The hard (but right) way: compute the whole equilibrium for all the investors.
What would be the impact of using a representative sample of investors as a computation-saving measure? By this I mean:
Look at the body of all of the investors
Identify the different investor types (hedge funds, index funds, day traders, etc)
Compute the whole equilibrium for a sample of investors that preserves the proportion of the investor types
I have a suspicion that investor types will correspond to the timelines over which they invest(?) but I am not sure that’s how it works from an analysis standpoint.
the sample is in fact representative, i.e. the investor types cover the large majority of the capital in the market, and
investors within each type have “similar” behavior—ideally they can all be captured by a representative agent.
(We could also circumvent the need for representative agents by estimating the demand function of each investor class directly, but then with n assets we need to estimate a function from R^n to R^n rather than a function from R^n to R, so the data and computation requirements are dramatically higher. Also, at that point there aren’t clear benefits to breaking out classes of investors in the first place.)
Investor types corresponding to timelines is indeed sensible; I use that a lot in my own models. For instance, I can use data on individual trades to estimate the portfolios held by market makers as a function of price.
What would be the impact of using a representative sample of investors as a computation-saving measure? By this I mean:
Look at the body of all of the investors
Identify the different investor types (hedge funds, index funds, day traders, etc)
Compute the whole equilibrium for a sample of investors that preserves the proportion of the investor types
I have a suspicion that investor types will correspond to the timelines over which they invest(?) but I am not sure that’s how it works from an analysis standpoint.
That would be correct assuming that
the sample is in fact representative, i.e. the investor types cover the large majority of the capital in the market, and
investors within each type have “similar” behavior—ideally they can all be captured by a representative agent.
(We could also circumvent the need for representative agents by estimating the demand function of each investor class directly, but then with n assets we need to estimate a function from R^n to R^n rather than a function from R^n to R, so the data and computation requirements are dramatically higher. Also, at that point there aren’t clear benefits to breaking out classes of investors in the first place.)
Investor types corresponding to timelines is indeed sensible; I use that a lot in my own models. For instance, I can use data on individual trades to estimate the portfolios held by market makers as a function of price.