L4 - Optimal Diversification I

Question 1

What are the two types of risk?

Answer 1

• Market risk
  
  • Marketwide risk sources
  • Remains even after diversification
  • Also called: Systematic or Nondiversifiable
• Firm-specific risk
  
  • Risk that can be eliminated by diversification I
  • Also Called: Diversifiable or Nonsystematic

Question 2

How do you calculate the risk and return between two risky investments when they are independent?

Answer 2

• In this case he is only worried about minimising risk more than maximising return without regard to it (risk averse investor)
• to increase expected return you would invest more in the more risky asset and thus take on more risk in the investmenet

Question 3

How do you calculate the risk and return between two risky investments when they are perfectly positively correlated?

Answer 3

risk of the portfolio is the weighted average of the individual risks

• when p = 1 then this offers the highest risk for the portfolio when combining the two securities
• any imperfect correlation between two securities will offer diversification benefits and reduce the risk
  
  • as the variance of a portfolio with p < 1 will reduce the value of the cross product in the equation in comparison to the variance equation in the perfect case (given that short sell is not allowed)

Question 4

How do you calculate the risk and return between two risky investments when they are perfectly negatively correlated?

Answer 4

• perfect hedging scenario
  
  • set variance equaiton equal to 0 and rearrange

Question 5

What happens to the portfolio standard deviation as we increase the proportion of invested capital into another risky asset?

Answer 5

• initial decrease but after a certain point the risk of the portfolio increases –> imperfect correlation
• Any point in diversification if p=1?
  
  • in this case now as the black line has a greater risk no matter how little you invest in intel
    
    • so should just invest in the one asset
      *

Question 6

When is a portfolio efficient?

Answer 6

• Minimum variance portfolio (one with lowest s.d.)

Question 7

What happens when you introduce multiple stocks and allow for short selling?

Answer 7

• more stock means more diversification and better shape ratios

Question 8

Risk-return combinations from combing a risk-free investment and risky portfolio?

Answer 8

• straight line indicate a CAL with a combination of a risky-asset and a specific efficient portfolio
• The best portfolio we can generate in this case (tangent or efficient risky portfolio) is at the point the line (and thus sharpe ratio) is tangent to the efficient frontier
  
  • The CAL that generate this is called the Capital Market Line

Question 9

What is the tangency portfolio optimisation problem?

Answer 9

• efficient risky portfolio
• REMEMBER EXCESS RETURN

Question 10

How do you find the optimal complete portfolio from the efficient risky portfolio?

Answer 10

Question 11

Summary of how we arrive at the optimal complete portfolio?

Answer 11

Let us summarize the steps we followed to arrive at the complete portfolio.

1. 1. Specify the return characteristics of all securities (expected returns, variances, covariances).
2. 2. Establish the risky portfolio (asset allocation):
   3. 2.1 Calculate the optimal risky portfolio, P (the tangent point E using the optimal risky portfolio equation (large one)).
   4. 2.2 Calculate the properties of portfolio P using the weights determined in step (2.1) and Equations for E(r_p) and σ_p
3. 3. Allocate funds between the risky portfolio and the risk-free asset (capital allocation):
   4. 3.1 Calculate the fraction of the complete portfolio allocated to portfolio P, x and to T-bills (the risk-free asset) (using rearrange risk aversion equation).
   5. 3.2 Calculate the share off the complete portfolio invested in each asset and in T-bills.

Question 12

What is the separation property of the optimal efficient portfolio and why is it good for fund managers?

Answer 12

• it tells us that the portfolio choice problem may be separate into two independent tasks
  
  • The first task, determination of the optimal risky portfolio, is surely technical
    
    • Given the manager’s input list, the best risky portfolio is the same for all clients, regardless of risk aversion,
  • However the second task, capital allocation depends on personal preference. Here the client is the decision maker Investors with varying degrees of risk aversion would be satisfied with a universe of only two mutual funds: a money market fund for risk-free investments and a mutual fund that holds the optimal risky portfolio p, the tangency portfolio
• This result makes professional management more efficient and hence less costly
• Oe management firm can serve any number of clients with relatively small incremental administrative cost
  
  • Should be noted how different managers will estimate different input lists, thus deriving different efficient frontiers, and offer different “ optimal” portfolios to their clients