Modern Portfolio Theory (Mpt) - AAII Milwaukee

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Tutorial from Milwaukee AAII mutual fund group on modern portfolio theory.

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  • http://en.wikipedia.org/wiki/Modern_portfolio_theory
  • http://en.wikipedia.org/wiki/Modern_portfolio_theory
  • http://www.morningstar.co.uk/uk/lc/article.aspx?lang=en-GB&articleID=55237&categoryID=240 The Pitfalls of MPT Statistics Alpha, Beta and R-squared: how meaningful is your use of these metrics? Muna Abu-Habsa | 05/03/2008 12:08 You can find a trio of modern-portfolio-theory statistics on most fund company fact sheets, and on the "Risk and Ratings" tab of our fund reports at Morningstar.co.uk. A quick glance at JPM UK Dynamic fund, for example, shows that it has a Beta of 1.21, an Alpha of 3.87, and an R-squared of 84.04. So what does this all mean, if anything? To start, you need to have a brief understanding of the basic assumptions of Harry Markowitz’s modern portfolio theory (MPT), which was thought to be the be-all and end-all of portfolio analysis in the 1950s but has come under fire more recently. To recap, the underpinnings of the theory are twofold. First, it assumes that rational investors will demand a higher rate of return to invest in a riskier asset than they will to invest in a less risky asset. Second, the cornerstone of the theory is that diversifying your portfolio by adding securities (or funds) which do not behave in the same way reduces its overall risk--even if those securities individually are higher risk. Investors probably keep the above in mind while building their portfolios without always realising it. Your asset allocation is the direct result of your time horizon, risk tolerance and financial goal, and to achieve that goal timely you take on a certain level of risk. Furthermore, you may mix different investments that are weakly correlated in the aim of protecting the value of your portfolio under different market conditions --for example stock and bond markets don’t typically move in the same direction. The Trio: Alpha, Beta and R-Squared MPT statistics provide a snapshot of the portfolio’s returns versus the return of the benchmark index. Morningstar calculates these for each portfolio using a standard set of benchmarks for each asset group and three years worth of return history. For example, the benchmark used for funds in the Morningstar UK Large-Cap Blend category is the FTSE 100 category index, the benchmark for Morningstar Emerging Market Equity category is the MSCI Emerging Markets index, and so forth. We also provide a set of these statistics that are calculated relative to a fund's "best fit" index, or the index with which its returns show the highest degree of correlation. Beta is an expression of a fund's sensitivity to movements in the benchmark index. It is thus a measure of volatility, or risk, relative to the index. The beta of the benchmark is by definition 1 (because it is simply measuring the benchmark's volatility relative to itself). So, if beta is greater than 1 then that implies the fund has been more volatile – hence more risky-- than the index; a beta of less than one indicates lower volatility. With a three-year beta of 1.02, Invesco UK Equity has performed 2% better than its MSCI UK Value index in up markets and 2% worse in down markets. Alpha measures the difference between a fund's actual returns and its expected performance, given its level of risk (as measured by beta). A positive alpha figure indicates the fund has performed better than its beta would predict. In contrast, a negative alpha indicates a fund has underperformed, given the expectations established by the fund's beta. Some investors see alpha as a measurement of the value added or subtracted by a fund's manager, and it is often cited as such in the media. Morningstar publishes an alpha that looks at a fund's returns over the risk-free rate relative to the benchmark's returns over the risk-free rate, commonly known as Jensen's alpha. R-squared ranges from 0 to 100 and reflects the percentage of a fund's movements that are explained by movements in its benchmark index. An R-squared of 100 means that all movements of a fund are completely explained by movements in the index. Thus, index funds that invest only in FTSE 100 stocks will have an R-squared very close to 100. Conversely, a low R-squared indicates that very few of the fund's movements are explained by movements in its benchmark index. An R-squared measure of 35, for example, means that only 35% of the fund's movements can be explained by movements in its benchmark index. Therefore, if you already own a fund with a very high r-squared with the FTSE All Share, you might avoid buying another that correlates too closely to that index. Use with Care! As we've seen MPT statistics can help inform you about your fund's risks, value-added, and ability to diversify your portfolio. However, one needs to be careful about placing too much faith in them. First, they are based purely on past performance. Looking at funds with attractive alphas and betas does not imply they will behave the same way in the future. For example, a fund might have had a different manager or strategy during the period over which the statistics were calculated. Further, the market environment could change dramatically. Also, whenever you use alpha or beta, you need to be aware of the index used and the fund's R-squared with the index. Without getting too technical, these figure all rely on taking a scatter-plot graph of a fund's returns (vertical axis) against the benchmark's returns (horizontal axis) and drawing a straight line through the middle of the scatter that represents the best fit to all the points. The beta is the slope of the line, and alpha marks where the line intercepts the vertical axis--i.e., the fund's return when the benchmark's return is zero. The weak link is the "fit" of the line to the scatter-plot of returns, which is what R-Squared measures. If R-squared is low, it means the points are widely scattered around the line and therefore that beta and alpha are not good estimates of actual fund behaviour. Thus, if you look at alpha and beta without checking R-squared, you may be misled by the results. Look beyond the numbers MPT stats can be very useful, subject to the limitations described above. However, investors should remember to look beyond mere past performance when making investment decisions. There are many fundamental risks which may not be apparent from past performance. Credit risk is one notable example. In a strong credit environment, a bond fund laden with poorly rated credits may do just fine for years, but if the credit environment changes sharply, as it has recently, the fund could find itself in a world of pain. To learn more about how to evaluate risk, click here .
