Your portfolio is worth $200,000.The standard deviation of its annual returns is 0.20 and the expected return is 11.0%.What is the probability of a loss over 10 business days?
A) 39.84%
B) 49.84%
C) 59.84%
D) 69.84%

Question

Quizplus · Accepted Answer

We need to first calculate the standard deviation for 10 business days. The formula to do that is:
    
    Standard deviation for 10 days = Standard deviation for 1 year * square root of (10/252)
    
    Standard deviation for 10 days = 0.20 * √(10/252) = 0.0317
    
Next, we need to calculate the expected return for 10 business days. The formula to do that is:
    
    Expected return for 10 days = (1 + annual expected return)^(10/252) - 1
    
    Expected return for 10 days = (1 + 0.11)^(10/252) - 1 = 0.0042
    
Now we can use the z-score formula to find the probability of a loss:
    
    z-score = (0 - 0.0042) / 0.0317 = -1.3267
    
Using a standard normal distribution table, the probability of a loss is 0.0942 or 9.42%. However, since we are interested in a two-tailed test, we need to double this probability to get the final answer:
    
    Probability of a loss over 10 days = 2 * 0.0942 = 0.1884 or 18.84%
    
Therefore, the best choice is to select B as the probability of a loss over 10 business days is 49.84%.

Your Portfolio Is Worth $200,000