Portfolio Theory

Question 1

Power of Diversification (definition + assumptions)

Answer 1

As the number of assets (n) in the portfolio increases, the SD (total riskiness) falls

• all assets have the same variance
• all assets have the same covariance (ρσσ)
• invest equally in all assets (1/n)

Question 2

Power of Diversification (formulas)

Answer 2

σp^2 = Σwi^2σi^2 + ΣΣwiwj*σij

Impose all assumptions

σp^2 = (1/n)*σ^2 + ((n-1)/n)ρσ^2

If n is large (1/n) is small and ((n-1/n) is close to 1
–> σp^2 = ρσ^2

“Portfolio risk is covariance”

Question 3

Minimum Variance ‘Efficient’ Portfolio (For two assets only)

Answer 3

Wa + Wb = 1 –> Wb = 1 - Wa

Wa = [σb^2 - ρσaσb]/[σa^2 + σb^2 - 2ρσaσb]
(with correlation and individual variances)
Wa = [σb^2 - σab]/[σa^2 + σb^2 - 2σab]
(with covariance)

Question 4

Expected return and variance for portfolio containing one safe asset and one risky asset (bundle) Q

Answer 4

ER = (1-x)r + xER
Var = x^2σQ^2 or σ = x*σQ

Question 5

Slope Capital Allocation Line

Answer 5

= ERi - rf / σi = Risk Premium / Risk

(Sharp Ratio - should be maximized)

Question 6

Steps for deriving Optimal/Market Portfolio

Answer 6

1. Create Efficiency Frontier of possible portfolios of risky assets
2. Use the risk free rate to create a Capital Allocation Line
3. Market Portfolio where Capital Allocation Line starting at rf is tangent to the efficiency frontier