Statistics for financial marketsCalculating the price of an annual bond is a fundamental skill for a finance professional.The mean daily return of a stock is 0%, and its daily standard deviation of the returns of a stock is 4%. How likely is it that the stock falls be more than 4% or more in a single day if the returns are normally distributed?15.9%34.1%64.0%5.0%
Question
Statistics for financial marketsCalculating the price of an annual bond is a fundamental skill for a finance professional.The mean daily return of a stock is 0%, and its daily standard deviation of the returns of a stock is 4%. How likely is it that the stock falls be more than 4% or more in a single day if the returns are normally distributed?15.9%34.1%64.0%5.0%
Solution
To calculate the likelihood of the stock falling by more than 4% in a single day, we can use the concept of standard deviations and the normal distribution.
Given that the mean daily return of the stock is 0% and the daily standard deviation of the returns is 4%, we can assume that the returns follow a normal distribution.
In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
Since we are interested in the likelihood of the stock falling by more than 4%, we need to calculate the probability of the returns falling beyond one standard deviation below the mean.
Using the empirical rule, we know that approximately 34.1% of the data falls beyond one standard deviation below the mean in a normal distribution.
Therefore, the likelihood of the stock falling by more than 4% in a single day is approximately 34.1%.
Similar Questions
A stock has had returns of 14%, 27%, 18%, and 5% for the past four years. Calculate the standard deviation of the returns.Group of answer choices9.1%8.2%8.8%6.4%
n a normal distribution, what percentage of data falls within one standard deviation of the mean? 25% 50% 68% 95.5%
tatistics for financial marketsStandard deviations are always expressed annually in the financial markets so being able to convert to annual standard deviations is critical.The daily standard deviation of the returns of a stock is 2%. What the annualized standard deviation?32.2%52.0%7.3%38.2%
In a normal distribution, how much of the data falls within one standard deviation?99.7%95%100%68%
In 2003, the average stock price for companies making up the S&P 500 was $30, and thestandard deviation was $8.20 (BusinessWeek, Special Annual Issue, Spring 2003). Assumethe stock prices are normally distributed.a. What is the probability that a company will have a stock price of at least $40?b. What is the probability that a company will have a stock price no higher than $20?c. How high does a stock price have to be to put a company in the top 10%?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.