This question is in the honor of Diamond Dyvbig bank run model for which they won the Nobel Prize in Economics this year. Consider a bank which begins at time t=0, operates for 2 periods, and ends at time t =2. At time t=0, the bank begins its operations by collecting $100 in deposits. Assume there are two depositors : you, and your friend Tony Stark. You deposit $75 dollars, while Tony gives $25. Either of you may decide to withdraw the deposits at time t=1, or may continue to keep the deposit with the bank till time t=2. Keep in mind the timelines, which is key to solving the problem. If you decide to withdraw at time t=1, you get a total amount of $1.0 per dollar deposited at time t=0. For example, if you deposited $10 at time t=0, you will get $10 from the bank at time t =1 if you wish to withdraw at this point. However, if you decide to keep the amount in the bank till t=2, you get a total of $1.20 per dollar invested. These rates also dictate your discounting in a risk neutral world. It means that you should discount all period 1 cash flows by 1 and all period 2 cash flows by 1.2. Also, at time t=1, the economy is in one of the two possible states: good and bad. We say the economy is in a bad state if there is a recession. Again, we will use Poisson distribution to model the arrival of a recession shock. Assume the rate of the Poisson recession shock is =0.2. We will use our approximation, and assume that the economy goes into recession, or enters the bad state, with probability 0.20. If the economy enters a recession at time t=1, it remains in recession at time t=2. Similarly, if the economy is in good state at time t=1, it will remain in the good state at time t=2 At time t=0, the bank uses $100 that it raised in deposits from you and your friend to invest in projects. There are two assets available. The first is a safe asset, and let's call it S. The other asset is a risky project, and let's call it R. The two projects have the following cash flows (again be careful here about the timings). i) Safe Project: The safe project gives a cash flow C1S=0.50 at time t=1. At time t =2, the safe project gives a cash flow C2S=0.8 if the economy is good, and C2S=0.40 if the economy is bad. ii) Risky Project: The risky project gives a cash flow C1R at time t=1. Irrespective of the state of the economy, the cash flow C1R=1 with probability 0.50, and C1R=0 with probability 0.50. The risky project also gives a second cash flow C2R at time t=2. If the economy is good, the second period cash flow C2R=2.4 with probability 0.50 and C2R=0 with probability 0.50. If the state of the economy is bad, the second period cash flow is C2R=0 with probability 1 . Important: The cash flows that you get in period 1 and period 2 from the risky project are independent of each other. That means, you can get $0 from the risky project at t =1, but still get $2.4 at date t=2. Another important thing to keep in mind. This is a technicality but important. All the risky projects have correlated risk. That is if one project pays $1 at t=1, all projects pay $1 at t=1. Similarly, if one project pays $2.4 at t=2, all projects pay $2.4 at t=2. The same thing happens for the safe project. The reason why I say this is to make your life easier. Otherwise, if the projects have independent risk, then your life will be a mess and you have to calculate Binomial Probabilities for n=100, or whatever weight you choose. That will immensely complicate your calculations. So, dont bother about calculating these Binomial probabilities. Now, with this setup at hand, let us answer the following questions. Calculate the expected return on the risky asset. Answer in percentages (that is convert the decimal into percentages by multiplying it by 100) Hint: Since the cost of the asset is $1, the rate of return on the safe asset is simply the net present value at t=0. This question is in the honor of Diamond Dyvbig bank run model for which they won the Nobel Prize in Economics this year. Consider a bank which begins at time t=0, operates for 2 periods, and ends at time t =2. At time t=0, the bank begins its operations by collecting $100 in deposits. Assume there are two depositors : you, and your friend Tony Stark. You deposit $75 dollars, while Tony gives $25. Either of you may decide to withdraw the deposits at time t=1, or may continue to keep the deposit with the bank till time t=2. Keep in mind the timelines, which is key to solving the problem. If you decide to withdraw at time t=1, you get a total amount of $1.0 per dollar deposited at time t=0. For example, if you deposited $10 at time t=0, you will get $10 from the bank at time t =1 if you wish to withdraw at this point. However, if you decide to keep the amount in the bank till t=2, you get a total of $1.20 per dollar invested. These rates also dictate your discounting in a risk neutral world. It means that you should discount all period 1 cash flows by 1 and all period 2 cash flows by 1.2. Also, at time t=1, the economy is in one of the two possible states: good and bad. We say the economy is in a bad state if there is a recession. Again, we will use Poisson distribution to model the arrival of a recession shock. Assume the rate of the Poisson recession shock is =0.2. We will use our approximation, and assume that the economy goes into recession, or enters the bad state, with probability 0.20. If the economy enters a recession at time t=1, it remains in recession at time t=2. Similarly, if the economy is in good state at time t=1, it will remain in the good state at time t=2 At time t=0, the bank uses $100 that it raised in deposits from you and your friend to invest in projects. There are two assets available. The first is a safe asset, and let's call it S. The other asset is a risky project, and let's call it R. The two projects have the following cash flows (again be careful here about the timings). i) Safe Project: The safe project gives a cash flow C1S=0.50 at time t=1. At time t =2, the safe project gives a cash flow C2S=0.8 if the economy is good, and C2S=0.40 if the economy is bad. ii) Risky Project: The risky project gives a cash flow C1R at time t=1. Irrespective of the state of the economy, the cash flow C1R=1 with probability 0.50, and C1R=0 with probability 0.50. The risky project also gives a second cash flow C2R at time t=2. If the economy is good, the second period cash flow C2R=2.4 with probability 0.50 and C2R=0 with probability 0.50. If the state of the economy is bad, the second period cash flow is C2R=0 with probability 1 . Important: The cash flows that you get in period 1 and period 2 from the risky project are independent of each other. That means, you can get $0 from the risky project at t =1, but still get $2.4 at date t=2. Another important thing to keep in mind. This is a technicality but important. All the risky projects have correlated risk. That is if one project pays $1 at t=1, all projects pay $1 at t=1. Similarly, if one project pays $2.4 at t=2, all projects pay $2.4 at t=2. The same thing happens for the safe project. The reason why I say this is to make your life easier. Otherwise, if the projects have independent risk, then your life will be a mess and you have to calculate Binomial Probabilities for n=100, or whatever weight you choose. That will immensely complicate your calculations. So, dont bother about calculating these Binomial probabilities. Now, with this setup at hand, let us answer the following questions. Calculate the expected return on the risky asset. Answer in percentages (that is convert the decimal into percentages by multiplying it by 100) Hint: Since the cost of the asset is $1, the rate of return on the safe asset is simply the net present value at t=0