Question 1

The standard deviation of the past five monthly returns for K and Company are 2.28 percent, 2.64 percent, −1.05 percent, 4.25 percent, and 9.25 percent. What is the standard deviation?

Accepted Answer

The standard deviation is a measure of the dispersion of a set of data. It is calculated by taking the square root of the variance. The variance is calculated by taking the average of the squared differences between each data point and the mean. In this case, the mean of the five monthly returns is 2.83 percent. The variance is calculated as follows:```Variance = [(2.28 - 2.83)^2 + (2.64 - 2.83)^2 + (-1.05 - 2.83)^2 + (4.25 - 2.83)^2 + (9.25 - 2.83)^2] / 4 = 13.76```The standard deviation is calculated as follows:```Standard deviation = sqrt(13.76) = 3.76 percent```Therefore, the standard deviation of the past five monthly returns for K and Company is 3.76 percent.

Question 2

The past five monthly returns for PG Company are 1.25 percent, −1.50 percent, 4.25 percent, 3.75 percent, and 1.98 percent. What is the average monthly return?

Accepted Answer

To find the average monthly return, add all the monthly returns and divide by the number of months. (1.25 - 1.50 + 4.25 + 3.75 + 1.98) / 5 = 1.946 percent.

Question 3

FedEx Corp. stock ended the previous year at $113.39 per share. It paid a $0.40 per share dividend last year. It ended last year at $126.69. If you owned 300 shares of FedEx, what was your dollar return and percent return?

Accepted Answer

The dollar return is calculated as the change in stock price plus dividends, multiplied by the number of shares: (126.69 - 113.39 + 0.40) * 300 = $4,110. The percent return is the dollar return divided by the initial investment: ($4,110 / (113.39 * 300)) * 100 = 12.08 percent.

Question 4

If you own 400 shares of Air Line Inc. at $44.50, 500 shares of BuyRite at $52.90, and 100 shares of MotorCity at $9.25, what are the portfolio weights of each stock?

Accepted Answer

To calculate the portfolio weights, first find the total value of each stock holding, then divide each by the total portfolio value. Air Line Inc. = 400 * $44.50 = $17,800. BuyRite = 500 * $52.90 = $26,450. MotorCity = 100 * $9.25 = $925. Total portfolio value = $17,800 + $26,450 + $925 = $45,175. Weights: Air Line = $17,800 / $45,175 = 0.3940, BuyRite = $26,450 / $45,175 = 0.5855, MotorCity = $925 / $45,175 = 0.0205.

Question 5

You have $15,040 to invest. You want to purchase shares of Company A at $42.50, Company B at $51.50, and Company F at $9.75. How many shares of each company should you purchase so that your portfolio consists of 20 percent Company A, 40 percent Company B, and 40 percent Company F? Report only whole stock shares.

Accepted Answer

First, calculate the total investment for each company based on the percentages: Company A = 20% of $15,040 = $3,008; Company B = 40% of $15,040 = $6,016; Company F = 40% of $15,040 = $6,016. Then, divide each amount by the share price of the respective company: Company A shares = $3,008 / $42.50 ≈ 70.78 ≈ 70 shares; Company B shares = $6,016 / $51.50 ≈ 116.82 ≈ 116 shares; Company F shares = $6,016 / $9.75 ≈ 616.82 ≈ 617 shares.

Question 6

You have $45,050 to invest. You want to purchase shares of Company A at $10.25, Company B at $15.10, and Company F at $9.05. How many shares of each company should you purchase so that your portfolio consists of 30 percent Company A, 50 percent Company B, and 20 percent Company F? Report only whole stock shares.

Accepted Answer

To allocate the investment according to the specified percentages, calculate the amount to invest in each company: Company A = 30% of $45,050 = $13,515; Company B = 50% of $45,050 = $22,525; Company F = 20% of $45,050 = $9,010. Then, divide each amount by the respective share price to find the number of shares: Company A = $13,515 / $10.25 ≈ 1,318 shares; Company B = $22,525 / $15.10 ≈ 1,491 shares; Company F = $9,010 / $9.05 ≈ 995 shares.

