MIP Chapter 5

Question 1

How can it be determined if adding a new asset to a portfolio makes it more efficient?

Answer 1

Sharp ratio of new asset is higher than sharp ratio of portfolio times correlation of new asset and existing portfolio

Question 2

What is the formula for the Safety First Ratio in Roy’s Safety First Criterion?

Answer 2

The higher the better

R_L is the threshold return

Question 3

What are some critieria for selection of asset classes?

Answer 3

• Assets within an asset class should be relatively homogenous
• Asset classes should be mutually exclusive
• Asset classes should be diversifying
• The asset classes as a group should make up a preponderance of world investable wealth
• The asset class should have the capacity to absorb a significant fraction of the investor’s portfolio without seriously affecting portfolio liquidity

Question 4

What are some examples of asset classes?

Answer 4

• Domestic equity
• Domestic fixed income
• Nondomestic equity
• Nondomestic fixed income
• Real estate
• Cash and cash equivalents

Question 5

Describe corner portfolios

Answer 5

Endpoints of a part on the efficient frontier where all interior portfolios on the efficient frontier are composed of the same assets.

Question 6

What are the two properties needed for a constrained mean-variance frontier?

Answer 6

Asset-class weights must be:

(1) non-negative (no shorting)
(2) sum to one

Question 7

State the corner portfolio theorem.

Answer 7

In a sign-constrained optimization, the asset weights of any minimum-variance portfolio are a positive linear combination of the corresponding weights in the two adjacent corner portfolios that bracket it in terms of expected return.

Question 8

State some advantages of segmentation.

Answer 8

1. Focus for meeting return objectives by product line / line of business
   
   1. Different investment horizons
   2. Different liquidity requirement
2. Easily allocate investment income by line of business
3. More accurate measurement of profitability by line of business
4. Better management of interest rate risk by product line
5. Assist senior management in assessing the suitability of investments
6. Establishes multiple acceptable asset allocations that are appropriate
7. Promote competitive crediting rates for each segment

Question 9

State some approaches/techniques that can be used to mitigate estimation error in Optimization (Mean-Variance Approach)

Answer 9

Sensitivity analysis
Resampled efficient frontier
Black-Litterman approach
Factor-based optimization

Question 10

State some special strategic asset allocation considerations for a bank

Answer 10

The bank’s security portfolio plays a key role in:

• Managing the balance sheet’s overall interest rate risk
• Managing liquidity
• Producing income
• Managing credit risk
• Regulatory considerations

Question 11

Explain the Role of Strategic Asset Allocation in Relation to Systematic Risk

Answer 11

1. A key cornerstone of investment analysis is that systematic risk is rewarded
2. Strategic asset allocation helps align a portfolio’s risk profile with the investor’s objectives
3. In the long run, investors expect compensation for bearing risk that they cannot diversify away
4. Measuring portfolio risk begins with an evaluation of the portfolio’s systematic risk
5. Systematic risk usually accounts for most of a portfolio’s change in value in the long run
6. Exposure to systematic risk over long time periods is rewarded
7. Groups of assets that are relatively homogenous should predictably reflect exposures to a certain set of systematic risk factors
8. Groups of assets that are distinct/differentiated should have distinct exposures to factors and/or exposures to different factors
9. The strategic asset allocation specifies the desired exposure to systematic risk

Question 12

Describe what is meant by the term cross-sectional variation of returns

Answer 12

The proportion of the variation among funds’ performance explained by funds’ different asset allocations

Question 13

Describe the analysis from Kritzman and Page (2003).

Answer 13

Kritzman and Page (2003) explored asset allocation versus security selection in terms of hypothetical potential to affect terminal wealth. The conclusions from Krtizman and Page are:

• Active security selection led to greater potential dispersion in final wealth than did varying asset allocation
• Skillful investors have the potential to earn higher incremental returns through security selection than through asset allocation
• Skill as a security selector may be highly valuable
• Security selection’s potentially higher incremental returns come at the cost of greater risk;
• thus, not only the investor’s skill, but also risk aversion must be considered

Question 14

When does the ALM approach tend to be favored over the AO approach?

Answer 14

• The investor has below-average risk tolerance
• The penalties for not meeting the liabilities or quasi-liabilities are very high
• The market value of liabilities or quasi-liabilities are interest rate sensitive
• Risk taken in the investment portfolio limits the investor’s ability to profitably take risk in other activities
• Legal and regulatory requirements and incentives favor holding fixed-income securities
• Tax incentives favor holding fixed-income securities

Question 15

State special issues to consider when investing internationally

Answer 15

1. Currency risk
2. Increased correlations in times of stress
3. Emerging market concerns
   
   • E.g. political risk, sovereign risk, limited free float of shares, limitations on the amount of nondomestic ownership, quality of company information, non-normality of returns.

Question 16

Describe the resampled efficient frontier

Answer 16

• There is little confidence in a single MVO (mean-variance optimization)
• The resampled efficient frontier looks at a number of different efficient frontiers using different assumptions
• The inputs to portfolio analysis are highly uncertain, so this can give more understanding for the range of possibilities

Question 17

Describe the two versions of the Black-Litermann model mentioned in MIP Ch 5.

