value & growth.

Growth typically means fast growing company, that is normally overvalued but have potential to create unexpected growth

Value typically refer to company that have already been large and mature, but are overlooked by investors, book value is high-qualitied, but market value is low.


Income associated with an Equity Portfolio

  1. Dividend Income

  2. Securities Lending Income: lend to short seller 借出后 div 和 voting right 都不归自己了, 但是可以主动 get cash equivalent to the dividend amount

    • By investopedia:

    • Rights and Dividends: When a security is transferred as part of the lending agreement, all rights are transferred to the borrower. This includes voting rights the right to dividends, and the rights to any other distributions. Often, the borrower sends payments equal to the dividends and other returns back to the lender.

    1. dividends on loaned stock are compensated by the borrower

    2. Reinvestment return of cash collateral are received

  3. Dividend Capture

    1. buy a stock before ex-dividend date

    2. hold it throng the ex-dividend date

    3. sell that stock after ex date

  4. Writing Options

    1. write Covered call: long stock + write a call = + S - c

    2. Cash-coverd put: sell a put + buy bond, at same strike price = K - p


  1. Management Fees 与业绩无关,只与 AUM 相关

    1. Performance Fees (incentive fee): high water mark

  2. Administration Fees, which is part of the management fees 如给证交所注册等

  3. Marketing and Distribution fees

  4. Trading Costs

    1. explicit cost: broker com mission, stock exchange fee, taxes, etc , directly visible

    2. implicit cost 在计算cost过程中不算,但是依然存在 : bid-ask spread, price impact cost from transaction 由于买卖量大导致价格被推高或拉低 造成的成本 Delay cost (slippage costs) 由于延迟下单导致的cost

  5. 弥补 trading cost 的方法

    1. Dividend Capture

    2. Security Lending

    3. Wirite Options

Shareholder Engagement 股东主义

Shareholder engagement refers to investors and managers interacting with companies in ways to potentially favourably impact the stock price.

Pros: (1) improve efficiency (2) get internal information about that firm (3) for active and large investors, so benefits all shareholders, and (4) good for non-financial interests such as ESG.

Cons: (1) time consuming and costly, (2) aim to increase stock price, so focus on short-term goals, not long-term goals, (3) acquisition of material non-public info, so may have risks of insider trading (4) conflict of interest between large and small stakeholders.

Passive Equity Investment (选 benchmark 拟合)


Tracking Error T.E. (active risks σA), (active return RA)


As RA¯=0


So, portfolio 偏离 Benchmark, 则 T.E 提升

Indexes as a Basis for Investment

Stock Index Benchmark

Screenshot 2023-11-15 at 21.35.44

Passive Investment Strategy (Smart Beta)

Screenshot 2023-11-15 at 21.40.43

因为是 passive strategy ,所以目的是与 benchmark 收益一致。

但是 实际操作上 要 face transaction cost, bid-ask spread etc。

所以 T.C. (transaction cost) 会导致portfolio 收益降低。

那么为了保证 port return 与 benchmark return 一样,就需要做一部分的 active management。如多投好的factor,挣positive active return;或者少投差的factor,挣positive active return

只需要一点点的盘子,做 active 来 cover transaction cost,所以主要还是 passive,smart beta 部分只有一点点

Pros and Cons of Smart Beta

Factor-based Strategy

Most benchmarket returns are driven by factors, which are risk exposures that can be identitfied and isolted. 因子之间 identified , isolated

Three Passive Factor Strategies

  1. Reutrn Oriented Strategy 为了挣钱

    • Divident Yield Strategy

    • Momentum Strategy

    • Fundamentally Weighted Strategy (value > Growth)

  2. Risk-Oriented Strategy 为了降低组合的风险

    • Volatility Weighting w=1/σi

    • Minimum Variance Investing

    Pros: lower risks

    Cons: use historical data may not indicate future

  3. Diverisifcation-oriented Strategy

    • Management fees:

      Broad market index < passive factor-based < active strategy

    • Passive factor-based strategy provide pure exposre

Approaches to Passive Equity Investment (Tools + SMA)

