L4 - Capital Allocation

Question 1

What is the equation for the utility function?

Answer 1

• If A > 0 you are risk-averse. The bigger A is the more risk-averse you are
• If A = 0 you are risk-neutral; you only care about the expected return
• If A < 0 you are risk-seeking

In modern portfolio theory, investors are assumed to be risk-averse (A>0)

Question 2

What is the Dominance principle?

Answer 2

• portfolios with higher return for the same risk, or lower risk for the same returns dominate
  
  • Northwest is the preferred direction for utility curves on a risk-return trade off profile (return on y, risk on x)

Question 3

Risk and the gradient of the indifference curve?

Answer 3

• risk averse –> steeply upwards sloping
• risk-seeking –> less steep but still upwards sloping

Question 4

How do you calculate a portfolios returns?

Answer 4

Question 5

How do you calculate portfolio variance?

Answer 5

• variance is based on how risky each asset is (first part) and how the assets comove with each other (second part)

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Question 6

How can we simplify the variance equation when using risk-free assets?

Answer 6

• risk free assets have no risk, and they do not move (returns are constant)
• this makes the first and last time equal to zero

Question 7

What is the equation for the Capital Allocation Line (CAL)?

Answer 7

Question 8

What does the CAL line look like?

Answer 8

• simply a line that connects the risky portfolio and the risk free asset

Question 9

How do you calculate the Sharpe Ratio?

Answer 9

Question 10

What are the different weights you can have on a portfolio?

Answer 10

• usually y is between 0 and 1 (a share of your portfolio is made up of risky assets)
• if y > 1: you are borrowing to invest in the risky asset
• If y < 0: you are shorting the risky asset

Question 11

How does the CAL change if the borrowing and lending rates are different?

Answer 11

• Usually they are the same
  
  • If the borrowing rate is higher margin trading because less desirable
  • Thus it leads to a flattening of the CAL after the point of y = 1 (limits the upsides due to the higher rate)

Question 12

What is the Mathematical intuition on why the CAL flattens when the borrowing rate is greater than the lending rate?

Answer 12

Question 13

How can you calculate the optimal Asset allocation of a portfolio?

Answer 13

Sub in for E(r_c) and σ_C = y x σ_P

Question 14

What can we learn from the optimal asset allocation equation?

Answer 14

• If the expected return on the risky portfolio is high, investors invest more in it
• if the risk of the risky portfolio increases, investors move away from it
• if the risk-free rate is high, investors invest less in the risky portfolio
• The more risk-averse the investor, the less they invest in the risky portfolio