3- Efficient portfolios with a risk-free asset Flashcards
What is the mean return of a portfolio with a risk-free asset?
μₚ = ωμ₁ + (1 - ω)r
What is the variance of a portfolio with a risk-free asset?
σₚ² = ω²σ₁²
What is the equation for the capital market line/opportunity set?
μₚ = r + (μᵧ-r/σᵧ)σₚ
Briefly explain the capital market line(CML)/opportunity set
The set of efficient portfolios in presence of a risk-less asset
What is the Optimal Risky Portfolio (ORP) and where is it’s line relative to the CML?
An efficient portfolio with no shares of riskless asset, tangential to the CML
Why is the CML the efficient set?
Because portfolios on this line have the largest (excess) return-to-risk ratio
What is the Sharpe ratio?
The risk-normalised excess return, hence is the same for all efficient portfolios
How can you find the Sharpe ratio?
Differentiate the CML wrt σₚ:
μᵧ-r/σᵧ
What is the expected utility with mean-variance preferences equation?
U(μₚ, σₚ) = μₚ - 1/2γσₚ²
How do you calculate the optimal portfolio?
-Sub mean return and variance into utility equation
-Differentiate wrt ω and solve for it
What is the expression for Beta (β)?
βᵢ = σᵢₚ/σₚ² = ρᵢₚ(σᵢ/σₚ)
Briefly explain Beta (β)
Correlation of asset with the market, showing relative volatility
What is Systematic risk?
The ‘market’ risk expressed by the beta, and is un-diversifiable
What is Idiosyncratic risk?
The un-systematic risk specific to asset i as residual of the model
How can Idiosyncratic risk be diversified away?
By increasing the number of assets
