Hoc Tieng Anh_Hoc CFA

Options can be combined with the underlying/ with other options in a variety of ways
- to modify investment positions
- to implement investment strategy
- even to infer market expectations.
Investment managers routinely use option strategies:
- for hedging risk exposures
- for seeking to profit from anticipated market move
- for implementing desired risk exposures in a cost-effective manner.

Bond Characteristics to Consider

It is important to consider several characteristics of the individual bonds that are used to construct an immunized portfolio.
- Credit rating
- Embedded option
- Liquidity

Immunization against Non-parallel shifts

Equating the duration of the portfolio with the duration of the liability does not guarantee immunization. Immunization risk can be thought of as a measure of the relative extent to which the terminal value of an immunized portfolio falls short of its target value as a result of arbitrary (nonparallel) changes in interest rates.
Immunized portfolios with cash flows that are concentrated around the investment horizon have the lowest immunization risk.

Spread duration

Spread duration measures the sensitivity of non- Treasury issues to a change in their spread above Treasuries of the same maturities. (The spread is a function of perceived risk as well as market risk aversion)

There are three spread duration measures used for fixed rate bonds:
- Nominal spread
- Zero – volatility spread (or static spread)
- Option adjusted spread (OAS)

Extensions to classical immunization

Where the goal is to immunize against a liability we must consider changes in the value of the liability, which in turn could change the amount of assets needed for the immunization. We must also consider the ability to combine indexing (immunization) strategies with active portfolio management strategies. Note that since active management exposes the portfolio to additional risks, immunization strategies are also risk-minimizing strategies.

The bottom line is that classical immunization strategies may not be sufficient in managing a portfolio to immunize against a liability. To address the deficiencies in classical immunization, four extensions have been offered:

- Multifuntional duration
- Multiple liability immunization
- Relaxation of the minimum risk requirement
- Contingent immunization

https://hoccfa.com/cfa-level-3/fixed-income-risk-consideration.html
Bond Characteristics to Consider

It is important to consider several characteristics of the individual bonds that are used to construct an immunized portfolio.
- Credit rating
- Embedded option
- Liquidity

Immunization against Non-parallel shifts

Equating the duration of the portfolio with the duration of the liability does not guarantee immunization. Immunization risk can be thought of as a measure of the relative extent to which the terminal value of an immunized portfolio falls short of its target value as a result of arbitrary (nonparallel) changes in interest rates.
Immunized portfolios with cash flows that are concentrated around the investment horizon have the lowest immunization risk.

Spread duration

Spread duration measures the sensitivity of non- Treasury issues to a change in their spread above Treasuries of the same maturities. (The spread is a function of perceived risk as well as market risk aversion)

There are three spread duration measures used for fixed rate bonds:
- Nominal spread
- Zero – volatility spread (or static spread)
- Option adjusted spread (OAS)

Extensions to classical immunization

Where the goal is to immunize against a liability we must consider changes in the value of the liability, which in turn could change the amount of assets needed for the immunization. We must also consider the ability to combine indexing (immunization) strategies with active portfolio management strategies. Note that since active management exposes the portfolio to additional risks, immunization strategies are also risk-minimizing strategies.

The bottom line is that classical immunization strategies may not be sufficient in managing a portfolio to immunize against a liability. To address the deficiencies in classical immunization, four extensions have been offered:

- Multifuntional duration
- Multiple liability immunization
- Relaxation of the minimum risk requirement
- Contingent immunization

Aligning risk exposure:

– To avoid the costs associated with purchasing every bond in the index yet maintain the same risk exposures. The manager will usually hold a sample of the bonds in the index. One sampling techniques often utilized is stratified sampling (cell matching). Constructing a portfolio with risk exposures identical to the index, however, does not require the composition of the portfolio to be representative of the index. A portfolio can be constructed with exactly the same risk factor exposures as the index.

Duration: Effective duration (option-adjusted or adjusted duration) which is used to estimate the change in the value of a portfolio given a small parallel shift in the yield curve, is probably the most obvious risk factor to be measured. Due to the linear nature of duration, which makes it overestimate the increase or decrease in the value of the portfolio, the convexity effect is also considered.

Key rate duration: Where effective duration measures the portfolio’s sensitivity to parallel shifts in the yield curve, key rate duration measures the portfolio’s sensitive to twists in the yield curve.

The manager should also consider the present value distribution of cash flows (PVD) of the index used as the portfolio benchmark. PVD measures the proportion of the index total duration attributable to cash flows falling within selected time periods.

The present value of all cash flows from the index that fall in each period is divided by the present value of all cash flows (the benchmark market value) to determine the percentage of the total market value that is attributable to cash flows falling in each period.

The manager multiplies the duration of a given period by the percentage of cash flows falling in that period to arrive at the duration contribution for that period. Dividing the duration contribution for each time period by the benchmark duration yields PVD.

If the manager duplicates the benchmark PVD, the portfolio and the benchmark will have the same sensitivity to both shifts and twists in the yield curve.

Sector and quality percent: The manager should match the weights of both the sectors and qualities in the index.

Sector duration contributions: The manager should match the proportion of the index duration that is contributed by each sector in the index.

