Estimating Unmarked Private Asset Returns with Conditional Covariance

# Neural Networks for Estimation of Unmarked Private Asset Returns from Market Data


# Neural Networks for Estimation of Unmarked Private Asset Returns from Market Data












Let's assume it is March and my illiquid private assets portfolio is only 50% marked for 12/31, but I want to get the most accurate estimate of my final return for the quarter ended on 12/31.

What is the state of the art for using known returns for that quarter to estimate the return on assets that I have not yet received a valuation for?

I'm looking to try training a neural network to do this sort of estimation, but I'm having trouble finding research along these lines to start from. What types and architectures of neural networks are most suitable to reach the highest estimation accuracy?

Any suggestions for key phrases to search for or pointers to relevant research (NN related or not) on this topic would be much appreciated.

Edit:

To clarify further based on comments, within the illiquid private assets there is no real structural difference between the marked and unmarked assets. Valuations trickle in over time rather than being known in real time like publicly traded assets. So between 12/31 and, say, 3/31 the private asset portfolio will go from 0% marked for that quarter to 100% marked in dribs and drabs.

The data available to train with would be quarterly time series of returns going back a few decades. I tend to agree with the comments that there probably aren't enough sets of time series data to train a great NN since the number to work with would be in the low thousands.

The reason I was thinking of neural networks was partly just curiosity, but partly that linear regressions seem too brittle to handle fluctuations in market conditions very well. There are no known non-linear relationships, but linear relationships don't seem to tell the whole story, though maybe I just need to use fancier residual techniques and lagged returns structures.

## Answer by Attack68 (score 4, accepted)

https://quant.stackexchange.com/a/44499

Based on an my updated understanding of your problem you have a portfolio consisting of $N$ illiquid assets. Valuations are not real time and usually lagged, by say, upto 3 months (or slightly longer), but at least valuations correspond to a consistent timestamp (or otherwise you interpolate a consistent timestamp).

You want to construct a predictive model that asserts the true valuation of your portfolio for time period $t$, given you know some of the immediate asset valuations and others you do not.

That is if $Y_i^t$ is the (random variable) valuation of the $i$'th illiquid asset at time $t$, you wish to know $P^t = \sum_i w_iY_i^t$ , for $w_i$ the nominal holding of asset $i$, given the data of the quarterly timeseries history for the assets.

Now if this was a question about regular asset prices I would point out that you have no other features associated with your assets other than historical timeseries (e.g. debt structure, CEO salary, geographic location, etc..), and if you assume the timeseries are stationary then knowledge of past prices is, by assumption, non-influential on the next price, besides having a correlation structure with other price movements and being able to estimate a confidence interval with estimated volatilites.

So what can you do? This is what I would do first...

I would start from a classical probabilistic perspective. Lets assume that your asset price changes follow a multivariate normal distribution:

$$ \mathbf{Y^t} - \mathbf{Y^{t-1}} \sim \mathcal{N}(\mathbf{\mu}, \mathbf{\Sigma}) $$

Then use a common strategy of estimating the mean and covariance parameters - basically estimate them from your timeseries history.

Now you want to calculate the expectation of the portfolio valuation given some known data, say you have 5 assets/samples and know the prices of the first 2: $i=1,2$:

$$E[P^t|y^t_1, y^t_2, \mathbf{y^{t-1}}] = \sum_{i=1,2} w_i y^t_i + \sum_{i=3,4,5} w_i \left ( y^{t-1}_i + E[Y^t_i-y^{t-1}_i | y_1^t, y_2^t] \right )$$

You can calculate the expectation of the unknown price movements by conditioning the multivariate normal distribution. See wikipedia multivariate normal distribution - if you scroll down to the section on conditional distribitions you are basically interested in the formula for $\bar{\mathbf{\mu}}$.

If you then wanted to extend this for confidence intervals you can use the conditioned covariance matrix ($\bar{\mathbf{\Sigma}}$) and assume a variance-covaraiance measure of risk.

This has the added convenience of being easily updated as new information becomes readily available. In my opinion far superior to the complexity of a neural network (with dynamic number of input variables), at least initially to get a basic model implemented and working - then look for its weaknesses and try to improve it.