1 Indexed Funds as Passive Investment Tools LARRAINVIAL Sergio Lucero V. Quantitative Analyst LarrainVial FIAP Santiago May 2006

2 Introduction Active funds tend to underperform their benchmarks in the long run, particularly when costs are taken into account Malkiel (2003) shows results for the US and Euro markets, both in fixed income and equities backing this fact (market efficiency) Our study explores indexation in Chilean equities and fixed income (IPSA, LVACLC, LVACLG) Market Return

3 Results in Developed Markets Median Return 10 yrs15 yrs20 yrs Large Cap Equity Funds10.98%11.95%13.42% S&P 500 Indexed Fund12.94%13.74%15.24% 1 YR5 YRS10 YRS 71% 69% 59% 0% 10% 20% 30% 40% 50% 60% 70% 80% European Funds underperforming MSCI Europe

4 Indexation Model Combinatorial (hard) optimization problem, either linear or quadratic depending on the chosen error function Model considers liquidity and efficiency, since it limits the number of liquid assets present in the approximating portfolio Additional properties of the underlying index can be sought after (duration, sector balance, currencies)

5 Fixed Income Indexation Lack of information solved by the birth of LVA Indices (2005) Low liquidity persists in this rigid market MBS Index too large to handle (yet) Days traded 2005CorpGobMBS Between 50 & Between 1 and TOTAL available instruments

6 Indexation Results for LVACLC (Corporate Bonds) and LVACLG (Government Bonds)

7 IPSA (Equities) Indexation Results Following a market cap weighted index is a tougher problem (without constant rebalance) We detect a need to find a better index for the Chilean Equity Market