2.48) + (0.152 \times 0) + (0.1 \times 0)\)Perform the calculations for each term and sum them.
06

Compute Weighted Dividend Yield

Complete the dividend yield calculation:\[= 0.1452 + 0.3256 + 0.28896 + 0.1152 + 0.2976 + 0 + 0 = 1.17256\]The weighted average dividend yield for the portfolio is 1.1726%.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Weighted Average
When analyzing an investment portfolio, one of the key concepts to understand is the weighted average. This is particularly important when you're dealing with multiple investments, each contributing differently to the overall performance of the portfolio. In simple terms, a weighted average accounts for the proportional significance of each component in a set, rather than considering them as equal contributors. This is crucial when determining the average outcome of various metrics, such as growth rates or dividend yields, across all investments. For example, if Citigroup is assigned a higher amount in the portfolio compared to Oracle, then more weight is given to Citigroup's performance when calculating the average.

How to Calculate a Weighted Average

To compute a weighted average:
  • First, identify the weight of each component. This is typically the share of the total value that each investment represents.
  • Then, multiply the weight by the value or performance metric of each component.
  • Finally, sum these results to find the weighted average.
This method ensures that larger investments proportionally affect the average more than smaller ones, thereby providing a more accurate picture of the portfolio's performance.
Investment Portfolio
An investment portfolio is a collection of financial assets such as stocks, bonds, commodities, and other securities held by an investor or managed by financial professionals. The primary goal of any investment portfolio is to balance risk and return according to an investor's financial objectives.

Diversification

Diversification is a key strategy in portfolio management. By investing in a variety of assets, investors can mitigate risks. This means if one investment performs poorly, others might perform better, thereby stabilizing the overall portfolio performance. In the given exercise, the portfolio includes companies from different sectors such as finance, technology, and telecommunications, which illustrates how diversification is employed to spread risk.

Allocation

Allocation is about deciding how much money to place in each investment. This decision involves various factors, like risk tolerance, investment goals, and market conditions. In the example provided, the allocation shows preferences towards certain companies, represented by the dollar amount invested, aligning with expected growth and risk assessment.
Dividend Yield Calculation
Dividend yield is a financial ratio that shows how much a company pays out in dividends each year relative to its stock price. It is an important measure for investors who are interested in earning income from their investments, in addition to any price appreciation. In this specific analysis, dividend yield calculations are made for each stock in the portfolio to assess their contribution to overall income.

Computing Dividend Yield

To compute the dividend yield:
  • Take the annual dividend payment per share.
  • Divide it by the stock's current price.
  • Multiply the result by 100 to get a percentage.
This ratio helps investors understand how much they earn in dividends for each dollar invested in the stock.

Weighted Dividend Yield

As with the weighted average growth rate, the weighted dividend yield considers the proportional weight of each investment's dividend yield in the portfolio. This way, investments with higher weights significantly impact the overall yield, offering a comprehensive view of the income-generating potential of an entire portfolio.

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Most popular questions from this chapter

The following data were used to construct the histograms of the number of days required to fill orders for Dawson Supply, Inc., and J.C. Clark Distributors (see Figure 3.2). \(\begin{array}{lcccccccccc}\text {Dawson Supply Days for Delivery:} & 11 & 10 & 9 & 10 & 11 & 11 & 10 & 11 & 10 & 10 \\ \text {Clark Distributors Days for Delivery:} & 8 & 10 & 13 & 7 & 10 & 11 & 10 & 7 & 15 & 12\end{array}\) Use the range and standard deviation to support the previous observation that Dawson Supply provides the more consistent and reliable delivery times.

Consider the sample data in the following frequency distribution. $$\begin{array}{ccc} \text { Class } & \text { Midpoint } & \text { Frequency } \\ 3-7 & 5 & 4 \\ 8-12 & 10 & 7 \\ 13-17 & 15 & 9 \\ 18-22 & 20 & 5 \end{array}$$ a. Compute the sample mean. b. Compute the sample variance and sample standard deviation.

Consider a sample with data values of \(10,20,12,17,\) and \(16 .\) Compute the variance and standard deviation.

The cost of consumer purchases such as housing, gasoline, Internet services, tax preparation, and hospitalization were provided in The Wall Street Journal, January 2, 2007. Sample data typical of the cost of tax-return preparation by services such as H\&R Block are shown here. \\[\begin{array}{lllll}120 & 230 & 110 & 115 & 160 \\ 130 & 150 & 105 & 195 & 155 \\ 105 & 360 & 120 & 120 & 140 \\\100 & 115 & 180 & 235 & 255\end{array}\\] a. Compute the mean, median, and mode. b. Compute the first and third quartiles. c. Compute and interpret the 90 th percentile.

Dividend yield is the annual dividend per share a company pays divided by the current market price per share expressed as a percentage. A sample of 10 large companies provided the following dividend yield data (The Wall Street Journal, January 16,2004 ). $$\begin{array}{lclc} \text { Company } & \text { Yield \% } & \text { Company } & \text { Yield \% } \\ \text { Altria Group } & 5.0 & \text { General Motors } & 3.7 \\ \text { American Express } & 0.8 & \text { JPMorgan Chase } & 3.5 \\ \text { Caterpillar } & 1.8 & \text { McDonald's } & 1.6 \\ \text { Eastman Kodak } & 1.9 & \text { United Technology } & 1.5 \\ \text { ExxonMobil } & 2.5 & \text { Wal-Mart Stores } & 0.7\end{array}$$ a. What are the mean and median dividend yields? b. What are the variance and standard deviation? c. Which company provides the highest dividend yield? d. What is the \(z\) -score for McDonald's? Interpret this z-score. e. What is the \(z\) -score for General Motors? Interpret this z-score. f. Based on z-scores, do the data contain any outliers?
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