QUT | Case Study 4: Market Efficiency | Bill Miller and Value Trust | | Name: Huey Ngu
Student ID: 08324093Tutor Name: David FairDate: 1 November 2013 | Words: 1097 |

Contents Introduction 2 Past and current performance of Value Trust 2 Investment strategy of Bill Miller 3 Efficient Market Hypothesis 3 Bill Miller’s letter to shareholders 4 Changes in Chief Investment Officer (CIO) 4 Recommendation and Conclusion 4 Reference 6 Appendices 8 Appendix A: Data of LMVTX, S&P 500, and 30 years bond 8 Appendix B: Alpha and Beta between 1991 and 2013 9 Appendix C: Alpha and Beta between 1991 and 2005 9 Appendix D: Alpha and Beta between 2006 and 2013 9

Introduction
Bill Miller is known as famous fund manager that hold the record of beating benchmark index for 15 years in a row. However, his poor performance after 2005 was the reason that the investors run away from his fund. Hence, arguments of whether Bill Miller’s previous performances involve luck or skills appear. Furthermore, this report will also discuss whether investors should invest in Bill Miller’s Value Trust.
Past and current performance of Value Trust

Figure [ 1 ]: LMVTX VS S&P500 (Morningstar Principia , 2013)
Bill Miller had made an achievement of longest streak performance of beating the market. Refer to figure 1, it had showed that Bill Miller’s Value Trust had consistently beat the benchmark index of Standard & Poor’s 500 (S&P 500) between 1991 and 2005, 15 years in a row. In 1998, Value Trust had the best performance, which had total return of 48.04% and outperformed S&P 500 around 20%. Moreover, between the periods, the average total return of Value Trust was 18% while S&P 500 was 13%. Betas of 1.16 indicate that Value Trust is 16% more volatile than the market (Appendix C).
However, everything was changed after 2006. Bill Miller’s Value Trust did not beat S&P 500, which end its longest streak. It had also encounter financial crisis in 2008 which cause them suffered huge losses. It had loss about 55% of total return by comparing to S&P 500 which had loss about 36.55%, an 18.45% gap between them. Betas of 1.38 indicate that Value trust is 38% more volatile than the market after 2006 (Appendix D). By comparing to the period between 1991 and 2005, it has higher sensitivity after 2006.
Investment strategy of Bill Miller
Bill Miller is an aggressive fund manager, who is willing to take risks in order to make huge profit. He weight profit higher than risk as he argue that investors will not recover from mistakes if they are making small returns (Davy, 2009). Furthermore, he invests in the market which has least promising outlook (Bruner, Eader, & Schill, 2010). For example, he invests in technology industry when most of the investors shied away due to the difficulty of valuation (Zweigh, 2007). He also argue that if investors believe stock’s future returns will goes up, then they should invest more now even if the current stock price has drop (Bruner et al., 2010). Additionally, he diversified his portfolio by holding only three dozen stocks at a time (Lauricella, 2008).
By comparing to Warren Buffett’s investment strategy, there are differences between them. Firstly, Warren Buffett avoids risk and weight risk higher than profit (Bruner et al., 2010). He will not invest in the market that he does not understand, such as technology industry as he defined risk as “not knowing what you are doing” (Bruner et al., 2010). Moreover, he disagrees with portfolio diversification. He argues that investors should invest in the market they fully understand in order to avoid risk. When no risk involve, portfolio diversification is not required (Bruner et al., 2010).
Efficient Market Hypothesis
According to Eugene Fama (1970), Efficient Market Hypothesis (EMH) suggests the idea of stock prices will reflect all information and no abnormal profit will be made. However, there is evidence such as “book/price” strategy and “specific-return-reversal” strategy shows that markets are inefficiency (Rosenberg, Reid, & Lanstein, 1985). Moreover, it is impossible to achieve perfect efficient market as it is based on unrealistic assumption (Martial Capital, 2007). If EMH hold, then Bill Miller will not be able to outperform S&P500 for 15 years unless he contains superior skills or luck.
Alpha is equal to 0 if EMH hold, which mean that there will be no abnormal return (Koba, 2012). According to appendix B, the alpha not equal to 0 had indicates that the market is inefficient between 1991 and 2013. However, it is suggested that investors should not invest in Bill Miller Value Trust because it has generate negative alpha since 2006 (Appendix D).
Therefore, it is likely that the market is inefficient because Bill Miller had earned abnormal profit. It is believed that his performance has mix of skills and luck. Without skills, he will not be able to beat the market in long run, which is the period between 1991 and 2005. However, the failure of dealing with financial crisis had shown that his superior performance between 1991 and 2005 involve luck.
Bill Miller’s letter to shareholders
Bill Miller’s Value Trust performs poorly during the financial crisis in 2008 and suffered with huge losses. As mentioned in his letters to shareholders, he had underrated the power of financial crisis and led to wrong investment strategy as he takes risk and continue to invest when the stock price had drop dramatically (Miller, 2008). He also mentioned in his letter that it is the best time to invest Value Trust when they are experience difficulty (Miller, 2008). For example, in 2009, Value Trust had outperformed S&P 500 which proves that his investment strategy of focus on pessimistic markets seems working when investors capitalize in Value Trust in 2008. However, this may cause by luck rather than skill as it only outperformed the market in short term. Moreover, he stated that financial crisis will end and led to future growth of US stock market (Miller, 2008). Therefore, this shows that he has confidence in the future.
Changes in Chief Investment Officer (CIO)
In 2012, Legg Mason Value Trust had changed their CIO to Sam Peters, after Bill Miller had lost his reputation since 2006 (B.Henriques, 2011). Both of them have share similar investment strategy such as invest in low price and focus on pessimistic markets (J.Kim, 2010). Hence, future performance of Value Trust is expected to be similar, disregard who is the CIO of Value Trust. Furthermore, Sam Peters weight luck heavier than skills when determines the outcomes (Kerber & Pressman, 2011). Even though he had beat S&P 500 for last 12 months, however, future returns will be unstable if he pick stocks just by luck and lack of skills (Ambrose, 2013).
Recommendation and Conclusion
As a conclusion, Bill Miller’s performances involve the mix of skill and luck. Without skill or luck, it is impossible for him to outperform the market in long run. His investment strategy is differing to Warren Buffett as he is willing to take risks in order to make enormous profits. It is not recommend the investors to invest in Bill Miller’s Value Trust because his performances after the financial crisis in 2008 are mainly based on luck, which mean that future returns of Value Trust will be unstable.

