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. 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