1 / 25

Measuring a Portfolio s Risk Profile by Frank J. Fabozzi

Chapter 17 Measuring a Portfolio's Risk Profile. Major learning outcomes:Explain why the standard deviation is used as a measure of risk and explain its limitations as a measure of risk for bonds.Discuss the alternative measures of risk that focus on downside risk

garren
Download Presentation

Measuring a Portfolio s Risk Profile by Frank J. Fabozzi

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

    1. Measuring a Portfolio’s Risk Profile by Frank J. Fabozzi

    2. Chapter 17 Measuring a Portfolio’s Risk Profile Major learning outcomes: Explain why the standard deviation is used as a measure of risk and explain its limitations as a measure of risk for bonds. Discuss the alternative measures of risk that focus on downside risk—target semivariance and shortfall risk—and the difficulties that arise when using these risk measures for bonds. Explain why it is important to compare the risk profile of a portfolio to the risk profile of a bond market index.

    3. Key Learning Outcomes Describe tracking error. Explain the difference between actual and predicted tracking error. Compute the duration of a portfolio and a bond market index. Compute the contribution to portfolio duration and the contribution to benchmark index duration. Describe yield curve risk and how it can be quantified.

    4. Key Learning Outcomes Define spread duration. Identify the different types of spread duration measures. Compare the spread duration exposure of a portfolio with the spread duration of a benchmark index. Describe sector risk and how it can be quantified. Explain how call and prepayment risk can be measured.

    5. Key Learning Outcomes Describe the types of prepayment risk associated with investing in mortgage-backed securities and how these risks can be measured. Describe a multi-factor risk model and how it is used to quantify the risk exposure of a portfolio and a benchmark index. Discuss the different types of risk in a multifactor risk model. Explain the role of tracking error in a multifactor risk model.

    6. Portfolio Risk Profile Standard deviation and the variance are measures of the variability of returns Standard deviation is used as a more understandable measure of the degree of dispersion It is assumed that the underlying probability distribution is normal distribution – the distribution is symmetric around the expected (average) value To apply normal distribution, it is necessary to assess whether a historical distribution is normally distributed

    7. Portfolio Risk Profile Bond returns: Lower limit on the loss: reflecting how high interest rates can rise Treasury rates have never exceeded 15% Maximum return: maximum price of the bond is the undiscounted value of the cash flows, assuming that negative interest rates are not possible.

    8. Portfolio Risk Profile Downside risk measures – the focus is only on that portion of the investment’s return distribution that is below a specified level. For downside risk measures, portfolio managers define target returns, and returns less than the target represent adverse consequences. The three more popular downside risk measures are: - Target semivariance - Shortfall probability - Value at risk

    9. Portfolio Risk Profile Downside risk measures Target semivariance – measure of the dispersion of the outcomes below the target return. This measure is not used in bond portfolio management extensively because of ambiguity, poor statistical understanding, and difficulty of forecasting.

    10. Portfolio Risk Profile Downside risk measures Shortfall risk – the probability that an outcome will have a value less than a target return. The measure fails to consider the magnitude of the losses below the target return. This measure also has the problems of the target semivariance.

    11. Portfolio Risk Profile Downside risk measures Value at risk – a target probability is specified; and the return will not fall below a yet-to-be determined value the percentage of time represented by the target probability.

    12. Portfolio Risk Profile Portfolio variance To estimate the portfolio variance we need: The variance of each bond The covariance of each pair of bonds

    13. Portfolio Risk Profile Portfolio variance Problems with this measure: Requires extremely large number of estimated inputs as the number of bonds in the portfolio increases In order to estimate these values, the portfolio manager needs historical data for which there are not many sources.

    14. Tracking Error Tracking error is used to analyze performance relative to a benchmark such as bond market index. Tracking error measures the risk of a portfolio relative to the risk of the benchmark index. The observation used in calculating tracking error is active return: Active return = portfolio’s return – benchmark index’s return Tracking error is the standard deviation of the portfolio’s active return

    15. Tracking Error Tracking error is used in two ways: Actual tracking error – the tracking error actually realized by a portfolio Predicted tracking error – used when constructing a portfolio to assess its probable risk profile relative to a benchmark index. When to use tracking error: Predicted tracking error is used when constructing a portfolio and analyzing its risk profile Actual tracking error is used to evaluate the performance of the bond portfolio manager.

    16. Measuring Interest Rate Risk Portfolio’s duration measures the portfolio’s exposure to changes in the level of interest rates, assuming parallel shift in the yield curve. Both modified and Macaulay durations fail to consider changes in cash flows when interest rates change, which is limitation when measuring exposure of bonds with embedded options. Effective duration, or option-adjusted duration, takes into account changes in interest rates and is the appropriate measure for bonds with embedded options.

    17. Measuring Interest Rate Risk Calculating portfolio’s duration Calculate the duration for each individual bond in the portfolio Calculate the weighted average of the durations of the bonds in the portfolio The effective duration of a bond market index can be computed in the same way

    18. Measuring Interest Rate Risk A better measure of exposure to an individual issue or sector is its contribution to portfolio duration or contribution to benchmark index duration: Contribution to portfolio duration = weight of issue or sector in portfolio x duration of issue or sector Contribution to benchmark index duration = weight of issue or sector in benchmark index x duration of issue or sector Convexity – provides an improved estimate on the portion of the effect on the change in value when interest rates change that is not explained by duration.

    19. Measuring Yield Curve Risk Duration does not indicate the exposure of a portfolio or a benchmark index to changes in the shape of the yield curve.

    20. Measuring Yield Curve Risk The effect of exposure of a portfolio to changes in the yield curve can be gauged by analyzing the distribution of the present values of the cash flows for the portfolio or by computing the key rate durations of the portfolio. Key rate duration is the sensitivity of the portfolio’s value to the change in a particular key spot rate.

    21. Other Risks Spread risk – the risk that the price of a bond changes due to change in spreads. Spread duration – a measure of the exposure of the portfolio to changes in spreads Types of spread duration measures Nominal spread Zero-volatility spread Option-adjusted spread

    22. Other Risks The spread duration for a portfolio is computed as a market weighted average of the spread duration for each sector. Credit risk of a portfolio can be gauged by the allocation of each rating Optionality risk – change in interest rates changes the value of the embedded option, which in turn changes the value of the bond.

    23. Risks of Investing in MBS Sector risk – MBS sector is divided into several subsectors based on the coupon rate, which has an impact on prepayments and therefore on the spread at which MBS trades relative to Treasuries.

    24. Risks of Investing in MBS Prepayment risk – the risk of an adverse price change due to changes in expected prepayments Prepayment sensitivity – the basis point change in the price of an MBS for a 1% increase in prepayments Convexity risk

    25. Multi-factor Risk Models Multi-factor risk models can be used to quantify the risk exposure of a portfolio. Multi-factor risk models seek to determine the major risks that contribute to the predicted tracking error

    26. Multi-factor risk models Systematic risks Term structure risk – the portfolio’s exposure to changes in the general level of interest rates in terms of parallel/nonparallel shift in the yield curve Non term structure risk – include sector risk, optionality risk, coupon risk and MBS risk Non-systematic risk, or residual risk, include risks that are issuer and issue specific. This is the risk resulting from exposure to specific issuers or issues that is greater than the exposure of the benchmark index.

More Related