  • A similar presentation used May 2004 data. The total number of funds increased by 2009 so the scale is normalized to percent of funds for that year. If you believe that a Sharpe ratio of zero means the manager isn’t doing better than an index, then in 2004 every manager was good while in 2009 none of them were.
  • Modern Portfolio Theory (Mpt) - AAII Milwaukee

    1. 1. Modern Portfolio Theory Risk, Diversification, Asset Allocation, Alpha, Beta and R-squared AAII – Milwaukee Milwaukee Mutual Fund Group July 22, 2009
    2. 2. Investment didn’t work out?
    3. 3. Outline <ul><li>History and Concepts of MPT </li></ul><ul><li>Basic Measurements </li></ul><ul><li>Example of Use </li></ul><ul><li>Opposing Opinions and Methods </li></ul><ul><li>Further Reading </li></ul>
    4. 4. Modern Portfolio Theory (MPT) <ul><li>Seminal publication was: </li></ul><ul><ul><li>Markowitz, Harry M. (1952). &quot;Portfolio Selection&quot;. Journal of Finance 7 (1): 77–91. </li></ul></ul><ul><li>Markowitz (1929-) was awarded the Nobel Prize in Economics in 1990 for this work. </li></ul>
    5. 5. Modern Portfolio Theory (MPT) Modern portfolio theory (MPT) proposes how rational investors will use diversification to optimize their portfolios, and how a risky asset should be priced. MPT uses statistics to model an asset's (stock, bond, etc.) return and models a portfolio as a weighted combination of assets yielding a combined return. The resulting portfolio has an expected value (average) and a variance. Risk is defined to be the standard deviation (how much a value bounces around over time, a common statistical concept) of return.
    6. 6. Put Another Way <ul><li>MPT assumes that rational investors will demand a higher rate of return to invest in a riskier asset than they will to invest in a less risky asset. </li></ul><ul><li>The cornerstone of the theory is that diversifying your portfolio by adding securities which do not behave in the same way ( uncorrelated ) reduces its overall risk. </li></ul>
    7. 7. Types of Risk <ul><li>Systematic (market) Risk – Unavoidable. You can’t run. Inflation, war, etc. This explains 2008. </li></ul><ul><li>Non-systematic (specific, business) Risk – Bad quarter, patent expires, lawsuit, etc. Many types, each of which affect some investments but not others. </li></ul><ul><li>Total risk is the sum of the two. </li></ul><ul><li>Diversification reduces non-systematic risk. One stock dives due to a non-systematic risk event that doesn’t affect other stocks. </li></ul>
    8. 8. Diversification Reduces Some Risk Market (Systematic) Risk Inflation, war, global credit crisis Business (Specific, Non-Systemic) Risk Bad quarter, lawsuit Few stocks Many Stocks
    9. 9. Outline <ul><li>History and Concepts of MPT </li></ul><ul><li>Basic Measurements </li></ul><ul><li>Example of Use </li></ul><ul><li>Opposing Opinions and Methods </li></ul><ul><li>Further Reading </li></ul>
    10. 10. Acknowledgement <ul><li>Throughout this presentation you will see excerpts from copyrighted Morningstar Corporation materials, including their web site and Principia software. The information is current as of June, 2009. </li></ul><ul><li>The definitions are industry standard and are pretty much timeless. The data is specific to the time. It can (and often does!) change suddenly and dramatically. </li></ul>
    11. 11. MPT - Beta β <ul><li>“ Beta is a measure of a fund's sensitivity to market movements. The beta of the market is 1.00 by definition. Morningstar calculates beta by comparing a fund's excess return over Treasury bills to the market's excess return over Treasury bills. </li></ul><ul><li>So, a beta of 1.10 shows that the fund has performed 10% better than its benchmark index in up markets and 10% worse in down markets, assuming all other factors remain constant. Conversely, a beta of 0.85 indicates that the fund's excess return is expected to perform 15% worse than the market's excess return during up markets and 15% better during down markets.” </li></ul><ul><li>© 2006 Morningstar, Inc. All Rights Reserved. </li></ul><ul><li>It’s a high beta that keeps you up at night, but when used wisely and for long enough it will make you money. </li></ul>
    12. 12. MPT - Beta β <ul><li>“ The market” is an appropriate index. Usually S&P 500 for us. </li></ul><ul><li>Usually compared over previous 3 years. </li></ul><ul><li>If you can’t sleep at night, lower your β . </li></ul><ul><li>If volatility doesn’t bother you (e.g. you have a long time to be invested) raise your β to capture the upsides. </li></ul>
    13. 13.
