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中文题目A PM says, "This market-neutral sleeve has a poor standalone Sharpe, so it should never receive weight in a Markowitz optimizer." The sleeve is mildly negatively correlated with the core book. How would you respond in two or three sentences?
打开 →A Markowitz backtest flips from +18% to -12% in one sleeve after a tiny revision to expected-return estimates, while the covariance matrix barely changes. What does this tell you, and what would you do before trading the result live?
打开 →A portfolio holds weights 0.6 and 0.4 in two assets with volatilities 0.02 and 0.08. What correlation would make the portfolio volatility exactly equal to 0.02, the volatility of the safer asset? Is that attainable without going outside the correlation bounds?
打开 →A two-asset portfolio has weights 0.3 and 0.7, volatilities 0.03 and 0.10, and current correlation 0.25. After a macro shock, correlation is revised to 0.75 with all else unchanged. What is the new portfolio volatility, and how many volatility points of diversification are lost r
打开 →A portfolio holds weights 0.4 and 0.6 in two assets with volatilities 0.06 and 0.12 and current correlation -0.4. If correlation normalizes to 0 while weights and volatilities stay fixed, by what percentage does portfolio variance increase?
打开 →An equal-weight portfolio holds two assets with volatilities 0.04 and 0.09. The current correlation estimate is -0.2, but stress testing revises it to +0.3. With weights unchanged, what is the new portfolio volatility, and by how many volatility points does it rise versus the ori
打开 →Two risky assets have volatilities 0.05 and 0.11, correlation 0.25, and expected returns 0.09 and 0.13. Under a fully invested long-only portfolio, choose weights so the two assets contribute equally to total variance. What are the weights and the portfolio expected return?
打开 →Two uncorrelated risky assets have expected returns 0.06 and 0.09, risk-free rate 0.02, and variances 0.025 and 0.07. Suppose asset 2 carries an annual implementation fee c that reduces its expected return from 0.09 to 0.09-c. What fee c would make the tangency portfolio weight o
打开 →Two risky assets have variances 0.04 and 0.09 and covariance 0.015. What weight on asset 1 gives the two-asset minimum-variance portfolio?
打开 →A fully invested long-only portfolio allocates weight w to asset 2 and 1-w to asset 1. Asset 1 has expected return 0.05 and volatility 0.025. Asset 2 has expected return 0.14 and volatility 0.12. Their correlation is 0.3. If portfolio variance must not exceed 0.006, what is the l
打开 →A fully invested two-asset portfolio places weight w in asset 1 and 1-w in asset 2. The assets have expected returns 0.06 and 0.10, volatilities 0.03 and 0.07, and correlation 0.1. If the PM wants expected return 0.082, what weight w is required, and what percentage of the result
打开 →Two uncorrelated risky assets have expected returns 0.10 and 0.14, risk-free rate 0.05, and asset 1 variance 0.05. What variance would asset 2 need so that the tangency portfolio puts exactly one-third of the risky allocation in asset 2?
打开 →Two uncorrelated risky assets have expected returns 0.09 and 0.13, risk-free rate 0.04, and variances 0.035 and 0.10. Risk control adds a variance penalty x to asset 1, so its effective variance becomes 0.035 + x. What x would make the tangency portfolio split the risky allocatio
打开 →An unconstrained optimizer wants a large short in one equity sleeve to hedge two crowded longs, but mandate rules require long-only weights. Explain why the long-only solution can look qualitatively different rather than just a clipped version of the unconstrained one.
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