Question 7

The following table shows your stock positions at the beginning of the year, the dividends that each stock paid during the year, and the stock prices at the end of the year. What is your portfolio percentage return?
$$\begin{array} { l r c c r } 
& & \text { Beginning of } & \text { Dividend } & \text { End of } \
\text { Company } & \text { Shares } & \text { Year Price } & \text { per Share } & \text { Year Price } \
\text { W } & 200 & \$ 45.00 & \$ 2.50 & \$ 44.00 \
\text { P } & 200 & \$ 5.00 & \$ 1.00 & \$ 5.25 \
\text { J } & 400 & \$ 20.00 & & \$ 22.00 \
\text { D } & 200 & \$ 27.00 & \$ 1.25 & \$ 27.50
\end{array}$$

Accepted Answer

The answer of The following table shows your stock positions...

Question 8

The standard deviation of the past five monthly returns for PG Company are 2.75 percent, −0.75 percent, 4.15 percent, 6.29 percent, and 3.84 percent. What is the standard deviation?

Accepted Answer

To calculate the standard deviation of these monthly returns, we first find the mean (average) of these returns, then calculate the variance by finding the squared differences from the mean, average those squared differences, and finally take the square root of that average to get the standard deviation.1. Calculate the mean:$$ \text{Mean} = \frac{2.75 + (-0.75) + 4.15 + 6.29 + 3.84}{5} = \frac{16.28}{5} = 3.256\% $$2. Calculate each squared difference from the mean, then the variance:$$ \text{Variance} = \frac{(2.75-3.256)^2 + (-0.75-3.256)^2 + (4.15-3.256)^2 + (6.29-3.256)^2 + (3.84-3.256)^2}{5} $$$$ \text{Variance} = \frac{(0.506)^2 + (-4.006)^2 + (0.894)^2 + (3.034)^2 + (0.584)^2}{5} $$$$ \text{Variance} = \frac{0.256 + 16.048 + 0.799 + 9.205 + 0.341}{5} $$$$ \text{Variance} = \frac{26.649}{5} = 5.3298 $$3. Calculate the standard deviation:$$ \text{Standard Deviation} = \sqrt{5.3298} \approx 2.309\% $$It appears there was a mistake in my calculation. Let's correct the process:1. **Mean (Average) Calculation**:$$ \text{Mean} = \frac{2.75 + (-0.75) + 4.15 + 6.29 + 3.84}{5} = 3.256\% $$2. **Variance Calculation**:$$ \text{Variance} = \frac{(2.75-3.256)^2 + (-0.75-3.256)^2 + (4.15-3.256)^2 + (6.29-3.256)^2 + (3.84-3.256)^2}{4} $$ (Note: The denominator is 4, not 5, because for sample variance, we divide by $n-1$, where $n$ is the number of observations.)$$ \text{Variance} = \frac{(-0.506)^2 + (-4.006)^2 + (0.894)^2 + (3.034)^2 + (0.584)^2}{4} $$$$ \text{Variance} \approx \frac{0.256 + 16.048 + 0.799 + 9.205 + 0.341}{4} $$$$ \text{Variance} \approx \frac{26.649}{4} = 6.66225 $$3. **Standard Deviation Calculation**:$$ \text{Standard Deviation} = \sqrt{6.66225} \approx 2.581\% $$The correct answer is B) 2.581 percent, acknowledging the error in the initial explanation.

Question 9

If you own 1,000 shares of Alaska Corporation at $19.95, 250 shares of Best Company at $17.50, and 250 shares of Motor Company at $2.50, what are the portfolio weights of each stock?