Quality spread duration contribution: The manager should match the proportion of the index duration that is contributed by each quality in the index, where quality refers to categories of bonds by rating.

https://hoccfa.com/cfa-level-3/fixed-income-portfolios-aligning-risk-exposure.html
Aligning risk exposure:

– To avoid the costs associated with purchasing every bond in the index yet maintain the same risk exposures. The manager will usually hold a sample of the bonds in the index. One sampling techniques often utilized is stratified sampling (cell matching). Constructing a portfolio with risk exposures identical to the index, however, does not require the composition of the portfolio to be representative of the index. A portfolio can be constructed with exactly the same risk factor exposures as the index.

Duration: Effective duration (option-adjusted or adjusted duration) which is used to estimate the change in the value of a portfolio given a small parallel shift in the yield curve, is probably the most obvious risk factor to be measured. Due to the linear nature of duration, which makes it overestimate the increase or decrease in the value of the portfolio, the convexity effect is also considered.

Key rate duration: Where effective duration measures the portfolio’s sensitivity to parallel shifts in the yield curve, key rate duration measures the portfolio’s sensitive to twists in the yield curve.

The manager should also consider the present value distribution of cash flows (PVD) of the index used as the portfolio benchmark. PVD measures the proportion of the index total duration attributable to cash flows falling within selected time periods.

The present value of all cash flows from the index that fall in each period is divided by the present value of all cash flows (the benchmark market value) to determine the percentage of the total market value that is attributable to cash flows falling in each period.

The manager multiplies the duration of a given period by the percentage of cash flows falling in that period to arrive at the duration contribution for that period. Dividing the duration contribution for each time period by the benchmark duration yields PVD.

If the manager duplicates the benchmark PVD, the portfolio and the benchmark will have the same sensitivity to both shifts and twists in the yield curve.

Sector and quality percent: The manager should match the weights of both the sectors and qualities in the index.

Sector duration contributions: The manager should match the proportion of the index duration that is contributed by each sector in the index.

Quality spread duration contribution: The manager should match the proportion of the index duration that is contributed by each quality in the index, where quality refers to categories of bonds by rating.

Approaches for asset allocation

1. The Mean – Variance Optimization (MVO) approach

A significant drawback to generating an efficient frontier through traditional mean-variance optimization methods is the sensitivity of the frontier to changes in the inputs.
The input themselves (e.g., expected return, covariance) are estimates. Reliance on an efficient frontier developed through a traditional, single mean-variance optimization is questionable.

2. Resampled Efficient Frontier (REF)

– Michaud developed a simulation approach utilizing historical mean, variances, and covariances of asset classes, which combined with capital market forecasts, assumes they are fair representations of their expectations. His resampling technique is bases on a Monte Carlo simulation that draws from the distributions to develop a simulated efficient frontier.
– The simulation is run thousands of times, the efficient portfolio at each return level, and hence the resulting efficient frontier is the result of an averaging process.
– Rather than a single, sharp curve, the resampled efficient frontier is a blur. At each level of return is a simulated efficient portfolio at the center with a distribution of portfolios above and below it.
– The asset mix at any point on the resampled efficient frontier is an average of many portfolios thay might have been constructed to meet that return.
– By utilizing this resampled technique, a portfolio manager is able to judge the need for rebalancing.

Advantages:

– It utilizes an averaging process and generates an efficient frontier that is more stable than a traditional mean-variance efficient frontier. Small changes in the inputs variables result in only minor changes in the REF.
– Portfolios generated through this process tend to be better diversified.
– By comparing any asset mix of an existing portfolio to the range of asset mixed across the multiple portfolios on the REF that could have generated the required return, it is possible to see if the current mix is within the boundaries of what is acceptable.

Disadvatages:

Ther is no theoretical reasoning to support the contention that a portfolio constructed through resampling should be superior relative to another constructed through traditional mean-variance analysis.
In addition, like MVO, the inputs are often based on historical data that could lack current relativance.

3. Black – Litteman

With the same motivation as Michaud (resampling), Black Litterman developed two modes for dealing with the problem associated with estimation error, especially expected return:
– The unconstrained Black-Littlerman model (UBL)
– The Black-Litterman model (BL)
The assigned reading focuses primarily on BL (i.e., constrained for no short selling)

Approaches for asset allocation | CFA Materials 1. The Mean – Variance Optimization (MVO) approach A significant drawback to generating an efficient frontier through traditional mean-variance optimization methods is the sensitivity of the frontier to changes in the inputs. The input themselves (e.g., expected return, covariance) are estimates. ...

https://hoccfa.com/cfa-level-3/asset-allocation-2.html
Reading 18: Asset allocation
1. Specifying risk and return objectives
- The return objective for an individual’s or institution’s portfolio is based upon the size of the portfolio, long-term spending (liquidity) needs, the time horizon, and the maintenance of the principal.
- Investors can be placed into numerical categories of risk aversion using a rough approximation or through answers to questionnaires.
We can determine the utility – adjusted return the investor will realize from the portfolio:
Utility – adjusted return
2. Downside risk
- In addition to standard deviation as measure of risk (volatility), the acceptable level of risk can be stated in terms of downside risk measures such as short fall risk, semivariance, and target semivariance.
- Shortfall risk is the risk of exceeding a maximum acceptable dollar loss.
- Semi variance is the bottom half of the variance (the variance calculated using only the returns below the expected return).
- Target semi- variance is the semi-variance using some target minimum return, such as zero.
Roy’s Safety- First Measure is one of the oldest and most cited measures of downside risk:

Never tell anyone your plans, let show them your results instead! :)