2. Suppose there are three assets: bonds, equities and cash. You currently have

Question

2. Suppose there are three assets: bonds, equities and cash. You currently have $1000 of cash to invest. Suppose $1 spent on a bond has a 50% chance of increasing in value to $1.50 and a 50% of decreasing in value to $0.50. Suppose $1 spent on equities has a 50% chance of increasing in value to $3 and a 50% chance of dropping in value to S0. $1 spent in cash always returns $1. Finally, assume that if the bond value increases, then the equity value must drop. In other words, bonds and equities are negatively correlated. a. Suppose you are risk neutral. What portfolio would you choose? b. Suppose you are unwilling to accept any risk, but would still like to make as much money as possible. What portfolio would you choose? Suppose you utility function for money is c. U(m) = 2NTn MUm(m) Vm For simplicity, suppose you only buy bonds and equities. What portfolio would you choose? (Hint: Suppose you spend Sb on bonds. What are the possible outcomes and their probabilities? Recall that if you spend S1 less on bonds, you can spend $1 more on equities. Now use marginal thinking (and maybe a little calculus)!)

Explanation / Answer

Ans: a) For bond, expected return =(1.5+0.5)/2 = 1,

For equity, expected return = (3+0)/2 = 1.5, and

For cash, expected return = (1+1)/2 = 1.

So, a risk neutral investor will invest $1000 cash in equities because the expected return is maximum in equity and risk neutral investor is indifferent to risk.

b) Though investor is not willing to take any risk, any investment in cash will be a bad option. This is beacuse bond and equity are negatively correlated, so one shuold invest in a portfolio of these assets in order to get some return without taking any risk.

Let the portfolio be w1*bond + w2*equity

Here w1 + w2 = 1, and (bond + equity) = 1000

Here, since equity has most return and also riskiest, so using different combination we find that 33.33% allocation to equity and 66.67% allocation to bond will yield most expected return without any risk.

Here, best scenario is : (333*3+667*0.5) = 1333.5

and worst scenario is : (333*0+667*1.5) = 1000

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