P3 - Active equity investing

Question 1

Describe the main goal of active equity portifolio

Answer 1

Aim to outperform a benchmark after all costs. By overweighting secutiries that are beating the bench and underweighting securities that are below the bench.

Question 2

Explain the sources of active return (3)

Answer 2

1) Rewarded factors - that are factor that offer positive long term return from and sizing the positions o maximaze the exposure to those factor’s
2) Mispriced securites - alpha given tatical allocation
3) Idiosyncratic risk - in concentraded bigger positions ca generate returns related to luck

Question 3

Explain how to reduce Idiosyncratic risk

Answer 3

Smaller and diversified position in a greater number os positions will lower the vol of the portifolio

Question 4

Describe the formula that dictates the fundamental law of active managment

Answer 4

👉 “I Can Beat Risk Totally”
Where:

I = IC (Information Coefficient → your skill/accuracy per decision)

B = √BR (Breadth → number of independent bets)

R = σ_RA (Volatility of active return → how much you take risk)

T = TC (Transfer Coefficient → ow well you implement your views into the actual portfolio.

Range: From 0 (can’t trade your views at all) to 1 (perfect execution).

Interpretation:

Constraints (like liquidity, limits, compliance) reduce TC.

Even with high skill and good ideas, if you can’t act on them, value is lost.

Question 5

Explain the approaches to portifolio construction (2)

Answer 5

Sistematic or discretionary: Manager follow sistematic rules vs. discretionary judment
Bottom up or top down: The degree which manager useses bottom-up - company specific info vs. top down macroeconomic factors.

Remember the table

Question 6

Active Share explain the concept and formula and explain the results (0 and 1, 1)

Answer 6

Measure the degree which the number and sizing of the positions are different from benchmark.

The formula is half of wheighting difference
1 = not benchmark
0 and 1 = have different wheighting from benchmark
and zero = to the benchmark

A result of 0.5 conclude that 50% of portifolio is identical to the port and 50% is not.

Question 7

Active Risk explain the concept and give the example that mesures improves active share and main drawback

Answer 7

Is called tracking error. Try to catch the difference between active risk from port vs. bech. For example if I underwheight a pharma sec vs. bech and overwheight another pharma, given the correlation are the same will not increase active risk taken.
The main drawnback is difficult to predict correlation and variance.

Question 8

Given the idiosyncratic risk decompsition explain the main reasearch conclusions (4)

Answer 8

Active share returns into factors, alpha, and idiosyncratic risk

Question 9

Explain the difference between the main active risk/ active share styles
Tips
(1) Factor Neutral
(2) Factor diversified
(3) Concetrated factor bets

Answer 9

Factor bets is like do concentrated position in a factor por exemple think that energy sector will be benefit by increase PLD, this increase the active share and active risk

Question 10

Explain the risk budgeting process

Answer 10

Process by which the total risk of a portifolio is allocated to constituents of portifolio in a efficient manner.

Question 11

Explain the effective risk management process following four steps (4). Remember the concept of absolute and relative risk.

Answer 11

Resume > (1) Determine the measure > (2) Understand the aspects that contributes do measure > (3) Level risk budget is appropriate
> (4)

Question 12

Explain the contribution of asset i to portifolio covariance formula

Answer 12

weight of asset A x weight asse A x cov with A and A
+ weight of asset A x weight asse B x cov with A and C
weight of asset A x weight asse B x cov with A and C

Second step is sum the absolute contributions

And the relative contribution of one portifolio over all is calculed by dividing for asolute contribution

Question 13

Formula to portifolio active variance (CAV) ad the sum of CAV can give ______

Answer 13

The sum of all CAV give the variance of the portifolio active return

Question 14

What’s the principal pratical limitations to increase active returns in an effecient way?
Try to think about restrictions, diversification and leverage

Answer 14

1. Implementation constraints:

Limits on short positions and leverage may restrict the manager’s ability to deviate from the benchmark.

Liquidity issues raise transaction costs as active risk increases → this degrades the information ratio.

2. Limited diversification opportunities:

From portfolio theory: increasing risk yields diminishing marginal returns.

At higher risk/return targets, attractive investment opportunities become scarce → less diversification → lower Sharpe ratio.

3. Leverage and risk implications:

Leverage can shift the portfolio up the capital allocation line in a single period.

But excessive leverage reduces geometric (compounded) returns in a multi-period setting → harming long-term performance.

Question 15

Explain other methods to mesure risk. (Think in main categories)

Answer 15

Can segregate into two categories Heuristic risk constrains and formal risk contrains.

Heuristic like good pratices based on experience or general ideias. (Ex. limit on exposure to individual positions, sectors or regions)

Formal statistical nature

Question 16

Explain the situations that lead to a higher market impact cost. (Think about the limitations of size of portifolio and number of trnasactions) (3)

Answer 16

1) The lower liquidity for smaller cap securities can be a liquidity barrier to manager with higher AUM > > because trades can change price
2) Higher portifolio turnover
3) Managers that our trades can trigger signals to other traders

Question 17

Explain the meaning of slippage and the relation w/ explicit costs, small/large cap, emerging markets, high vol (high of low for those situations)

Answer 17

The difference between the execution price and the midpoint of the quoted market bid/ask spread at the time the trade was first entered.

Question 18

What’s the relationship with increase in AUM and change of strategy given the increase of slipege cost (give an example)

Answer 18

A Manager that focus on small cap stocks can have difficult to sustain the strategie given the increase on slippage cost. In this situation the manager have two options (i) limit the new investors > limiting AUM
(ii) or change strategy

Question 19

Describe the caracteristcs of a well constructed portifolio

Answer 19

Question 20

How to evaluate and chose between equity portfolios for risk efficiency and return potential?
(Think: fewer positions, risk factor alignment, and Active Share.)

Answer 20

Question 21

Explain the concept of short selling

Answer 21

Processos o buying securities and selling them into market, with intention of buying the securities back later at lower price and return them to the lender.

Create the ability to the PM of take advantage of negative insights gained trought their investment research.

Question 22

Explain how to calculate the gross and net long/ short exposure of a fund
Ex. R$ 100 MM capital, R$ 80 MM long position, R$ 30 MM sell position.

Answer 22

Question 23

A fund with a tracking error of 10 bps over the last year means

Answer 23

Question 24

What’s the difference between avg macaulay dur. and macaulay dur

Answer 24

Avg is wheight by market value, in a upward slopping scenario can increase model risk. Because avg. macaulay < macaulay dur.

Question 25

Answer 25

B, in duration matching BPV need to be equal with slight higher convexity for safety

Question 26

Explain why BVP more precise than duration when choosing to imunizing

Answer 26

Question 27

Minimizing portifolio dispersion is the same of ______

Answer 27

The sabe of reducing the portifolio convexity

Question 28

Explain the relationship of active share and active risk

Answer 28

🎯 Active Share Definition: Measures how much the portfolio differs from the benchmark by looking at the allocation. Interpretation: "How different is my portfolio from the benchmark?" Range: 0% to 100% Example: If you pick stocks that the benchmark doesn’t hold, your Active Share is high. 🎯 Active Risk Definition: Measures how much the portfolio’s returns deviate from the benchmark’s returns (volatility). Interpretation: "How much does my portfolio’s return fluctuate compared to the benchmark?" Range: Measured in volatility (e.g., 5% risk) Example: If your portfolio’s returns move differently from the benchmark’s, you have high Active Risk. uick Metaphor Active Share: How different your plate is from the standard menu (benchmark). Active Risk: How different the flavor of your meal is compared to the expected one.