# Formula 8.11 noted that the minimum-variance portfolio without a risk-free asset invests about 76.2%

Formula 8.11 noted that the minimum-variance portfolio without a risk-free asset invests about 76.2% in H and about 24.8% in I. (Work with the rounded numbers to make your life easier.) With the risk-free asset offering 4%, what portfolio would you purchase that has the same risk, and what would its improvement in reward be? First think about how to solve this. However, this is a difficult question, so we will go through it step by step. (a) Copy down the risk of this minimum-variance portfolio when there is no risk-free asset. (b) What is the reward of this minimum-variance portfolio? (c)

»Formula 8.11 noted that the minimum-variance portfolio without a risk-free asset invests about 76.2% in H and about 24.8% in I. (Work with the rounded numbers to make your life easier.) With the risk-free asset offering 4%, what portfolio would you purchase that has the same risk, and what would its improvement in reward be? First think about how to solve this. However, this is a difficult question, so we will go through it step by step. (a) Copy down the risk of this minimum-variance portfolio when there is no risk-free asset. (b) What is the reward of this minimum-variance portfolio? (c) With a risk-free rate of 4%, it turns out that the tangency portfolio invests 30% in H and 70% in I. What are its returns in each of the four scenarios? (d) What is its reward? (Check this visually in the graph!) (e) What is its risk? (Check this visually in the graph!) (f) Using the analog of Formula 8.14, what investment weight w T in T would give you the same risk as the minimum-variance portfolio? (If you had \$100, how much would you put into T, and how much would you put into a risk-free savings account?) (g) Given this weight wT, what is the reward of this combination portfolio? How much better is this than the situation where no risk-free asset was available?

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