Suppose you are considering investing in two opportunities, a Dow Jones Fund and a Weak-Economy Fund. The following information is available on the return from investing $1000 in each fund. Probability Economic Scenario DJ Fund Return W-E Fund Return 0.2 Recession -51 243 0.5 Stable 249 168 0.3 Expanding 649 -82 a. Calculate the mean and standard deviation of returns for each fund. Which do you prefer and why? b. Compute the return in each scenario for a portfolio which has 70% invested in the DJ Fund and 30% in the W-E Fund. c. For the portfolio which has 70% invested in the DJ Fund and 30% in the W-E Fund, find the mean and standard deviation of portfolio returns. Do you prefer the portfolio? d.How would you decide on the percentages to invest in the DJ and W-E funds?
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
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Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
Suppose you are considering investing in two opportunities, a Dow Jones Fund and a Weak-Economy Fund. The following information is available on the return from investing $1000 in each fund.
|
Probability |
Economic Scenario |
DJ Fund Return |
W-E Fund Return |
|
0.2 |
Recession |
-51 |
243 |
|
0.5 |
Stable |
249 |
168 |
|
0.3 |
Expanding |
649 |
-82 |
a. Calculate the mean and standard deviation of returns for each fund. Which do you prefer and why?
b. Compute the return in each scenario for a portfolio which has 70% invested in the DJ Fund and 30% in the W-E Fund.
c. For the portfolio which has 70% invested in the DJ Fund and 30% in the W-E Fund, find the mean and standard deviation of portfolio returns. Do you prefer the portfolio?
d.How would you decide on the percentages to invest in the DJ and W-E funds?
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