Chapter 5, Problem 10CRE

a.

To determine

To find: The probability portfolio will go up for three years.

Answer to Problem 10CRE

The probability is 0.275.

Explanation of Solution

Given:

  $P\left(\text{Rise in one year}\right)=0.65$

Calculation:

The probability portfolio will go up for three yearsdeer is calculated as:

  $\begin{array}{c}P\left(\text{Rise in three years}\right)=P{\left(\text{Rise in one year}\right)}^3\\ ={\left(0.65\right)}^3\\ =0.275\end{array}$

The required probability is 0.275.

b.

To determine

To find: The probability that portfolio would move in same direction in three years.

Answer to Problem 10CRE

The probability is 0.3175.

Explanation of Solution

Calculation:

The probability that portfolio would move in same direction in three years can be calculated as:

The probability of fall in one year is calculated as:

  $\begin{array}{c}P\left(\text{Fall in one year}\right)=1-P\left(\text{Rise in one year}\right)\\ =1-0.65\\ =0.35\end{array}$

From above part, it is known that $P\left(\text{Rise in three years}\right)=0.275$

Now, the probability of fall in three consecutive three years can be calculated as:

  $\begin{array}{c}P\left(\text{Fall in three consecutive years}\right)={0.35}^3\\ =0.043\end{array}$

The required probability is:

  $\begin{array}{c}P\left(\text{Same direction}\right)=0.275+0.043\\ =0.3175\end{array}$

Thus, the probability is 0.3175.