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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 →mean-variance · portfolio-theory · markowitz · expected-utility · quadratic-utility · gaussian-returns · risk-aversion · budget-constraint
打开 →某上海私募的初级量化:把 L2 的闭式 MV 直接套到 100 只 A 股、5 年月度数据上,优化器吐回的组合在三只票上占 90%(其中两只各做多 60%、一只做空 200%)。回测夏普 3.2,PM 拍板上线。半年后实盘亏 12%,同期沪深300 涨 8%。「教科书的东西在实盘上不工作」——但 不是 教科书错了,是 他没装收缩 (no sh...
打开 →周五上午,你在上海的一家 量化 私募 ——明汯、 幻方、 九坤、 灵均 风格 的 多 因子 私募。 L3 把 四 条 信号 正交化 完了: mom 12 1 , book to market , gross profitability , pead sue 都 残差化 通过 了 IC break even 门槛。 桌面 上 还 没有 量产 复合 信号。 投决...
打开 →周一上午,你在某沪上私募基金的组合构建台,PM 把一个文件丢到你桌上:沪深300 成份股加上一篮子中证500 小盘票,共 500 只,每只都给了下一季度的预期收益 公式;另外附一张 500×500 的协方差矩阵 公式,是研究部用 60 个月滚动样本估出来的。PM 的指令只有一句:「按这个开个仓,目标年化波动 12%。」 你面前的问题就是单期(single p...
打开 →L1 把 N 资产的单期投资问题落到了一行目标函数 公式 s.t. 公式,又用两资产示例把代数走通。但 PM 周五拍着桌子要的不是一个孤立点——他要看一张图:横轴是组合波动率 公式,纵轴是组合预期收益 公式,所有 MV 最优组合按 公式 串起来形成一条曲线;同时他要知道 有没有一个最好的组合 (无关 公式 的那种),以及加现金后这张图是怎么变的。 这...
打开 →国内某量化私募的因子研究负责人,在沪深300成分股范围内向新来的研究员提出一个任务:「在我们的股票宇宙里把 AQR 的 quality minus junk 因子搭出来,然后告诉我它该以常规权重、收缩权重、影子组合、还是直接剔除的方式进入生产合成因子。」研究员对前四节内容了然于胸——L1 因子定价模型、L2 异象清单、L3 构建工艺、L4 经济故事。这个问题...
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 →某上海私募的多空策略台,周一早会上分析师汇报:某只白酒龙头跑赢沪深300 5.2 个百分点,「显著的 alpha」。基金经理把数据敲到 Bloomberg,跑了一遍 CAPM 回归,Jensen alpha 的 t 值 1.3——「不,这只是 beta 的 1.4 倍,加上沪深300 这一年涨了 4%,你看到的 5.2% 全在 beta 解释范围内,没有 a...
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.
打开 →某沪深300指增私募的中级量化研究员,用 L1 的「无成本」约束 MV 优化器跑 30 只 CSI 300 行业龙头基础上的 12 1 截面动量信号,样本内纸面 Sharpe(paper Sharpe)= 1.4。她把同样的换仓单丢进自家交易台的事后成本归因系统,扣掉佣金、印花税、半价差(half spread)和 Almgren Chriss 市场冲击之后...
打开 →周四早上,你在上海的一家 量化 私募 的 因子 评估 会 上。 桌面 上 堆 着 K 条 信号 的 L1 + L2 诊断 包: 12 1 动量、 账面市值比、 毛利率 质量、 PEAD (post earnings announcement drift) ——每 一条 都 通过 了 L2 的 break even IC 门槛、 每 一条 月度 IC 都 在 ...
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