Reference
Ambrose, E. (2013, June 29). Legg Mason's flagship Value Trust fund no longer lagging. Retrieved from The Baltimore Sun: http://articles.baltimoresun.com/2013-06-29/business/bs-bz-peters-20130629_1_value-trust-legg-mason-capital-management-sam-peters
B.Henriques, D. (2011, November 17). Star Manager Giving Up Legg Mason Fund. Retrieved from The New York Times: http://www.nytimes.com/2011/11/18/business/star-manager-giving-up-legg-mason-fund.html?_r=0
Bloomberg L.P. (2013). United States Government Bonds. Retrieved from Bloomberg: http://www.bloomberg.com/markets/rates-bonds/government-bonds/us/
Bruner, R. F., Eader, K. M., & Schill, M. J. (2010). Case studies in finance: managing for corporate value creation. Boston: McGraw-Hill Irwin.
Davy. (2009, October 14). Contrast in Aproach: Bill Miller vs. Warren Buffett. Retrieved from The Enlightened American: http://enlightened-american.com/2009/10/14/contrast-in-approach-bill-miller-vs-warren-buffett
F.Fama, E. (1970). Efficient Capital Markets: A review of theory and empirical work. The Joutnal of Finance, 384.
J.Kim, J. (2010, May 21). Legg Mason Names Successor for Bill Miller. Retrieved from The Wall Street Journal: http://online.wsj.com/news/articles/SB10001424052748704167704575258823512076924
Kerber, R., & Pressman, A. (2011, November 17). Analysis: Bill Miller's fall shows luck at play in investing. Retrieved from Reuters: www.reuters.com/article/2011/11/18/us-leggmason-miller-luck-idUSTRE7AH03G20111118
Koba, M. (2012, January 19). Alpha and Beta: CNBC Explains. Retrieved from CNBC: http://www.cnbc.com/id/45777498
Lauricella, T. (2008, December 10). The Stock Picker's Defeat. Retrieved from The Wall Street Journal: http://online.wsj.com/news/articles/SB122886123425292617
Martial Capital. (2007, August 29). What About the Efficient Market Hypothesis? Retrieved from Martial Capital: http://www.martialcapital.com/pdf/Martial_Whitepaper_Efficient_Market_Hypothesis_002.pdf
Miller, B. (2008, July 27). 2Q 2008 Bill Miller commentary.
Miller, B. (2008, November 12). 3Q 2008 Bill Miller Commentary.
Morningstar Principia . (2013, June 30). History-table. Retrieved from Morningstar Principia
Rosenberg, B., Reid, K., & Lanstein, R. (1985). Persuasive evidence of market inefficiency. The Journal of Portfolio Management, 9-16.
Zweigh, J. (2007, July 18). Bill Miller: What's luck got to do with it? Retrieved from CNN Money: http://money.cnn.com/2007/07/17/pf/miller_interview_full.moneymag/

