Transcribed image text: Exercise 1. Financial market climates and predicting the likelihood of future market conditions depend on the following trends: Bull markets: periods of time where prices generally are rising, due to the actors having optimistic hopes of the future. Bear markets: periods of time where prices generally are declining, due to the actors having a pres- simistic view of the future. Stagnant markets: periods of time where the market is characterized by neither a decline nor rise in general prices. Consider a hypothetical market with Markov properties where historical data has given as the following patterns: After a week characterized of a bull market trend there is a 90% chance that another bullish week will follow. Additionally, there is a 7.5% chance that the bull week instead will be followed by a bearish one, or a 2.5% chance that it will be a stagnant one. After a bearish week there's an 80% chance that the upcoming week also will be bearish, there is 2.5% of a bullish week, and a 17.5% chance of a stagnant week. You should create your own transition probabilities for going from a stagnant week to a bullish, bearish, or stagnant week, and construct a transition matrix M that shows all possible states of the market. Given the state of the current week, calculate the possibilities of a bull, bear or stagnant week for any number of 4 weeks into the future. Conclude what the probabilities will be after n weeks. Hint: Create a 1 x 3 vector which contains information about which of the three different states any current week is in. Transcribed image text: Exercise 1. Financial market climates and predicting the likelihood of future market conditions depend on the following trends: Bull markets: periods of time where prices generally are rising, due to the actors having optimistic hopes of the future. Bear markets: periods of time where prices generally are declining, due to the actors having a pres- simistic view of the future. Stagnant markets: periods of time where the market is characterized by neither a decline nor rise in general prices. Consider a hypothetical market with Markov properties where historical data has given as the following patterns: After a week characterized of a bull market trend there is a 90% chance that another bullish week will follow. Additionally, there is a 7.5% chance that the bull week instead will be followed by a bearish one, or a 2.5% chance that it will be a stagnant one. After a bearish week there's an 80% chance that the upcoming week also will be bearish, there is 2.5% of a bullish week, and a 17.5% chance of a stagnant week. You should create your own transition probabilities for going from a stagnant week to a bullish, bearish, or stagnant week, and construct a transition matrix M that shows all possible states of the market. Given the state of the current week, calculate the possibilities of a bull, bear or stagnant week for any number of 4 weeks into the future. Conclude what the probabilities will be after n weeks. Hint: Create a 1 x 3 vector which contains information about which of the three different states any current week is in