Portfolio Construction

Question 1

What are the inputs to the construction of the optimal investment portfolio?

Answer 1

a. Current Portfolio
b. Alphas
c. Covariances between assets
d. Transaction costs
e. Active risk aversion

Question 2

Higher the preference for lower volatility

Answer 2

Higher the risk aversion

Question 3

What is the need for refining alphas?

Answer 3

To account for the several constraints imposed by the client or manager or any third party stakeholder

Question 4

What do you mean by “refining alpha”?

Answer 4

From my understanding;

Alpha will increase as we take on more risk. However, constraints will be there to limit this risk, or limit certain actions (like putting in a short trade for example)

In that case, we need to calculate, what the maximum alpha will be, given the constraints

Question 5

What are the techniques employed after refining alpha for various imposed constraints?

Answer 5

a. Scaling and b. Trimming

Question 6

How can we represent alpha? And how this affects scale

Answer 6

Alpha = volatility X information coefficient X Score

volatility is residual risk
IC is managers ability
Score is Z score with a mean of 0 and SD of 1

Hence Alpha is proportional to Score

Hence, SD of alpha is proportional to SD of Score

Question 7

What if we do not have an appropriate scale when refining alpha?

Answer 7

We can calculate scale refined alpha/scale original alpha and calculate the decrease in IC, from decrease in scale of alpha due to constraints

Question 8

What do you mean by trimming? in context of alpha refinement?

Answer 8

This is simple, there might be very large alpha values for securities, we simply re-examine why this is the case, and any alpha found to be the result of questionable data is set to zero, and the remaining alpha is reduced to some maximum value.

Question 9

What is neutralization and what are its types?

Answer 9

Neutralization is the process of removing biases and undesirable bets from alpha.
They are of the following major types:
a. Benchmark
b. Cash
c. Risk Factor

Question 10

What is benchmark neutralization?

Answer 10

Matching the beta of the active portfolio to the beta of the benchmark portfolio is called benchmark neutralization.

This eliminates any difference between the benchmark beta and the beta of the active portfolio.

Modified benchmark neutral alpha» Alpha (Active)-Benchmark (alpha) X Active position beta

Question 11

What is cash neutralization?

Answer 11

Here, we adjust the alphas so that the portfolio has no active cash position. Its possible to make the alpha values both cash and benchmark neutral.

Question 12

What is risk factor neutralization?

Answer 12

The active portfolio may also be neutralized with respect to industry risk factors, by matching the portfolio weights of each industry to those of the benchmark portfolio.

Question 13

What are transaction costs and when are they realized?

Answer 13

Transaction costs are the costs of changing portfolio allocations, primarily trading commissions and spreads.

These costs occur at two times, (at the buying or selling point), but, this will be amortized (yearly) over that time when the security was bought and sold.

Question 14

Measure of active risk aversion

Answer 14

Active risk aversion = IR/(2 X Active Risk)

=> IR = 2 X Active risk aversion X Active Risk

Question 15

Measure of Utility

Answer 15

Utility = Active Return - Risk Aversion X Variance

Question 16

Why is aversion to specific factor risk important?

Answer 16

1. Can help manager address risks associated with having a position with potential for large losses
2. High risk aversion values reduces dispersion across portfolios when manager manages more than one portfolio.

Question 17

What is alpha coverage?

Answer 17

This refers to addressing situations where the manager has forecasts of stocks that are not in the benchmark or where the manager does not have alpha forecasts for stocks in the benchmark.

Question 18

What to do when manager has info on stocks not on benchmark?

Answer 18

A benchmark weight of zero should be assigned for benchmarking, but active weights can be assigned to these to generate active alpha

Question 19

What to do when info on stocks within the benchmark is not there?

Answer 19

Adjusted alphas can be inferred from the alphas of stocks for which there are forecasts.

Question 20

On what does the decision of rebalancing a portfolio depend on?

Answer 20

Depends on the tradeoff between transaction costs and the value added from changing the position.

Question 21

What is the no trade region?

Answer 21

Where the benefits of rebalancing are less than the costs.

-(cost of selling)<marginal contribution to value added<cost of purchase; where…

Marginal contribution to value added = alpha-IR X marginal contribution to the active risk of the asset

Question 22

What is the size of the no trade region determined by?

Answer 22

1. Transaction cost
2. Risk Aversion
3. Alpha
4. Riskiness of the assets

Question 23

State the main four procedures for institutional portfolio construction

Answer 23

1. Screening
2. Stratification
3. Linear programming
4. Quadratic programming

Question 24

Discuss how an active manager generates value?

Answer 24

It depends on her ability to increase returns relative to the benchmark portfolio that are greater than the penalty for active risk and the additional transaction costs for active management.

Portfolio alpha - risk aversion X Active risk ^ 2 - transaction costs

Question 25

What is Screening

Answer 25

Allow some through, and restrict others. Another method is to assign buy, hold and sell ratings to all the stocks in the manager's universe of investable stocks.

Question 26

What is stratification

Answer 26

Divide the stocks into multiple mutually exclusive categories prior to screening This is a method of risk control, if the size and sector categories are chosen in a way that they capture the risk dimensions of the benchmark well, portfolio risk control will be significant. This will eliminate bias in estimated alphas across categories of firm size and sector. But, it also takes away possibility of adding value by deviating from benchmark size-sector weights.

Question 27

What is Linear Programming?

Answer 27

Linear programming is an improvement over stratification. It's strength is that it can closely resemble the risk of the benchmark, but the result can be a portfolio very different from the benchmark in terms of assets included, and different dimensions of risk

Question 28

What is quadratic programming?

Answer 28

Designed to include alphas, risks and transaction costs, and any number of constraints can be imposed. Best method of optimization. One consideration is estimation error.

Question 29

What is portfolio return dispersion?

Answer 29

Variability of returns across client portfolios. Can be reduced by reducing differences in asset holdings. Different portfolio constraints across accounts will increase dispersion. Given transaction costs, there is an optimal level of dispersion that balances transaction costs and gains from rebalancing. Dispersion is proportional to active risk for a given no. of portfolios.