Tools: Pooled Investment

  1. open-end mutual fund

    • 买卖价格:(substription, redemption 申购赎回) 如在当日交易日前买,以当日3点收盘价 NAV 为成交价

    • 买卖地方:可以在 market place买 去找蚂蚁金服买,要费, 2. Advisor 买 直接找直销账户买

  2. ETFs

    • 可以在交易所买,所以基金份额可以在二级市场交易

    • 可以在交易所 做空,融资融券,leverage, short 因为可以在交易所交易。不像 open-end mutual fund 只能找基金公司申购赎回,不能用于申购赎回

    • 不用现金交割,而是用 in kind 以物易物的方式交割,sponsor 拿一篮子stock 换 ETFs。也因此没有现金的 gain / loss realised,gain loss are un-realised 所以可以达到 tax defer 的好处

对比 mutual fund & ETFs

Screenshot 2023-11-15 at 22.17.16

ETFs v.s. Mutual Funds


避免额外的 cash 产生 cash drag 拖累 fund收益

Portfolio Construction

Full Replication

Full replication is preferred for indexes with small numbers of liquid stocks 因为 less liquid stock 会大幅增加交易成本T.C.

Screenshot 2023-11-16 at 08.28.25

如果复制的 stocks 少,则复制的不准确,T.E. 大,如果复制的stocks 多,则 T.C. 大,T.E. 大。That is a tradeoff

Stratified Sampling 分组抽样

把 constituent stock 分为 subset,之后从中选取。 Create strata that are mutually exclusive and exhaustive 遍历但不重叠的分组


Using Algorithm to find parameter w weights that can optimise the objective func.

The optimisation process accounts explicitly for the covariances in the portfolio constituents and results in lowering tracking error when compared with stratified sampling alone.

Blended Approach

其中一部分股票 full replication ,其他股票 optim or stratified。三种方法排列组合


Causes of Tracking Error T.E.

In no cost world, Full replication produce lowest T.E., but real world there has be a tradeoff between # of constituents and Cost.

Sources of Return and Risks

  1. Attribution Analysis 见后面reading

  2. Security lending 借给 short seller

    • The securities lending income can be an additional return, and then reduce T.C. and T.E.

    • 但是 由于借出了stock,会面临 credit risks, mkt risks, liquidity, etc 所以可能要 collateral 去弥补风险

  3. Activism and Engagement

    • Passive Investment 也可以有 积极的股东主义 去 increase return

Active Equity Investing

(1) Fundamental Approach (2) Quantitative Approach

Fundamental & Quantitative Approach

Fundamental Approach

Quantitative Approach


Screenshot 2023-11-16 at 13.26.12

Quantitative model consider correlation between factors, so it consider risks at portfolio level.

Active Strategies



Value-Based Approach 价值型,关注未来的 div 收益
Growth-Based Approach 成长型 关注未来的 增长



  1. Country / Geography allocation

  2. Industry Sector Rotation

  3. Thematic Investment Strategies: Focus on opportunities presented by new technologies, changes in regulations, and economic cycles.

  4. Volatility-based Strategies: Volatility trading can be conducted through VIX futures, variance swap, option volatility strategy

Factor-Based Strategies

Hedged Portfolio Approach (Fama & French)


Factor-tilting portfolio

Long only. Will expose to a factor. Controlled level of tracking error 因为只expose to a factor

Factor-Mimicking Portfolio (FMP)

Implement a pure factor portfolio 找只暴露一种risk factor 的stocks

Factor Timing 因子则时

Equity Style Rotation

Activist Strategies 积极的股东主义

  1. 持有 < 10%,号召其他小股东以其反对管理层

  2. short-term interest 和 long-term interest。activist追求短期利益,但是管理层追求长期

  3. 不受上市公司欢迎,所以用 dual class, staggered board 防止investor做 activist

  4. 东西方culture 差异。东方喜欢集权,西方喜欢分立

taking stakes in companies and pushing for companies to make changes that are expected to enhance the value of the activist’s stake. 通过参股,参与公司运营决策,推动公司战略向为股东好的方向走