Accepted Answer

The total value of the portfolio is $19,950 (Alaska) + $4,375 (Best) + $625 (Motor) = $24,950. The weights are calculated as the value of each stock divided by the total portfolio value: Alaska = $19,950/$24,950 = 0.7996, Best = $4,375/$24,950 = 0.1754, Motor = $625/$24,950 = 0.0250.

Question 10

Compute the standard deviation of the five monthly returns for PG&E: 1.25 percent, −1.50 percent, 4.25 percent, 3.75 percent, and 1.98 percent.

Accepted Answer

The answer of Compute the standard deviation of the five...

Question 11

Sprint Nextel Corp. stock ended the previous year at $25.00 per share. It paid a $2.57 per share dividend last year. It ended last year at $18.89. If you owned 650 shares of Sprint, what was your dollar return and percent return?

Accepted Answer

The answer of Sprint Nextel Corp. stock ended the previous...

Question 12

At the beginning of the month, you owned $8,000 of Company G, $8,000 of Company S, and $3,000 of Company N. The monthly returns for Company G, Company S, and Company N were 7.80 percent, 1.50 percent, and −0.75 percent. What is your portfolio return?

Accepted Answer

The answer of At the beginning of the month, you...

Question 13

At the beginning of the month, you owned $6,000 of Company G, $8,000 of Company S, and $1,000 of Company N. The monthly returns for Company G, Company S, and Company N were 7.25 percent, −1.50 percent, and −0.23 percent. What is your portfolio return?

Accepted Answer

To calculate the portfolio return, we need to find the weighted average of the returns based on the initial investment amounts. The total initial investment is $15,000 ($6,000 + $8,000 + $1,000). The weights are 0.4 for Company G, 0.5333 for Company S, and 0.0667 for Company N. The portfolio return is (0.4 * 7.25%) + (0.5333 * -1.50%) + (0.0667 * -0.23%) = 2.08%.

Question 14

Rank the following three stocks by their total risk level, highest to lowest. Night Ryder has an average return of 14 percent and standard deviation of 30 percent. The average return and standard deviation of WholeMart are 12 percent and 25 percent; and of Fruit Fly are 25 percent and 40 percent.

Accepted Answer

Total risk in stocks is best represented by their standard deviation, with a higher standard deviation indicating higher risk. Fruit Fly has the highest standard deviation (40%), followed by Night Ryder (30%), and WholeMart has the lowest (25%).

Question 15

Rank the following three stocks by their risk-return relationship, best to worst. Night Ryder has an average return of 33 percent and standard deviation of 40 percent. The average return and standard deviation of WholeMart are 10 percent and 20 percent; and of Fruit Fly are 19 percent and 33 percent.

Accepted Answer

The risk-return relationship is often evaluated by the Sharpe ratio, which is the return in excess of the risk-free rate divided by the standard deviation. Without a risk-free rate provided, we can simplify by comparing returns to standard deviation directly. Night Ryder has the highest return but also the highest risk, making it potentially the best for those willing to accept high risk. Fruit Fly has a moderate return and risk, placing it in the middle. WholeMart has the lowest return but also the lowest risk, making it the least favorable for those seeking high returns for their risk.

Question 16

The following table shows your stock positions at the beginning of the year, the dividends that each stock paid during the year, and the stock prices at the end of the year. What is your portfolio percentage return?
$$\begin{array} { l r c c c } 
& & \text { Beginning of } & \text { Dividend } & \text { End of } \
\text { Company } & \text { Shares } & \text { Year Price } & \text { per Share } & \text { Year Price } \
\text { W } & 500 & \$ 5.00 & \$ 0.50 & \$ 4.00 \
\text { P } & 100 & \$ 15.00 & \$ 1.00 & \$ 15.25 \
\text { J } & 200 & \$ 25.00 & & \$ 22.00 \
D & 200 & \$ 30.00 & \$ 2.00 & \$ 33.50
\end{array}$$

Accepted Answer

The answer of The following table shows your stock positions...

