Analysis of Active Portfolio Management

Question 1

Active weights

Answer 1

Difference between the weight of the security between the portfolio and the benchmark.

Δ portfolio - benchmark

Question 2

What is the components / formula for asset allocation

Answer 2

(ΔWeight of stocks X Return benchmark stocks ) + (ΔWeight bonds X Returns benchmark bonds)

∑(Active weights x Benchmark Return)

Question 3

What is the components / formula for Security selection

Answer 3

(Portfolio weight stocks X Active return stocks) + (Portfolio bond weights X Active return bonds)

Question 4

Where does active return come from?

Answer 4

Overweighing securities that will do better than benchmark, and underweighting stocks that will perform poorly than the benchmark

Question 5

How to calculate cash in the Sharpe ratio?

Answer 5

1. New desired standard deviation / previous standard deviation
   σ₁ / σ₀ = Weight in portfolio = Wp

(1- Wp) = Cash

Question 6

How to calculate weight in the Sharpe ratio?

Answer 6

New desired standard deviation / previous standard deviation
σ₁ / σ₀ = Weight in portfolio = Wp

Question 7

The formula for combined return in Sharpe ratio

Answer 7

(Rp * Wp) + (1-Wp)*RfR

Question 8

Does cash or leverage change the Sharpe ratio?

Answer 8

No, it does not.

Question 9

Does cash or leverage change the Information Ratio?

Answer 9

Yes, it does!!

Question 10

How can we change the risk in the Sharpe ratio?

Answer 10

With cash and leverage
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But this does not change the Sharpe Ratio

Question 11

How can we change the risk in the Information ratio?

Answer 11

Through the aggressiveness of active weights in the portfolio

We can change the risk by investing in the active portfolio and the benchmark portfolio

Question 12

Property of active management theory

Answer 12

Implies that the active portfolio with the highest IR will also have the highest Sharpe Ratio

Question 13

Optimal amount of active risk (Active risk) Formula

Answer 13

(Information Ratio X Standard deviation of benchmark) / Sharpe Ratio of benchmark

Question 14

Optimal expected active return is a function of …

Answer 14

Forecasting ability
Breath
Active risk

Question 15

The basic fundamental law formula

Answer 15

IC* √BR * σA

Question 16

The full fundamental Law formula

Answer 16

TC * IC* √BR * σA

Question 17

In regards to fundamental law, what if we assume all securities have the same standard deviation

Answer 17

Then, the correlation does not have to be risk-adjusted

Question 18

What does it mean if we have a Transfer Coefficient = 1?

Answer 18

Unconstrained portfolio.
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Our information ratio is invariant to changes in active risk

Question 19

What is the relationship with IR and a constrained portfolio?

Answer 19

If we have constraint in our portfolio our information ratio drops

Question 20

Formula to calculate combined Sharpe Ratio

Answer 20

SRP^2=(SRB^2+IR^2)
SRP=(SRB^2+IR^2)^0.5

Question 21

What is the formula to determine a portfolio managers ability to achieve active return?

Answer 21

Information ratio.

Using Full fundamental law
IR=(TC)(IC)√BR

Basic Fundamental law
IR=(IC)*√BR

Question 22

Does adding cash to the portfolio change the portfolio’s information ratio?

Answer 22

Yes it does!

The information ratio for a portfolio of risky assets will generally shrink if cash is added to the portfolio.

If we add cash, our Information ratio will decrease.

Question 23

Does increasing the aggressiveness of active weights change the portfolio’s information ratio?

Answer 23

No it doesn’t !!
Because the diversified asset portfolio is an unconstrained portfolio, its information ratio would be unaffected by an increase in the aggressiveness of active weights.

Question 24

Characteristics of A closet index

Answer 24

• Low active risk
• Sharpe Ratio close to benchmark
• Information ratio can be Inconclusive because of low active risk
• IR can be negative due to management fee

A closet index will have a very low active risk and will also have a Sharpe ratio very close to the benchmark.
A closet index’s information ratio can be indeterminate (because the active risk is so low) and is often negative due to management fees.

Question 25

What does the Information coefficient measure?

Answer 25

**Signal Quality** The IC measures an investment manager’s ability to forecast returns

Question 26

How can we measure which factor most influences our active returns?

Answer 26

Return from factor tilts = Sum of the absolute contribution to active return = ∑[(Portfolio sensitivity) − (Benchmark sensitivity)] × (Factor return)

Question 27

Formula for active Value

Answer 27

∑ Weights of security ( Return of security - Return of Benchmark)

Question 28

Formula for Information Ratio

Answer 28

(Portfolio Return - Benchmark Return) / Standard deviation (Portfolio Return - Benchmark Return)

Question 29

Is the Information Ratio affected by the aggressiveness by active weights?

Answer 29

No, it is not!!!

Question 30

What does the transfer coefficient measure?

Answer 30

**Portfolio Construction** The correlation between forecast and actual weights of the portfolio

Question 31

What Is Breath? (BR)

Answer 31

The number of independent decision made in a year in constructing a portfolio

Question 32

Combined portfolio Sharpe Ratio (Including TC)

Answer 32

(Combined portfolio^2) = (IR^2)x (TC^2) + (Benchmark Sharpe Ratio^2) Combined portfolio Sharpe Ratio = ROT(Combined portfolio^2)

Question 33

Formula for proportion of benchmark in combined portfolio

Answer 33

1 - (Optimal level of risk / portfolio active risk)

Question 34

Formula for optimal IR

Answer 34

Expected Return / Optimal volatility

Question 35

Formula for optimal active weights

Answer 35

Δwi∗ = μi / σi^2 μi = Forecasted active return σi^2 = Forecast volatility of active return

Question 36

How can the The transfer coefficient be expressed as?

Answer 36

The transfer coefficient can be expressed as the risk-weighted correlation between the optimal active weights and the actual active weights, which is 𝐶𝑂𝑅(Δ𝑤𝑖∗𝜎𝑖,Δ𝑤𝑖𝜎𝑖)

Question 37

For a **constrained portfolio**, how will aggressiveness of active weights afect the IR?

Answer 37

Aggressiveness of active weights will decrease IR

Question 38

For a **unconstrained portfolio**, how will aggressiveness of active weights afect the IR?

Answer 38

Aggressiveness of active weights does not affect IR