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Assuming I want to run an optimization over a short period, say 2 years, I would decide to take daily values in order to compute the efficient frontier of a portfolio. That works fine as long as I have classical assets with daily indices.

For other asset classes, these indices might not exists. How would you then proceed?

Do you use monthly values? If so, it looks like there won't be enough observations in the sample (only 24 for 2 years)... Would you then increase the period?

I guess one could try to do a linear interpolation of the points during the months, but it would be useless as the resulting series would have more "generated" points than original ones.

Is there another alternative?

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Just curious, what other asset classes do you refer to? –  klon Nov 29 '11 at 21:11
    
The "common" ones, like Equities, Fixed Income, Cash, the one you would use with common indices (MSCI World, BBA Libor 3 months, ...) with daily data for portfolio optimization. –  SRKX Nov 29 '11 at 21:15
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Yes, but I was curious about the ones which do not have indices or daily return series? –  klon Nov 30 '11 at 18:13
    
@klon : Hedge Funds, Private Equity, essentially those 2. –  SRKX Nov 30 '11 at 19:54

2 Answers 2

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I would not think of this in terms of modern portfolio theory at all, but rather include ideas that form the mathematical basis of MPT. In particular, construct a joint distribution for the various assets using some kind of copula, but with non-normal marginals derived from some combination of empirical returns, bayesian estimates, and "mapping" of illiquid asset return distributions to liquid ones.

Once the joint distribution is specified, you can choose your favorite objective (which needn't be the same utility function as found in MPT) and optimize it over the joint distribution, likely using Monte Carlo and a quasirandom sequence.

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This comes down to the approach 1 of this post right? –  SRKX Nov 29 '11 at 20:39
    
I suppose there are two parts: (A) get the joint distribution, and (B) use the joint distribution in an optimization. That (excellent) post addresses part (B). –  Brian B Nov 30 '11 at 15:05

The alternative is hedge fund replication. Many hedge funds' returns may be broken down into (possibly time-varying) exposures to known risk factors. Andrew Lo has done much work on this topic. In principle, one may perform a returns attribution over a rolling window for some number of months, then use the daily time-series for the risk factors to fill in the gaps.

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Yes, that's what I meant by mapping. Frankly I don't like any of the possibilities...the problem with all of them is that hedge funds, especially macro hedge funds, can and do change their asset mix and quantities drastically on relatively short timescales. A major fund-of-funds investor like Grosvenor will often demand something like a weekly position report to help get around this problem. Having that information makes the mapping option much more palatable. Without it, I would probably skip the mapping. –  Brian B Nov 29 '11 at 18:13

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