Optimal portfolio choice

Optimal portfolio choice

1. 1. The efficient frontier consists of:

   All possible portfoliosMinimum-variance portfolios for each given expected return levelEqual-weighted portfolios across all assetsOnly risk-free portfolios

2. 2. The tangent portfolio is special because:

   It contains only the risk-free assetAmong all risky portfolios on the efficient frontier, it has the highest Sharpe ratio (best risk-return trade-off)It always has zero betaIt's the lowest-variance portfolio

3. 3. Two-fund separation says:

   Every investor's optimal allocation is a combination of the risk-free asset and the tangent (market) portfolioEvery investor should hold exactly two funds named A and BThe market should be divided into long-only and long-short fundsBond and stock allocations must be 50/50

4. 4. Under what conditions does mean-variance analysis give exactly correct portfolio recommendations?

   Returns are normally distributedInvestors have quadratic utilityMarkets are perfectly efficientReturns are heavily skewed with fat tails

5. 5. Two assets: σ₁ = 20%, σ₂ = 10%, correlation ρ = 0. You hold 50% in each. What is the portfolio standard deviation, in percent? (σ_p² = w²σ₁² + (1−w)²σ₂² + 2w(1−w)ρσ₁σ₂.)

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