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Chapter 5: Q R5.10. (page 335)

A random walk on Wall Street? The 鈥渞andom walk鈥� theory of stock prices holds that price movements in disjoint time periods are independent of each other. Suppose that we record only whether the price is up or down each year, and that the probability that our portfolio rises in price in any one year is 0.65. (This probability is approximately correct for a portfolio containing equal dollar amounts of all common stocks listed on the New York Stock Exchange.)

(a) What is the probability that our portfolio goes up for three consecutive years?

(b) What is the probability that the portfolio鈥檚 value moves in the same direction (either up or down) for three consecutive years?

Short Answer

Expert verified

Part (a) The probability is 0.275

Part (b) The probability is 0.3175

Step by step solution

01

Part (a) Step 1. Given

P(Riseinoneyear)=0.65

02

Part (a) Step 2. Concept

Theprobabilityofanevent=numberoffavorableoutcomestotalnumberofoutcomes

03

Part (a) Step 3. Calculation 

The probability that your portfolio will increase in value over the next three years is determined as follows: P(Riseinthreeyears)=P(Riseinoneyear)30.275 is the required probability.

04

Part (b) Step 1. Calculation

The likelihood of a portfolio moving in the same direction in three years can be computed as follows:

The likelihood of a one-year fall is computed as follows:

P(Fallinoneyear)=1鈭�P(Riseinoneyear)=1鈭�0.65=0.35

It is clear from the preceding section that P(Riseinthreeyears)=0.275

The chance of a drop in three consecutive years can now be computed as follows:

P(Fallinthreeconsecutiveyears)=0.353=0.043

The probability that is required is: P (Same direction) =0.275+0.043=0.3175

As a result, the chance is 0.3175

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