Target Companies 大原则是经营不太好的公司,这样才有改进的空间



Other Strategies

  1. Statistical Arbitrage: mean-reverting, exploit pricing inefficiency

    • Market microstructure-based arbitrage strategies (high frequency)

    • Pairs trading (highly correlated stocks)

  2. Event Driven

    • M&A

    • Earnings on Restructuring announcements

    • Share buybacks, special div, etc

    Risks: deal fails, deal duration is long, overestimated

Style Classification 分辨基金经理的投资风格

Active Equity Investing

(Systematic + Discretionary) X (Top-down + Bottom-up)

2*2 一共四种管理组合的方式

Targeting low idiosyncratic risk along with low concentrations indicates a systematic approach

Active Return


Sources of Active Returns

We all play with factors (not stocks) in this part.

By regression,

(1) for the portfolio: Rp=β0p+β1pF1+β2pF2+ϵp

(2) for the benchmark: RB=β0B+β1BF1+β2BF2+ϵB

(1) - (2): RA=β0pβ0B+(β1pβ1B)F1+(β2pβ2B)F2+ϵpϵB

The intercepts are approximately equal, so we get the


Finally, the Ex Post Active Returns are


Let ϵpϵb=α+ϵ 把 error 拆解为active return & pure error

According to the above function, we decompose it into three parts.

  1. Strategically Adjusting, exposure to rewarded risks. Return from factor weighting:


  2. Tactically Adjusting. factor timing, security selection. Return from identifying misplacing, 因为回归的factors 都是 rewarded factor,所以residuals会留下 unrewarded factors。这部分体现了基金经理的的能力 (security selection + CME factor timing),即 Alpha α

    • Sustainable 可持续,取决于基金经理的能力,基金经理越nb alpha越大

  3. Luck and unluck return, Idiosyncratic Return, ϵ <- luck

    • Un-sustainable 不可持续,为 Luck

    • 可以根据 diversification程度调整,越diversified 系统性风险越小 epsilon越小

Three Building

  1. Factor Weighting 多配好的,少配差的

  2. Alpha Skills

    1. CME: factor timing 根据宏观经济择时配置 factors (配置 rewarded factors)

    2. Unrewarded Factors (thematic exposure) 选择了不常规用的factors

  3. Sizing Position 权衡购置单一因子的权重 balance confidence in alpha and factors insights

    如控制 factor weighting 与 alpha skill 的权重,体现 level of confidence of analytics

    • A factor-orientated manager 主要从weighting获利的投资者,unexplained part α,ϵ 都比较小 who spreads their portfolio across many assets is likely to minimise the impact of idiosyncratic risk.

      Systematic manager 不做 factor timing

    • A stock-picker, with higher confidence 更愿意投资个股,所以α,ϵ,对于个股(看好的stock)position的集中度也比较高 in her analysis of individual securities, is likely to hold more concentrated positions and assume a higher degree of idiosyncratic risk.

      所以discretionary managers are likely to run concentrated portfolio

  4. Breadth of Experience (BR)


    IR=IC×TC×BR , and combine those two


Portfolio Construction Approaches

Screenshot 2023-11-17 at 16.05.21

Relative Risks 衡量 active investment的指标

Relative risk is measured w.r.t. the benchmark. There are two measures of the benchmark-relative risks.

  1. Active Share: =12|wpwb| 主动偏离benchmark投资的份额。

    • 要除以 2 因为有主动偏离的部分,需要有其他share 让开匀给 active部分,所以要/2

    • % of portfolio assets deployed the same as benchmark

      =1active share

      即为 一个 portfolio 中,和 benchmark 表现一致的部分

    • Between (0,1)

    • Sources 来源:(1) 与 benchmark 中成分股不同 (2) weights 不同。P.S. 如果 portfolio 中 stocks 数比 index 少很多,那么active share一定会大,因为如果数少,则 concentration 集中度大

