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- 1. Modern Portfolio Theory Risk, Diversification, Asset Allocation, Alpha, Beta and R-squared AAII – Milwaukee Milwaukee Mutual Fund Group July 22, 2009
- 2. Investment didn’t work out?
- 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. Modern Portfolio Theory (MPT) <ul><li>Seminal publication was: </li></ul><ul><ul><li>Markowitz, Harry M. (1952). "Portfolio Selection". 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. 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. 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. 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. 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. 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. 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. 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. 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.
- 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. 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.
- 17. Sharpe Ratio <ul><li>" [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." </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.
- 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. 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. July, 2009 Note how cash (row 11) doesn’t correlate with anything. non-US (5, 6, 10) usually doesn’t track US much.
- 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. 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. 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. 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. 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. 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. SPY and the S&P500 index are almost on top of each other
- 29. It tracks the index High correlation (r 2 = 100) of fund to index.
- 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. SSO (blue) bounces in same direction at same time, but twice as far
- 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. 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. <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. <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. <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. <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. <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. Value Portfolio
- 40. For the same return of 10.47%, we could lower risk.
- 41. Re-allocate among underlying sectors.
- 42. <ul><li>Using the funds you specified (already own) this is the best re-allocation to meet your goal. </li></ul>
- 43. For the same risk of 20.54, we could raise return from 10.47% to 12.49%
- 44. Same risk, Higher return Lower risk, Same return
- 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. 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. International Portfolio
- 48. We’re almost on the frontier already!
- 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.
- 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.
- 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.
- 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. 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. 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. 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. "Stock-market losses are only losses on paper. Use Wite-Out to your advantage." - The Onion
- 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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