To calculate the probability of losing money on an asset with normally distributed returns, we can use Excel’s NORM.DIST function. In this scenario, we are given:

• Mean return (μ) = 12.2% (or 0.122 as a decimal)
• Standard deviation (σ) = 27.8% (or 0.278 as a decimal)
• We want to find the probability of the return being less than 0% (which represents a loss).

Here’s how to set it up in Excel:

Step-by-Step Solution

1. Set up the data in Excel:

   • In cell A1, enter "Mean Return".
   • In cell B1, enter 0.122 (for 12.2%).
   • In cell A2, enter "Standard Deviation".
   • In cell B2, enter 0.278 (for 27.8%).
   • In cell A3, enter "Threshold Return (Loss)".
   • In cell B3, enter 0 (since we want to find the probability of a return less than 0%).

2. Use the NORM.DIST function:

   • In cell B4, enter the following formula:

     excelCopy code
     =NORM.DIST(B3, B1, B2, TRUE)

   • This formula calculates the cumulative probability that the return will be less than or equal to 0%.

3. Interpret the result:

   • The value returned in cell B4 will be the probability of losing money (i.e., having a return less than 0%).

Explanation of NORM.DIST Parameters

• x: The value for which we want the cumulative probability (in this case, 0 in cell B3).
• Mean: The mean return (in this case, 0.122 in cell B1).
• Standard_dev: The standard deviation of returns (in this case, 0.278 in cell B2).
• Cumulative: Set to TRUE to calculate the cumulative probability.

Expected Output

After entering the formula, Excel will display a probability (likely less than 0.5), which represents the likelihood that the return in any given year will be below 0%, indicating a loss.

Would you like further assistance with this calculation or any other aspect of probability distribution?

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Here are some related questions you might find interesting:

1. How would the probability change if the mean return was higher?
2. What is the probability of returns exceeding 20%?
3. How does increasing the standard deviation affect the probability of loss?
4. What would be the probability of returns falling within a specific range, like -10% to +10%?
5. How can we calculate the 95% confidence interval for returns based on the given data?

Tip: Using NORM.INV in Excel allows you to find the return level corresponding to a specific probability, useful for understanding potential extreme outcomes.