Portfolio

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Assignment Portfolio Theory and Management
Individual Assignment
Introduction
This report exams the performance of fund 49 from different perspectives. Then, I composed a portfolio for client Jim using fund 49 and other four asset classes. The report contains five parts, first part identifies the style of fund 49 and pick out its corresponding benchmark. Second part conducts performance evaluation by different ratios. Third part compares fund 49 and fund 50 from different aspects. Forth part exams whether Jim’s objectives under some assumptions can be achieved or not and also provides possible alternative scenarios to him. 1. If we want to know the fund style, we should use different style benchmarks to exam what my fund style is. Usually, according to factor model, we should run regression between Rf and six benchmarks together and exam the relationship between my fund and six benchmarks. Then we constrain α=0, Ʃβi=1 and 0<βi<1. So picking out the largest and most significant β is the way to define the fund style. Rf=α+βL-B*FL-B+βL-G*FL-G+βL-V*FL-V+ΒM/S-B*FM/S-B+ΒM/S-G*FM/S-G+ ΒM/S-V*FM/S-V+ Ɛ Unlike U.S financial market which contains substantial difference between value and growth, in Australian, the different styles have high correlation with each other. So we can just use Jensen measure involves running regressions between six different Australian Equity Benchmarks less risk free rate (cash) and my fund 49 less risk free rate respectively. Rp -Rf= α+ β *( RBM - Rf) + Ɛ

Here we assume cash return is the risk free rate because cash has the relatively low variance or volatility. The results show Australia Mid/Small Blend provides the largest R square (0.97088). That means fund 49 has the highest match level with the Australia Mid/Small Blend compared with other five benchmarks. So Australia Mid/Small Blend can be determined as the Benchmark of fund 49. (Appendix A) 2. Some data such alpha, beta, tracking error can be known from the regression result while other data can be calculated. All the results are quarter figures. (Appendix B) Jensen Alpha = α=0.23 Sharpe=(Rp-Rf)/ σ(Rp-Rf)=0.197 Treynor=(Rp-Rf)/ β=1.793 Tracking Error=SE=1.58 Information Ratio= α /SE=0.1455

Based on the all statistic data of fund 49, we can exam its performance. Fund 49 have β approximately equal to 1, abnormal return (α) is 0.23 which is quite low and t-stat of α is lower than 2 which means α is insignificant and cannot produce abnormal return constantly. As for tracking error, it is not too big (1.58%). These three indicators can demonstrate the Benchmark-- Australia Mid/Small Blend is proper and fund 49 performance seems satisfied. As for Sharpe ratio and Information Ratio, they are not very high. While to further evaluate fund 49, I need compare fund 49 and fund 50. 3. For fund 50 (Appendix C), the sensitive of fund 49 is highly related with style benchmark because R2 =97% and β approximately equal to 1. They all cannot acquire abnormal return constantly. Tracking error of fund 50 much higher and R2 = 0.647 is lower than fund 49 that illustrates fund 50 is another style (Australia Large Value). Sharpe ratio and Treynor ratio all preformed a little better of fund 50 than fund 49. Treynor ratio measures average excess return for each systematic risk while Sharpe ratio measures average excess return for total risk. Both of the two funds has low information ratio. From the above analysis it illustrates fund 49 is a passive fund management simply replicating benchmark—Australia Mid/Small Blend. The average return of fund 49 is higher (3.01%) than fund 50 (2.49%) but also has a larger volatility (standard deviation is 9.14%) than fund 50 (6.45%) which means fund 49 should bear more risk. But we cannot say fund 49 outperforms fund 50. Because they are belongs to different equity styles and replicate with their own style’s benchmarks. To evaluate their performance should be against...
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