Stock Market Investor: Probability of Retirement as a Winner

  • Thread starter Lisawmi
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In summary, the problem involves a stock market investor who must sell her stock if it goes down to 10 or up to 40. The change in price is either up or down by 1 point with probabilities of .55 and .45 respectively, and the changes are independent. To calculate the probability of the investor retiring as a winner, a binomial tree model can be used by considering the number of successes (stock up) and failures (stock down). By working out the problem with 1 success or failure and then with 2 successes or failures, the probability for n=15 can be easily determined. There are only 3 possible outcomes, but one can be ignored due to its low probability.
  • #1
Lisawmi
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I am struggling with this problem, and overall have found probability to be a very difficult subject. I was hoping someone could explain to me how to work this problem.

A stock market investor owns shares in a stock whose present value is 25. She has decided that she must sell her stock if it either goes down to 10 or up to 40. If each change of price is either up 1 point with probability .55 or down 1 point with probability .45, and the successive changes are independent, what is the probability the investor retired a winner?

Thanks
 
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  • #2
A few hints:

1. Binomial tree model.

2. You want either a net number (n) of 15 successes(= stock up) or 15 failures (=stock down).

3. Work it out instead with 1 success or failure (should be easy), then with 2 successes or 2 failures, or n=2. Once you figure out n=2, n=15 should be pretty easy.

4. For n>=2, there are only 3 possible types of outcomes:
a. Retired winner in the stock market
b. Retired loser in the stock market
c. An infinite loop where the number of successes is equal to the number of failures.

I think we can ignore case (c) because the weighted probability of such an event is small.
 
  • #3
for reaching out and expressing your struggles with probability. It can definitely be a difficult subject, but with practice and understanding of the concepts, it can become more manageable. Let's break down the problem and see if we can find a solution together.

First, let's define what it means for the investor to retire as a winner. In this scenario, the investor will be considered a winner if she sells her stock at a price of 40 or higher. This means that any price below 40 would result in the investor not retiring as a winner.

Next, we need to consider the different outcomes that can occur with the stock price. There are two possible outcomes: the stock price can either go up by 1 point or down by 1 point. We also know the probabilities associated with each outcome: a .55 probability for the stock price to go up and a .45 probability for it to go down.

Now, let's think about the different paths the stock price can take to reach a value of 40 or higher. The stock price can either go up by 15 points (from 25 to 40) or go up by 10 points and then down by 5 points (from 25 to 35 and then back up to 40). In both of these paths, the investor would retire as a winner.

To calculate the probability of each path, we need to multiply the probabilities of each individual outcome. For the first path, the probability would be (.55)^15, or approximately 0.0000000000000001. For the second path, the probability would be (.55)^10 * (.45)^5, or approximately 0.00000000000005.

Now, we add these two probabilities together to get the total probability of the investor retiring as a winner. This gives us a final probability of approximately 0.000000000000050000000000001, or 0.000000000005%.

In conclusion, the probability of the stock market investor retiring as a winner is extremely low, at approximately 0.000000000005%. This highlights the importance of carefully considering and managing risk when investing in the stock market. I hope this explanation helped in understanding how to approach this type of problem. Remember, practice makes perfect when it comes to probability!
 

1. What is a stock market investor?

A stock market investor is someone who buys and sells stocks, which are shares of ownership in a publicly traded company, in order to make a profit. They typically research and analyze the performance of different companies and their stocks before making investment decisions.

2. How do stock market investors make money?

Stock market investors make money through buying stocks at a lower price and selling them at a higher price, known as capital appreciation. They may also receive dividends, which are a portion of a company's profits distributed to shareholders, as another source of income.

3. What are the risks involved in stock market investing?

Stock market investing carries a certain level of risk, as the value of stocks can go up or down depending on market conditions and company performance. There is also the risk of losing the entire investment if the company goes bankrupt. It is important for investors to diversify their portfolio and research the companies they are investing in to manage these risks.

4. How do I start investing in the stock market?

To start investing in the stock market, you will need to open a brokerage account with a reputable investment firm. You can then research and select stocks to purchase, or invest in a mutual fund or index fund that holds a variety of stocks. It is important to have a clear investment strategy and to regularly monitor and adjust your portfolio.

5. How can I minimize my taxes as a stock market investor?

One way to minimize taxes as a stock market investor is to hold stocks for at least a year before selling them, as this can qualify for a lower tax rate known as the long-term capital gains tax rate. Investors can also consider investing in tax-advantaged accounts, such as a 401(k) or IRA, to save on taxes. Consulting with a financial advisor can also help in developing a tax-efficient investment strategy.

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