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Similar to Modern Portfolio Theory (Mpt) - AAII Milwaukee
Similar to Modern Portfolio Theory (Mpt) - AAII Milwaukee (20)
Modern Portfolio Theory (Mpt) - AAII Milwaukee
- 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?
- 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.
- 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
- 21. July, 2009 Note how cash (row 11) doesn’t correlate with anything. non-US (5, 6, 10) usually doesn’t track US much.
- 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
- 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.
- 31. SSO (blue) bounces in same direction at same time, but twice as far
- 39. Value Portfolio
- 40. For the same return of 10.47%, we could lower risk.
- 41. Re-allocate among underlying sectors.
- 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
- 48. We’re almost on the frontier already!
- 59. "Stock-market losses are only losses on paper. Use Wite-Out to your advantage." - The Onion
Editor's Notes
- 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.