Financial Market Theory

Παρουσίαση με θέμα: "Financial Market Theory"— Μεταγράφημα παρουσίασης:

1 Financial Market Theory
Thursday, October 5, 2017 Professor Edwin T Burton

2 Diagram with 2 Assets Asset 2 (μ2, σ2) Asset 1 (μ1, σ1) Mean
Where are the portfolios that can be formed from these two assets? Asset 1 (μ1, σ1) Standard Deviation = √(Variance) October 5, 2017

3 All Portfolios That Can Be Constructed:
𝑃= α ∗ 𝑎𝑠𝑠𝑒𝑡 1 𝑝𝑙𝑢𝑠 1 − α ∗(𝑎𝑠𝑠𝑒𝑡 2) where 0 ≤ α ≤ 1 𝑀𝑒𝑎𝑛 𝑜𝑓 𝑃= α times Mean of Asset plus (1 – α) times Mean of Asset 2 October 5, 2017

4 Variance of a Portfolio with two assets
 P2 =  (P - P)2 n = {α(X1- 1) + (1-α)(X2 - 2)}2 n October 5, 2017

5 After some mild heavy lifting:
σ 𝑃 2 = α 2 σ −α 2 σ α 1−α Cov(1,2) Note that Cov(1,2) ≡ σ1,2 So: σ 𝑃 2 = α 2 σ −α 2 σ α 1−α σ 1,2 October 5, 2017

6 Make use of correlation coefficient:
σ 𝑃 2 = α 2 σ −α 2 σ α 1−α σ 1,2 ρ 1,2 ≡ σ 1,2 σ 1 σ 2 σ 𝑃 2 = α 2 σ −α 2 σ α 1−α ρ 1,2 σ 1 σ 2 October 5, 2017

7 σ 𝑃 2 = α 2 σ −α 2 σ α 1−α ρ 1,2 σ 1 σ 2 What happens when ρ1,2 = 0 ? σ 𝑃 2 = α σ 1 + 1−α σ 2 2 Now, take square roots of both sides: σ 𝑃 = α σ −α σ 2 If α= ½, then σ 𝑃 = σ σ 2 October 5, 2017

8 So, the half/half case is:
σ 𝑃 = σ σ 2 So, the half/half case is: Mean μ2 Asset 2 (μ2, σ2) Asset 1 (μ1, σ1) μ1 σ1 ½ σ1 + ½ σ2 σ2 October 5, 2017

9 If ρ < 1 σ 𝑃 2 = α 2 σ 1 2 + 1−α 2 σ 2 2 +2α 1−α σ 1,2
σ 𝑃 2 = α 2 σ −α 2 σ α 1−α σ 1,2 The right hand side will be smaller than before This implies a smaller variance of P And a smaller standard deviation October 5, 2017

10 So, if σ < 1 σ1 ½ σ1 + ½ σ2 σ2 Asset 2 (μ2, σ2) Asset 1 (μ1, σ1)
P will lie to the left of the Line joining the Assets Mean μ2 Asset 2 (μ2, σ2) μ1 Asset 1 (μ1, σ1) σ1 ½ σ1 + ½ σ2 σ2 October 5, 2017

11 Portfolio Choice σ σ Mean
Green Curve is Markowitz’s “Efficient Portfolio” set More risk Less risk σ σ October 5, 2017

12 October 5, 2017