Appendices
Appendix A: Data of LMVTX, S&P 500, and 30 years bond Years | LMVTX | S&P 500 | Risk Free Rate (30 years bond rates) | Abnormal Return (LMVTX-S&P 500) | Risk Premium (S&P 500 – Risk Free Rate) | 1991 | 34.73% | 30.47% | 3.63% | 31.11% | 26.85% | 1992 | 11.44% | 7.62% | 3.63% | 7.82% | 4.00% | 1993 | 11.26% | 10.08% | 3.63% | 7.64% | 6.46% | 1994 | 1.39% | 1.32% | 3.63% | -2.24% | -2.31% | 1995 | 40.76% | 37.58% | 3.63% | 37.14% | 33.96% | 1996 | 38.43% | 22.96% | 3.63% | 34.81% | 19.34% | 1997 | 37.05% | 33.36% | 3.63% | 33.43% | 29.74% | 1998 | 48.04% | 28.58% | 3.63% | 44.42% | 24.96% | 1999 | 26.71% | 21.04% | 3.63% | 23.09% | 17.42% | 2000 | -7.14% | -9.10% | 3.63% | -10.77% | -12.73% | 2001 | -9.29% | -11.89% | 3.63% | -12.92% | -15.52% | 2002 | -18.92% | -22.10% | 3.63% | -22.55% | -25.73% | 2003 | 43.53% | 28.69% | 3.63% | 39.91% | 25.07% | 2004 | 11.96% | 10.88% | 3.63% | 8.34% | 7.26% | 2005 | 5.32% | 4.91% | 3.63% | 1.70% | 1.29% | 2006 | 5.85% | 15.79% | 3.63% | 2.23% | 12.17% | 2007 | -6.66% | 5.49% | 3.63% | -10.29% | 1.87% | 2008 | -55.05% | -36.55% | 3.63% | -58.68% | -40.18% | 2009 | 40.64% | 26.46% | 3.63% | 37.02% | 22.84% | 2010 | 6.67% | 15.06% | 3.63% | 3.05% | 11.44% | 2011 | -4.00% | 2.11% | 3.63% | -7.63% | -1.52% | 2012 | 15.09% | 16.00% | 3.63% | 11.47% | 12.38% | 2013 | 15.00% | 13.82% | 3.63% | 11.38% | 10.20% |
(Bloomberg L.P., 2013); (Morningstar Principia , 2013)

Appendix B: Alpha and Beta between 1991 and 2013 Summary Output | | | | | | | | | Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | Intercept | -0.003 | 0.017 | -0.162 | 0.873 | -0.039 | 0.033 | -0.039 | 0.033 | Risk Premium | 1.276 | 0.089 | 14.275 | 0.000 | 1.090 | 1.462 | 1.090 | 1.462 | | | | | | | | | | Alpha | -0.003 | | | | | | | | Beta | 1.276 | | | | | | | |

Appendix C: Alpha and Beta between 1991 and 2005 Summary Output | | | | | | | | | Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | Intercept | 0.04 | 0.02 | 2.41 | 0.03 | 0.00 | 0.07 | 0.00 | 0.07 | Risk Premium | 1.16 | 0.08 | 14.06 | 0.00 | 0.98 | 1.33 | 0.98 | 1.33 | | | | | | | | | | Alpha | 0.04 | | | | | | | | Beta | 1.16 | | | | | | | |

Appendix D: Alpha and Beta between 2006 and 2013 Summary Output | | | | | | | | | Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | Intercept | -0.06 | 0.03 | -2.48 | 0.05 | -0.13 | 0.00 | -0.13 | 0.00 | Risk Premium | 1.38 | 0.14 | 9.68 | 0.00 | 1.03 | 1.73 | 1.03 | 1.73 | | | | | | | | | | Alpha | -0.06 | | | | | | | | Beta | 1.38 | | | | | | | |