Question 17

If you own 100 shares of Air Line Inc. at $42.50, 250 shares of BuyRite at $53.25, and 350 shares of MotorCity at $7.75, what are the portfolio weights of each stock?

Accepted Answer

To calculate the portfolio weights, first find the total value of each investment and then divide by the total portfolio value. Air Line Inc. = 100 shares * $42.50 = $4,250. BuyRite = 250 shares * $53.25 = $13,312.50. MotorCity = 350 shares * $7.75 = $2,712.50. Total portfolio value = $4,250 + $13,312.50 + $2,712.50 = $20,275. Portfolio weights: Air Line = $4,250 / $20,275 = 0.2096, BuyRite = $13,312.50 / $20,275 = 0.6566, MotorCity = $2,712.50 / $20,275 = 0.1338.

Question 18

The following table shows your stock positions at the beginning of the year, the dividends that each stock paid during the year, and the stock prices at the end of the year. What is your portfolio percentage return?
$$\begin{array} { l r c c c } 
\text { Company } & \text { Shares } & \begin{array} { c } 
\text { Beginning of } \
\text { Year Price }
\end{array} & \begin{array} { c } 
\text { Dividend } \
\text { per Share }
\end{array} & \begin{array} { c } 
\text { End of } \
\text { Year Price }
\end{array} \
\mathrm { W } & 100 & \$ 25.00 & \$ 1.00 & \$ 24.00 \
\mathrm { P } & 200 & \$ 14.00 & \$ 0.75 & \$ 15.25 \
\mathrm {~J} & 400 & \$ 8.00 & & \$ 10.00 \
\mathrm { D } & 200 & \$ 3.00 & \$ 0.50 & \$ 3.50
\end{array}$$

Accepted Answer

To calculate the portfolio percentage return, we need to calculate the total initial value, the total dividends received, and the total final value of the stocks. Then, we use the formula for percentage return, which is $(\text{Final Value} + \text{Dividends} - \text{Initial Value}) / \text{Initial Value} \times 100$.1. Initial Value:- W: $100 \times \$25.00 = \$2500$- P: $200 \times \$14.00 = \$2800$- J: $400 \times \$8.00 = \$3200$- D: $200 \times \$3.00 = \$600$- Total Initial Value = \$2500 + \$2800 + \$3200 + \$600 = \$91002. Dividends:- W: $100 \times \$1.00 = \$100$- P: $200 \times \$0.75 = \$150$- J: $400 \times \$0.00 = \$0$ (No dividend mentioned)- D: $200 \times \$0.50 = \$100$- Total Dividends = \$100 + \$150 + \$0 + \$100 = \$3503. Final Value:- W: $100 \times \$24.00 = \$2400$- P: $200 \times \$15.25 = \$3050$- J: $400 \times \$10.00 = \$4000$- D: $200 \times \$3.50 = \$700$- Total Final Value = \$2400 + \$3050 + \$4000 + \$700 = \$101504. Percentage Return:$\frac{\$10150 + \$350 - \$9100}{\$9100} \times 100 = \frac{\$1400}{\$9100} \times 100 \approx 15.38\%$Therefore, the portfolio percentage return is approximately 15.38 percent.

Question 19

If you own 600 shares of Alaska Corporation at $23.25, 450 shares of Best Company at $34.50, and 150 shares of Motor Company at $6.95, what are the portfolio weights of each stock?

Accepted Answer

The answer of If you own 600 shares of Alaska...

Question 20

Rank the following three stocks by their risk-return relationship, best to worst. Rail Haul has an average return of 10 percent and standard deviation of 19 percent. The average return and standard deviation of Idol Staff are 12 percent and 22 percent; and of Poker-R-Us are 11 percent and 25 percent.

Accepted Answer

The risk-return relationship is evaluated by comparing the return per unit of risk (standard deviation). Idol Staff has the highest return per unit of risk, followed by Rail Haul, and then Poker-R-Us.

Quiz 9: Characterizing Risk and Return