L3 Capital Allocation

Question 1

What did Markowitz’s contribution to the field of finance help us understand?

Answer 1

Thanks to William Markowitz we can rewrite the question to: how much of your wealth you should invest across risk-free and optimal portfolio of risky assets in order to control the risk of your portfolio.

we know that the optimal portfolio of risky assets is the same for all investors (with any level of risk aversion) T

his makes the risky portfolio choice independent of investors attitude towards risk

Question 2

Portfolio Mean and variance?

Answer 2

Question 3

What is the return of the COMPLETE PORTFOLIO which is a combination of a risky and risk free asset?

Answer 3

Question 4

How do you calculate the volatility and risk of the complete portfolio?

Answer 4

Question 5

What is the formula for the Capital Allocation Line?

Answer 5

Question 6

What does the CAL look like on a graph?

Answer 6

• isnt CML the CAL line that goes through the optimal efficient portfolio –> using the broad market index
• if σ_c = σ_p then E(r_c) = E(r_p) –> figure this out from the CAL
  
  • when w = 0, σ_c = 0
  • w = 1 when σ_c = σ_p –> looking at the weight ratio
• above w = 1 we are borrowing at the risk-free rate
• below is the combinations of holdings between a risk-free asset and the risky asset
  
  • implies that you are lending e.g. w = 0.5 implies that 50% is invested in the risk free asset amounts to lending

Question 7

What is the Sharpe Ratio?

Answer 7

• The objective function that wants to be maximised to help you decide the balance between risk and reward

Question 8

What happens if we have a different lending and borrowing rate with concern to the CAL?

Answer 8

• rB is greater than rf (lending rate)
  
  • if it was a straight line we would see a higher risk free ratio but the line would be flatter due to the (rp-rb) term at the end

Question 9

What is the Utility Function for risk aversion?

Answer 9

• Will maxmise their utlity based of a equation of expected return,risk and their risk tolerance
• If the asset is risk free, U is scaled to equal the risk-free rate.
• If the investor is risk neutral, A = 0 and U depends only on expected return.
• If A < 0 the investor is risk lover
• For a risky portfolio, U is a certainty equivalent: a risk-free return that gives the same utility as the risky investment.

Question 10

What do indifference curves look like in a mean-variance space?

Answer 10

• when they are but on a risk-return diagram the utility line curve like normal

Question 11

Different indifference curve with different risk aversion?

Answer 11

Question 12

What is the Capital Allocation optimisation problem for a complete portfolio?

Answer 12

• basically the tangent point between the Utility function and the CAL
• `substitute the CAL in to the Utility function and replace for the variance of the complete portfolio to find the maximisation problem