Answer 17

1. Unconstrained Black-Litterman (UBL) Model
   
   • Adjust weights in a global benchmark to reflect investor’s views of expected returns in different asset classes
   • This direct method usually results in only minor adjustments
2. Black-Litterman (BL) Model
   
   • Reverse engineers implicit expected returns
   • More commonly used in practice

The investor’s view of returns could be on an absolute or relative basis
Must first calculate the equilibrium returns because that is the starting point
Advantages of incorporating equilibrium returns
1. Dampens extreme views of investors
2. Ensures greater consistency across estimates
Ripple effects are common in the estimates when using the BL process

Question 18

Describe the implementation choices for strategic asset allocation.

Answer 18

1. Passive Investing
   
   • A tracking portfolio of cash market securities
   • Cash position plus long swap on index
   • Cash position plus long futures on index
2. Active Investing
   
   • Cash market securities
   • Derivatives-based position
3. Semi-active Investing or Enhanced Indexing
   
   • Cash position that permits some over- or under-weighting
   • Derivatives-based position with some active management permitted
4. Combination of the Above

Question 19

Describe tactical asset allocation (TAA) and describe its key principles.

Answer 19

• TAA is active management at the asset-class level
• Involves deliberately overweighting or underweighting particular asset classes
• Key Principles:
  
  1. Market prices tell explicitly what returns are available
  2. Relative expected returns reflect relative risk perceptions
  3. Markets are rational and mean reverting

Question 20

The Efficient Frontier in a Mean-Variance Approach

Answer 20

• Efficient Frontier is part of minimum variance frontier (MVF) that maximizes the return for a given amount of risk (or minimizes the risk for a given amount of return)
• The Unconstrained Minimum-Variance Frontier (MVF)
  
  • Simply make the weights sum to one as the only restriction
• The Sign-Constrained MVF: The Case Most Relevant to Strategic Asset Allocation
  
  • Asset-class weights must be non-negative and sum to one
  • This eliminates the option to sell classes short
  • Corner portfolios are important in the analysis
  • The asset weights of any minimum-variance portfolio are positive linear combinations of the corresponding weights in the two adjacent corner portfolios
  • The first corner portfolio (top right on the efficient frontier) is normally 100% invested in the highest-expected-return asset class

Question 21

The Importance of the Quality of Inputs in a Mean-Variance Approach

Answer 21

The results are very sensitive to the estimated inputs (e.g. expected returns)
Should conduct sensitivity testing on the inputs

Question 22

Selecting an Efficient Portfolio

Answer 22

Risk and return objectives are established in the IPS
Cash Equivalents and Capital Market Theory

• From a single-period perspective T-bills have no uncertainty and thus no risk
• There is a standard deviation from a multi-period perspective
• The investor’s portfolio will fall on the capital allocation line, which is a combination of the optimal risky portfolio and the risk-free rate
• Need enough cash to cover the liquidity needs

Question 23

Leverage in Selecting an Efficient Portfolio

Answer 23

Utility
If the investor can borrow/lend at risk free , margin can be used to:

• Leverage the position in the tangency portfolio to achieve a higher expected return than the tangency portfolio
• Or split money between the tangency portfolio and the risk-free asset to achieve a lower risk position than the tangency portfolio

The investor’s portfolio would fall on the capital allocation line, which describes the combinations of expected return and standard deviation of return available to an investor from combining his or her optimal portfolio of risky assets with the risk-free asset.
Limitations

• Many investors face restrictions against buying risky assets on margin (particularly pension plans).
• Even without a formal constraint against using margin, a negative position in cash equivalents may be inconsistent with an investor’s liquidity needs.
• Leveraging the tangency portfolio may be practically challenging for many investors.

Question 24

Monte Carlo Simulation in the asset allocation optimization

Answer 24

• Can use this to test the strategic asset allocation under various scenarios
• Can use simulation to calculate the impact of items such as tax changes
• Usually terminal wealth is path dependent because positive and negative cash flows are present over the horizon
• Simulation can evaluate an investors existing portfolio relative to the goals

Question 25

Asset/Liability Management in Asset Allocation Optimization

Answer 25

The focus is on funding the liabilities
Should use the surplus efficient frontier to optimize the net worth
Some will choose the minimum surplus variance (MSV) portfolio while others will take on some beta risk
This approach is common for pension plans
The funding ratio for the pension plan will influence the optimal portfolio
Asset/Liability Modeling with Simulation
Use simulation to test the asset allocation
Steps to follow

1. Select a limited set of efficient portfolios
   
   • U^ALM _m = E(SR_m) - 0.005R_Asigma²(SR_m)
2. Use Monte Carlo simulation to determine which portfolios meet the risk and return objectives
   
   • Produce frequency distribution of assets, liabilities, and net worth
3. Choose the best allocation
   
   • Can use quantitative and qualitative criteria

Question 26

The tangency portfolio in MVO

Answer 26

• the tangency portfolio is the efficient portfolio with the highest Sharpe Ratio.
• When the expected return of the Tangency portfolio exceeds the return objective, it may be optimal for the investor to hold the highest Sharpe-ratio efficient portfolio in combination with the risk-free asset (Capital allocation line analysis).
• If the expected return of the tangency portfolio is lower than the return objective, assuming that margin is not allowed, this portfolio is not optimal.

Question 27

Adjacent corner portfolios

Answer 27

• A segment of the MVF within where: Portfolios hold identical assets
• As the MVF passes through a corner portfolio, an asset weight either changes from 0 to positive or from positive to 0.
• Corner portfolios allow to create other minimum-variance portfolios