Q:
XYZ Company stocks have an expected return of 12% and a standard deviation of 8%. Assuming that the returns of this company are a continuous random variable that is normally distributed, what is the probability that the returns will be -1.2% or less?
A) 45%
B) 1.65%
C) 10%
D) 5%
A:

The correct answer is: D)
First, transform the actual value of this outcome (-1.2%) into its standardized z-score:
Zx= [(X - ux) ÷ σx] = [(-1.2 - 12.0) ÷ 8] = -1.65
Using the Normal Rule, candidates should realize that approximately 90% of the outcomes are expected to occur within 1.65 standard deviations of the mean. This would mean that 45% (half of 90%) of the observations must lie within the mean and -1.65 standard deviations away from the mean. If this is so, then 5% of all the observations must lie below -1.65 standard deviations away from the mean.


RELATED FAQS

  1. What is the difference between standard deviation and z score?

    Understand the basics of standard deviation and Z-score; learn how each is calculated and used in the assessment of market ...
  2. What does standard deviation measure in a portfolio?

    Dig deeper into the investment uses of, and mathematical principles behind, standard deviation as a measurement of portfolio ...
  3. How is standard deviation used to determine risk?

    Understand the basics of calculation and interpretation of standard deviation and how it is used to measure risk in the investment ...
  4. What is standard deviation used for in mutual funds?

    See how standard deviation is helpful in evaluating a mutual fund's performance. Use it in combination with other measurements ...
  5. What is the difference between standard deviation and average deviation?

    Understand the basics of standard deviation and average deviation, including how each is calculated and why standard deviation ...
  6. How is risk aversion measured in Modern Portfolio Theory (MPT)?

    Find out how risk aversion is measured in modern portfolio theory (MPT), how it is reflected in the market and how MPT treats ...
RELATED TERMS
  1. Standard Deviation

    1. A measure of the dispersion of a set of data from its mean. ...
  2. Empirical Rule

    A statistical rule stating that for a normal distribution, almost ...
  3. Residual Standard Deviation

    A statistical term used to describe the standard deviation of ...
  4. Z-Score

    A Z-Score is a statistical measurement of a score's relationship ...
  5. Standard Error

    The standard deviation of the sampling distribution of a statistic. ...
  6. Downside Deviation

    A measure of downside risk that focuses on returns that fall ...

You May Also Like

Hot Definitions
  1. Law Of Demand

    A microeconomic law that states that, all other factors being equal, as the price of a good or service increases, consumer ...
  2. Cost Of Debt

    The effective rate that a company pays on its current debt. This can be measured in either before- or after-tax returns; ...
  3. Yield Curve

    A line that plots the interest rates, at a set point in time, of bonds having equal credit quality, but differing maturity ...
  4. Stop-Limit Order

    An order placed with a broker that combines the features of stop order with those of a limit order. A stop-limit order will ...
  5. Keynesian Economics

    An economic theory of total spending in the economy and its effects on output and inflation. Keynesian economics was developed ...
  6. Society for Worldwide Interbank Financial Telecommunications ...

    A member-owned cooperative that provides safe and secure financial transactions for its members. Established in 1973, the ...
Trading Center