Consider an economy over three periods At t 0, the stock market index is priced at 100 At t 1, the index either rises by 30 or falls by 10 with equal probabilities Following a rise at t 1, the index either rises by 30 with probability 0 25, or falls by 10 with probability 0 75 at t 2 Following a fall at t 1, the index either rises by 30 with probability 0 75, or falls by 10 with probability 0 25 Thus, the highest possible index value at t 2 is 160, and the lowest possible index value at t 2 is 80 The stock index pays no dividends, and the risk free rate in each period is Rf 0 Draw the event tree for the stock index in this economy Include the price of the stock index for each node and the probability for each branch For both nodes at t 1, compute the net simple return between periods 0 and 1 What is the expected return of the index between t 0 and t 1 For each node at t 2, compute the probability of reaching that node, and the net simple return between periods 0 and 2 What is the expected return and the variance of the return between t 0 and t 2 Suppose you form a portfolio of the risky stock index and the risk free asset at t 0 and hold it until t 2 with no rebalancing If you are a mean variance optimiser with risk aversion coefficient A 5, how should you invest Hint Recall that a mean variance optimiser seeks to maximise Now, suppose you follow a market timing strategy At t 0, invest 100 in the stock index At t 1, if the market has gone up, sell all your holdings and invest everything in the risk free asset If the market is down at t 1, then continue to hold 100 in the stock index If you started with 100 at t 0, what is the net simple return between periods 0 and 2 for each possible outcome at t 2 f What is the expected return and the variance of the return for the strategy in part (e) As a risk averse mean variance optimising investor, would you prefer the buy and hold strategy of part (d) or the market timing strategy of part (e)

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Consider an economy over three periods. At t = 0, the stock market index is priced at 100. At t = 1, the index either

Consider an economy over three periods. At t = 0, the stock market index is priced at 100. At t = 1, the index either rises by 30 or falls by 10 with equal probabilities. Following a rise at t = 1, the index either rises by 30 with probability 0.25, or falls by 10 with probability 0.75 at t = 2. Following a fall at t = 1, the index either rises by 30 with probability 0.75, or falls by 10 with probability 0.25. Thus, the highest possible index value at t = 2 is 160, and the lowest possible index value at t = 2 is 80. The stock index pays no dividends, and the risk-free rate in each period is Rf = 0.

Draw the event tree for the stock index in this economy. Include the price of the stock index for each node and the probability for each branch.

For both nodes at t = 1, compute the net simple return between periods 0 and 1. What is the expected return of the index between t = 0 and t = 1?

For each node at t = 2, compute the probability of reaching that node, and the net simple return between periods 0 and 2. What is the expected return and the variance of the return between t = 0 and t = 2?

Suppose you form a portfolio of the risky stock index and the risk-free asset at t = 0 and hold it until t = 2 with no rebalancing. If you are a mean-variance optimiser with risk aversion coefficient A = 5, how should you invest? [Hint: Recall that a mean-variance optimiser seeks to maximise .]

Now, suppose you follow a “market timing” strategy. At t = 0, invest 100% in the stock index. At t = 1, if the market has gone up, sell all your holdings and invest everything in the risk-free asset. If the market is down at t = 1, then continue to hold 100% in the stock index. If you started with £100 at t = 0, what is the net simple return between periods 0 and 2 for each possible outcome at t = 2?

f. What is the expected return and the variance of the return for the strategy in part (e)? As a risk-averse mean-variance optimising investor, would you prefer the buy and hold strategy of part (d) or the market timing strategy of part (e)?

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Answer Draw the event tree for the stock index in this economy Include the price of the stock index for each node and the probability for each branch The event tree for this economy is shown in the di... blur-text-image