    14. 14. MPT - Alpha α <ul><li>“ Alpha is a measure of the difference between a fund's actual returns and its expected performance, given its level of risk measured by beta. A positive alpha figure indicates the fund has performed better than its beta would predict . In contrast, a negative alpha indicates the fund is under performing given the expectations established by the fund's beta. </li></ul><ul><li>All MPT statistics (alpha, beta, and R-squared) are based on a least-squared regression of the fund's return over Treasury bills (called excess return) and the excess returns of the fund's benchmark index.” </li></ul><ul><li>© 2006 Morningstar, Inc. All Rights Reserved. </li></ul><ul><li>An alpha of 1.0 means the fund outperformed similar investments with identical risk by 1.0%. </li></ul>
    15. 15. MPT - Alpha α <ul><li>For a given value of β , higher α is better </li></ul><ul><li>Slang expression for a hot investment: “ Seeking Alpha ” </li></ul><ul><li>http://seekingalpha.com </li></ul>
    16. 16.
    17. 17. Sharpe Ratio <ul><li>&quot; [Sharpe Ratio] is calculated by using standard deviation and excess return to determine reward per unit of risk . The higher the Sharpe ratio, the better the fund's historical risk-adjusted performance.&quot; </li></ul><ul><li>© 2006 Morningstar, Inc. All Rights Reserved. </li></ul><ul><li>A Sharpe ratio of 0.0 means the manager isn’t adding value, 1.0 is good, >2.0 is outstanding. </li></ul>
    18. 18.
    19. 19. MPT - r-squared r 2 <ul><li>“ R-squared reflects the percentage of a fund's movements that can be explained by movements in its benchmark index. An R-squared of 100 indicates that all movements of a fund can be explained by movements in the index. </li></ul><ul><li>Thus, index funds that invest only in S&P 500 stocks will have an R-squared very close to 100. Conversely, a low R-squared indicates that very few of the fund's movements can be explained by movements in its benchmark index . Therefore, an R-squared measure of 35 means that only 35% of the fund's movements can be explained by movements in the benchmark index.” </li></ul><ul><li>© 2006 Morningstar, Inc. All Rights Reserved. </li></ul><ul><li>An r 2 less than about 80 means you can’t trust the other measures. </li></ul>
    20. 20. Correlation <ul><li>Correlation is the amount to which two investments act the same at the same time. </li></ul><ul><li>Morningstar uses the previous three years of prices to determine this. </li></ul><ul><li>Values range from -1 (highly correlated but in opposite direction) to 0 (no correlation) to 1 (highly correlated in same direction). </li></ul><ul><li>More about this in a few slides. </li></ul>
    21. 21. July, 2009 Note how cash (row 11) doesn’t correlate with anything. non-US (5, 6, 10) usually doesn’t track US much.
