There seems to be a large amount of interest in fund of funds vehicles nowadays.I am wondering how constructing a portfolio of hedge funds would differ from constructing a stock and bond portfolio, say. Does Markowitz theory apply?I have the feeling that a fund should be viewed as an option on macro level factors (such as volatility, etc.) and a fund of funds should be managed like an option book. For example, investing in a CTA would give you long vega exposure. Any help, references or suggestions?Thanks in advance,Hari

...fund should be viewed as an option on macro level factors...that's an interesting idea. i think the investing style of the funds would be key, and there's obviously considerable disparity here. some (e.g. long/short or market neutral) seem more akin to mutual funds, albeit with added flexibility, while others (e.g. global macro) seem, intuitively, a lot more option-like, as you suggest. i know jp morgan fleming have a fund of funds for private clients, but i don't know how it's run. i heard deutsche bank actually offer a hedge fund ISA! (a UK tax-empt Individual Savings Account). i can't think of any references i'm afraid. regards, jungle

"I am wondering how constructing a portfolio of hedge funds would differ from constructing a stock and bond portfolio, say. Does Markowitz theory apply?"I have a very naive question: Has the optimisation problem for a portfolio of stocks/bonds and options been solved? Even at a level analogous to that of Markowitz theory for stocks and bonds alone? If yes, where can I read about that?

Q1 "I am wondering how constructing a portfolio of hedge funds would differ from constructing a stock and bond portfolio, say. Does Markowitz theory apply?"

As far as I know most use a multi-manager type methodology. This
is similar to strategic asset allocation where instead of the usual
asset classes a broad range of hedge funds are combined with
risk constraints. Typically Return-VaR type optimizations as MV
theory does not help much because of the strong non-Gaussian
nature of the returns on these funds, in addition many hedge funds
have very short histories making risk analysis tricky, most of the
databases also suffer from survivor bias. A good hedge fund multi-
manager is very efficient if well constructed and suppose alot of
fun to model. These seem to be about style diversification and
requires choosing a fairly homogenous opportunity set, enough data to
bootstrap the risk measures and a good style neutral benchmark
to shoot for.

Q2 : "I have a very naive question: Has the optimisation problem for a portfolio of stocks/bonds and options been solved? Even at a level analogous to that of Markowitz theory for stocks and bonds alone? If yes, where can I read about that?"

I have not seen this explicitly dealt with in the literature but
there are many know ways of doing this sort of thing. There are
also some papers, such as the one by Haugh and Lo which get pretty
close to it. Typically they all boil down to getting the correct
utility function in order to deal with the non-normality. The game
is to maximize the utility within numerical noise and risk bounds
over a given buy-hold horizon, you got to have at least four moments
to get things to look believable. Noise is a real problem because
of the combination of non-Normality and optimizations. The
optimizations need to be quick which pretty much rules out most
GA's and Monte-Carlo type methods unless you have some serious
hardware, SQP and simulated annealing corrected SQP works pretty
well as long as the optimizations are heavily resampled in order
to smooth-out the corner solutions found at low and high
risk thresholds. These are typically pretty big optimizations
which are really sensitive to the initial conditions. I have seen
some references on Viablity theory which can be potentially useful
in this regard, do not know much about the details though. Mertons
book on continous time finance is quite thorough with utility
functions, The idea is that constant relative risk aversion is good
for myopic traders and constant absolute risk aversion for
institutional investors.


Tim

In 90th the idea of indexing became very popular. Indexing is designed to track a broad market index, e.g. S&P500, with a portfolio whose weights are different from those of the index (say portfolio consisting of 50 stocks).

An advantage of this strategy over MVO is that indexing does not require expected returns. The strategy is easier to implement using the single index model developed by Sharpe, since one needn’t input index weights in the analysis. Essential inputs are index volatility and stocks’ betas and unsystematic risks.

Does anybody know whether this strategy is popular nowadays? Are there developed some modifications, improvements of indexing?

World Cup on Indexing and Related Products February 25-26, 2002, Barcelona, Spain