Week 3 - Optimal Diversification (1) (EFFICIENT FRONTIER CURVE) Flashcards
What are the differing types of risk?
Mkt risk:
- > Mkt wide risk sources
- > Remains after diversification
- > AKA Systematic/Non-diversifiable risk
Firm Specific Risk
- > Can be removed via diversification
- . AKA Non-Systematic/ Diversifiable risk
How do you calculate the weight of the portfolio if expected return is all that’s cared about? (Assuming 0 correlation)
Invest everything into the portfolio with higher return
How do you calculate the weight of the portfolio if minimising return is all that’s cared about? (Assuming 0 correlation)
- Take VAR of portfolio (δ2P = W2 δ2A + (1-w)2 δ2b + 2w (1-w) δab)
- Minimise it via F.O.C
- Then calculate weights
SEE EXAMPLE IN NOTES
What is the VAR of the portfolio when correlation is perfect (p=1) (JUST USEFUL TO KNOW)
Given δab = p δa δb (COV)
δ2p = w2δ2a + (1-w)2 δb2 + 2w(1-w) p δa δb (COV)
= (δb + w (δa - δb))2
Two is the power of 2
When two assets are perfectly correlated what can we say about diversification?
No point in diversifying since the two assets share the same risk and same good news
What is the VAR of the portfolio when correlation is perfectly negative (p = -1) (JUST USEFUL TO KNOW)
δ2p = w2δ2a + (1-w)2 δ2b - 2w(1-w) p δa δb
= (wδa - (1-w)δb2)
When two assets are perfectly negatively correlated what can we say about diversification?
Investing in 2 assets deducts the volatility of one asset using another
What happens to ST DEV with each correlation?
P = 1 -> Perfect: ST DEV is weighted avg of component ST DEV
P<1 -> Negatively: ST DEV less than weighted avg
P= -1 -> Perfectly Negative: Perfect Hedge position available
What are the effects of correlation graphically?
SEE GRAPH IN NOTES
What exactly is an inefficient portfolio and how do we know where it is?
It is whenever its possible to find a better portfolio in terms of both return and risk
TO SEE WHERE IT IS LOOK AT GRAPH
What do we see with 3 assets portfolio choices? (EFFICIENT FRONTIER)
SEE GRAPH IN NOTES
How do you pick the best combination on the efficient frontier line?
Using Sharpe ratio
Where is the best portfolio choice?
The one tangent to the efficient frontier
SEE GRAPH IN NOTES
Using the constraints of the best portfolio choice being tanget to efficient frontier how do we calculate the maximum sharpe ratio?
Max Se = E(rp) - rf /δp
How do we calculate the weight of the optimal risky portfolio in the case of 2 risky assets?
w = R(Ri) δ2 - E (Rc) COV (R1,R2) / δ(Ri) δ2C + E (Rc) δ2i - {E(Ri) + E(Rc)} COV (Ri,Rc)
Shows how much to invest in coke
Where:
Ri = Return on Intel
Rc = Return on coke
2 is to the power of 2