    22. 22. Efficient Frontier <ul><li>Every portfolio can be analyzed using past pricing as a guide to how much risk it has and how much it should return. </li></ul><ul><li>Efficient frontier is a picture showing the mix of investments that will give you the best return for the amount of risk you are willing to take on (or the mix of investments that will get you a certain return with the least amount of risk). </li></ul>
    23. 23. Low Risk High Risk Std Dev = 0 Std Dev = 35 Low Reward High Reward Ret = 1% Ret >= 15% Textbook Efficient Frontier Impossible Cash Invest Bond Junk Bonds Large Value Mid Cap Developing Markets Lottery Large Growth Commodities Non-US Large Cap
    24. 24. Summary <ul><li>Higher reward means higher risk (Roller coaster BUT make money over time) </li></ul><ul><li>High risk does NOT guarantee high reward (Roller coaster until you are broke) </li></ul><ul><li>Low risk and high reward is NOT possible (outside efficient frontier) </li></ul><ul><li>Select your risk, MPT finds best portfolio </li></ul>
    25. 25. In General… <ul><li>Higher alpha ( α ) is always better </li></ul><ul><li>The lower (more conservative) your personal risk tolerance, the lower your beta ( β ) should be. </li></ul><ul><li>The lower the r 2 the more difficult it is to apply MPT. </li></ul><ul><li>Higher Sharpe is always better. Sometimes interpreted as measuring the fund manager’s skill. </li></ul>
    26. 26. Outline <ul><li>History and Concepts of MPT </li></ul><ul><li>Basic Measurements </li></ul><ul><li>Example of Use </li></ul><ul><li>Opposing Opinions and Methods </li></ul><ul><li>Further Reading </li></ul>
    27. 27. S&P500 ETF (SPY) vs. S&P 500 <ul><li>SPDRs (SPY) </li></ul><ul><li>ETF tracking Standard & Poors 500 </li></ul><ul><li>Expect alpha of 0.0 – it tracks the index </li></ul><ul><li>Expect beta of 1.0 – it tracks the index </li></ul><ul><li>Expect r 2 of 100 – it tracks the index </li></ul><ul><li>Expect two to be identical </li></ul>
    28. 28. SPY and the S&P500 index are almost on top of each other
    29. 29. It tracks the index High correlation (r 2 = 100) of fund to index.
    30. 30. Ultra S&P500 Proshares (SSO) vs. S&P 500 <ul><li>Ultra S&P500 Proshares (SSO) </li></ul><ul><li>ETF tracking TWICE the S&P 500 </li></ul><ul><li>Expect alpha of ?? </li></ul><ul><li>Expect beta of 2.0 – it doubles the index </li></ul><ul><li>Expect r 2 of 100 – it tracks the index </li></ul><ul><li>Same general shape, but more volatile </li></ul>
    31. 31. SSO (blue) bounces in same direction at same time, but twice as far
    32. 32. <ul><li>Beta is 2.02. It meets its goal of doubling its index. </li></ul><ul><li>Note alpha is -5.86. It DOESN’T track the index. </li></ul><ul><li>Losing 50% today means you need to gain 100% tomorrow just to break even. Error compounds. </li></ul><ul><li>High correlation of fund to index. </li></ul>
    33. 33. Vanguard Total Bond Market Index Fund (VBMFX) vs. Barclays Capital U.S. Aggregate Bond Index <ul><li>“ The fund strives to approximate the performance of the Barclays Capital U.S. Aggregate Bond Index, which is a commonly used proxy for the broad, investment-grade U.S. bond market.” - Morningstar </li></ul><ul><li>Expect alpha of 0.0 – it tracks the index </li></ul><ul><li>Expect beta of 2.0 – it doubles the index </li></ul><ul><li>Expect r 2 of 100 – it tracks the index </li></ul><ul><li>Same general shape, but more volatile </li></ul>
    34. 34. <ul><li>VBMFX generally tracks its target and appropriate index, a broad based bond index. (green and blue on top of each other) </li></ul><ul><li>Both fund and index are very different from the Intermediate term bond index (orange) </li></ul>
    35. 35. <ul><li>Alpha is 0.05 – Tracks the index </li></ul><ul><li>Beta is 1 – Tracks the index movement exactly </li></ul><ul><li>r 2 is 99/100 – Tracks the index </li></ul>
    36. 36. <ul><li>VBMFX compared to S&P 500 </li></ul><ul><li>Very UN-correlated. Note drop in S&P500 in 2008/09 while bonds rose. Apples & Oranges. </li></ul><ul><li>Essence of MPT – Diversify and hold uncorrelated </li></ul>
    37. 37. <ul><li>SPDR (1) is highly (1.00) correlated to SSO (2) even though they are inverses. </li></ul><ul><li>SPDR (1) is poorly (0.28) correlated to VBIMX (3). Stocks vs. bonds. </li></ul><ul><li>SPDR (1) is highly (0.93) correlated to EFA (4). Domestic stocks vs. international. No longer a haven? </li></ul>
    38. 38. <ul><li>Solid returns, but less than market </li></ul><ul><li>Limited risk </li></ul><ul><li>Use of money (retirement?) out 10+ years </li></ul><ul><li>Domestic stocks, limited bonds </li></ul>Value Portfolio
    39. 39. Value Portfolio
    40. 40. For the same return of 10.47%, we could lower risk.