  2. Active Risks ( Tracking Error )

    • Source of Risks




      收益被拆成了 3 部分(或者说 2 部分,即 1 和 2+3,同理 风险也将被拆成 2 部分

      σA2=σ2((βipβib)×Fi)1.factor exposure+σe22. idiosyncratic risks/ active share


      1. 与 factor exposure 相关的

      2. 和与 个股相关的

      • high net exposure to a risk factor leads to high active risks 来自beta (risk exposure)差异 提升active risks

      • neutralised factor exposure will have active risk entirely attributed to active share 如果beta差异(risk exposure) =0 ,那么 active risk 全部来自 active share。因为 alpha & epsilon 即FM主动管理的程度,这个东西可以由 active share 衡量 (注意上面公式,active share 指的是 σe2 的部分)

      • active risks attributed to active share will be smaller if the number of securtities is large or idiosyncratic risk is small 如果组合中股票数量多,diversification大,σϵ2 active share 小,那么active risks 小

      • active risk increase with the increse in factor and idiosyncratic volatility

  3. Active Share v.s. Active Risks

    1. The level of active risk will rise with an increase in factor and idiosyncratic volatility

    2. High net exposure to a risk factor will lead to a high level of active risk, irrespective of the level of idiosyncratic risk 即 weights diff 会提升 σA active risks

    3. A portfolio with neutralised factor exposure will have active risk attributed entirely to Active Share. 因为 factor neutral 所以 factor exposure risk 为 0,idiosyncratic risks 贡献了所有的 active risks

    4. If # of stocks 小,那么 concentration 小, active weights 小,所以 active share 小,active risks 也小

    5. Correlation 会影响 active risks 但是不影响 active share

    6. active share 高, active risk不一定高。因为active risk 受 cross correlation影响,越相关,越concentration,risks越大

    7. FM 可以控制 active share ,但是不一定能调整 active risks

Screenshot 2023-11-17 at 17.01.42

Risk Budgeting

Absolute and Relative Risks

Screenshot 2023-12-25 at 22.22.00

Screenshot 2023-12-25 at 22.21.22

Allocating the Risk Budget

Risk Constraints

由于很多 securities 不符合正态分布,或者其他原因,所以用以下三个补充方法

  1. Heuristic Risk Constraint

    • Liquidity Constraint

    • Allocation Constraint

      • AllocationConstraint=AUM×MaximumPositionSizeThreshold

      • Index Weight Constraint

  2. Formal Risk Constraint

    • VaR (Conditional VaR, Incremental VaR, Marginal VaR, etc)

    • Drawdown

Implicit Cost

Delay Cost
Ask-Bid Spread
Market Impacts Cost

由于买卖时推高或者拉低price Slippage Cost 带来的价格变化,而产生的成本

Slippage Cost = Market Impact Cost + Delay Cost

Four Conclusion about slippage cost

  1. slippage cost is more important than commission ocst

  2. greater for small cap stock than large cap stock

  3. no necessarily greater in emerging mkt

  4. slippage cost is higher if market volatility is higher



Behavioural Bias

Value and Growth Trap

Well Constructed Portfolio

weights 能清晰的 体现 investment philosophy

Factor Risk Contribution 中 unexplained 部分少。unexplained 越多表示 FM 自己都不能解释自己 fund risks

组合中 number 越多,按理说 越 diversified。此时 如果 number多的 portfolio 的 active risk 大,那么管理的不有效。

Number 和 active risks 不能 contradict

Fee / Active Share 越小,说明 fee 越便宜

Sample Text

Screenshot 2023-12-26 at 19.37.16

The risk targets for Fund Z are most likely those of a manager using a diversified multi-factor approach. Low single-security risk of 1% and modest overall portfolio risk of 4%, combined with flexibility on sector risk, demonstrate a highly diversified portfolio that primarily emphasizes factor exposures. Fund X has risk targets consistent with an emphasis on stock picking—namely, high active risk, high exposure to risk from a single security, and low sector deviations. Fund Y has risk targets consistent with an emphasis on sector rotation—namely, high active risk and a high tolerance for sector deviations.