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)

Active Management vs. Passive Management

7 8 9 10 11 12 Yearly Return (%)

w/o Costs with Costs

mgmt costs

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

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Indexation Model

kx

Mxx

LiqMinxLiquidityts

xError

i

i

0#

0,1

)(..

ns)IndexRetur,rns*(AssetRetumin

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+ 0 13 1

Between 50 & 100 13 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