1. LARRAINVIAL Indexed Funds as Passive Investment Tools Sergio Lucero V.
Quantitative Analyst
LarrainVial
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 yrs
15 yrs
20 yrs
Large Cap Equity Funds
10.98%
11.95%
13.42%
S&P 500 Indexed Fund
12.94%
13.74%
15.24%
1 YR
5 YRS
10 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 2005
Corp
Gob
MBS
100+ 13 1
Between 50 & 100 17 22
Between 1 and 50
358
934
5057
TOTAL available instruments
433
1254
13350

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