Questions: Suppose that Apple decides to release a scaled-down, less expensive Iphone to developing economies. The company is unsure if this venture will be successful or not. The success of the project will impact shareholder return. An analyst for PJ Morton has projected the following outcomes: OUTCOME Stock Return Probability Success 15.00 % 0.60 Failure -10.00 % 0.40 What is the standard deviation or risk of this venture? Submit Answer format: Percentage Round to: 2 decimal places (Example: 9.24 %, % sign required. Will accept decimal format rounded to 4 decimal places (ex: 0.0924))

Suppose that Apple decides to release a scaled-down, less expensive Iphone to developing economies. The company is unsure if this venture will be successful or not. The success of the project will impact shareholder return. An analyst for PJ Morton has projected the following outcomes: OUTCOME Stock Return Probability Success 15.00 % 0.60 Failure -10.00 % 0.40 What is the standard deviation or risk of this venture? Submit Answer format: Percentage Round to: 2 decimal places (Example: 9.24 %, % sign required. Will accept decimal format rounded to 4 decimal places (ex: 0.0924))
Transcript text: Suppose that Apple decides to release a scaled-down, less expensive Iphone to developing economies. The company is unsure if this venture will be successful or not. The success of the project will impact shareholder return. An analyst for PJ Morton has projected the following outcomes: \begin{tabular}{|lrr|} \hline OUTCOME & Stock Return & Probability \\ \hline Success & $15.00 \%$ & 0.60 \\ \hline Failure & $-10.00 \%$ & 0.40 \\ \hline \end{tabular} What is the standard deviation or risk of this venture? $\square$ Submit Answer format: Percentage Round to: 2 decimal places (Example: $9.24 \%, \%$ sign required. Will accept decimal format rounded to 4 decimal places (ex: 0.0924))
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Solution

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Solution Steps

Step 1: Calculate the Mean

The mean (expected value) of the stock returns can be calculated using the formula:

\[ \text{Mean} = (0.15 \times 0.6) + (-0.1 \times 0.4) = 0.05 \]

Step 2: Calculate the Variance

The variance \( \sigma^2 \) is calculated using the formula:

\[ \text{Variance} = \sigma^2 = (0.15 - 0.05)^2 \times 0.6 + (-0.1 - 0.05)^2 \times 0.4 \]

Calculating each term:

\[ = (0.10)^2 \times 0.6 + (-0.15)^2 \times 0.4 \] \[ = 0.01 \times 0.6 + 0.0225 \times 0.4 \] \[ = 0.006 + 0.009 = 0.015 \]

Step 3: Calculate the Standard Deviation

The standard deviation \( \sigma \) is the square root of the variance:

\[ \text{Standard Deviation} = \sigma = \sqrt{0.015} \approx 0.1225 \]

Step 4: Convert to Percentage

To express the standard deviation as a percentage:

\[ \text{Standard Deviation (Risk)} = 0.1225 \times 100 = 12.25 \% \]

Final Answer

\(\boxed{12.25 \%}\)

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