probability distribution

Examples of probability distribution in the following topics:

• Monte Carlo Simulation

  • Each potential factor is assigned a probability or statistical distribution.
  • For example, the investor may estimate the probability of default on a bond as 20%.
  • The investor may also estimate that the inflation rate is normally distributed around a mean of 3% and standard deviation of 0.5%.
  • The investor estimates the probability or distribution of every factor that could change the result of the investment.
  • By running many simulations based on the probability or distribution of an input (x), the analyst can see the average output (y).

• Overview of How to Assess Stand-Alone Risk

  • In probability theory and statistics, the coefficient of variation is a normalized measure of dispersion of a probability distribution.

• Variance

  • In probability theory and statistics, the variance is a measure of how far a set of numbers is spread out.
  • It is one of several descriptors of a probability distribution, describing how far the numbers lie from the mean (expected value).
  • In the figure, we started with three scenarios and a probability (P) and return (R) associated with each.
  • Calculate deviations from mean (blue), square the deviations (yellow), multiply the squared deviation by its original probability (orange).

• Regression Analysis for Forecast Improvement

  • Less commonly, the focus is on a quantile, or other location parameter of the conditional distribution of the dependent variable given the independent variables.
  • In regression analysis, it is also of interest to characterize the variation of the dependent variable around the regression function, which can be described by a probability distribution.

• Risks Involved in Capital Budgeting

  • It might further seek to determine correlations and assign probabilities to the scenarios.
  • Then it will be in a position to consider how to distribute assets between asset types (i.e., asset allocation).

• Setting the Target Payout Ratio

  • It is calculated by dividing the dividends distributed by the net income for the same period.
  • Some investors, such as young people saving for retirement, may prefer higher returns later than smaller cash distributions now.
  • A more established firm with an established market probably does not need to expand its operations, and would prefer to use its earning to compensate its investors.

• Receipts

  • In shorter term situations, most forecasting is done through implementing what is known with the probability that these obligations will be met.
  • By creating a normalized distribution, and identifying the percentage likelihood of a certain outcome, organizations can better prepare for all likely outcomes.

• Financial Management Before and During Bankruptcy

  • The formula may be used to predict the probability that a firm will go into bankruptcy within two years.

• Long-Term Debt

  • The difference in yield reflects the higher probability of default and liquidity and risk premium.
  • If it then distributes these profits to its owners as dividends, then the owners in turn pay taxes on this income, say 20 on the 70 dollars of dividends.

• Approaches to Assessing Risk

  • The assessment of risk is an integral part of risk management in general, and includes probability studies, impact of events, and takes into account the affect of every known risk on the project, and the actions needed to resolve these issues, should they occur.
  • In the more general case, every probable risk can have a pre-formulated plan to deal with its possible consequences.
  • From the average cost per employee over time, or cost accrual ratio, a project manager can estimate: the cost associated with the risk, if it arises, estimated by multiplying employee costs per unit time by the estimated time lost (cost impact, C where C = cost accrual ratio * S), the probable increase in time associated with a risk (schedule variance due to risk, Rs where Rs = Probability * S).
  • This is intended to cause the greatest risks to the project to be attempted first so that risk is minimized as quickly as possible.This can be slightly misleading as schedule variances with a large P (probability) and small S (estimated time lost) and vice versa are not equivalent.
  • The probable increase in cost associated with a risk (cost variance due to risk, Rc where Rc = P*C = P*Cost Accrual Ratio*S = P*S*CAR): sorting on this value puts the highest risks to the budget first, which can raise concerns about schedule variance.