    41. 41. Re-allocate among underlying sectors.
    42. 42. <ul><li>Using the funds you specified (already own) this is the best re-allocation to meet your goal. </li></ul>
    43. 43. For the same risk of 20.54, we could raise return from 10.47% to 12.49%
    44. 44. Same risk, Higher return Lower risk, Same return
    45. 45. <ul><li>Value Portfolio </li></ul><ul><li>Correlation Matrix. How much do two funds move in the same direction at the same time? </li></ul><ul><li>Pretty high correlation all around. Mix it up a bit? </li></ul>
    46. 46. International Portfolio <ul><li>Greater than market returns </li></ul><ul><li>High risk </li></ul><ul><li>Use of money (retirement?) out 30+ years </li></ul><ul><li>Non U.S. stocks, limited bonds </li></ul>
    47. 47. International Portfolio
    48. 48. We’re almost on the frontier already!
    49. 49. Growth Portfolio <ul><li>Greater than market returns </li></ul><ul><li>High risk </li></ul><ul><li>Use of money (retirement?) out 30+ years </li></ul><ul><li>Domestic stocks, limited bonds </li></ul>
    50. 50.
    51. 51. Bond Portfolio <ul><li>Stable returns, less than stocks </li></ul><ul><li>Low risk </li></ul><ul><li>Use of money (retirement?) out 10+ years </li></ul><ul><li>Domestic bonds only </li></ul>
    52. 52.
    53. 53. Allocation Portfolio <ul><li>Stable returns – Morningstar Growth profile </li></ul><ul><li>Market risk </li></ul><ul><li>Attempt to overweight sectors that will outperform in the coming year </li></ul><ul><li>Domestic stocks only </li></ul>
    54. 54.
    55. 55. The Big Boys & MPT <ul><li>Big institutions use MPT but have to consider many other constraints. </li></ul><ul><li>Universe (domestic stocks, large caps, etc.) </li></ul><ul><li>Limit to amount in one stock or sector </li></ul><ul><li>Required minimum amount of cash </li></ul><ul><li>Minimize transaction costs </li></ul><ul><li>Minimize turnover (tax consequences) </li></ul>
    56. 56. Outline <ul><li>History and Concepts of MPT </li></ul><ul><li>Basic Measurements </li></ul><ul><li>Example of Use </li></ul><ul><li>Opposing Opinions and Methods </li></ul><ul><li>Further Reading </li></ul>
    57. 57. Drawbacks <ul><li>MPT is still very mainstream, but the cracks have appeared. “Post MPT Movement” PMPT </li></ul><ul><li>Recall the phrase rational investor ? In fact, emotions and psychology are important, especially for us little guys. </li></ul><ul><li>MPT uses past performance to predict future performance. Didn’t you read the prospectus? </li></ul>
    58. 58. Sortino Ratio <ul><li>Equating risk to volatility means going up suddenly is as bad as going down. Yet, upside “risk” movement is usually welcome. </li></ul><ul><li>The Sortino Ratio is similar to the Sharpe ratio, but only considers value going down as risk. Going up suddenly is not figured in. </li></ul><ul><li>Very difficult to find a source for values, especially for free. </li></ul><ul><li>Mostly an academic concept? </li></ul>
    59. 59. &quot;Stock-market losses are only losses on paper. Use Wite-Out to your advantage.&quot; - The Onion
    60. 60. Further Reading <ul><li>http://www.morningstar.com/ </li></ul><ul><li>http://www.aaii.com/ </li></ul><ul><li>http://www.travismorien.com/FAQ/portfolios/mptcriticism.htm </li></ul><ul><li>http://www.wisegeek.com/what-is-modern-portfolio-theory.htm </li></ul><ul><li>http://en.wikipedia.org/wiki/Post-modern_portfolio_theory </li></ul>

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