Why Weighted Asset Utility May Not Measure Portfolio Wealth Utility

Summary

The document asks how to measure an individual investor’s utility over a year when only daily stock holdings are observed. It proposes calculating each asset’s share of the portfolio, applying a utility function to each asset’s dollar value, weighting those utilities by portfolio shares, and averaging the daily result across the observation period.

The text presents this as a question rather than a validated method, and supplies no empirical evidence or recommended utility function. A central modeling issue is that utility is generally applied to total wealth or consumption, while a weighted average of utilities of individual holdings describes a different preference structure. The data also omit other wealth, so stock holdings alone may not represent the investor’s full wealth or the relevant changes in wealth. Any estimate depends on the chosen utility model, wealth definition, and treatment of time and rebalancing.

Key ideas

• The proposed daily measure weights each asset’s utility by its fraction of stock portfolio value.
• The suggested annual measure averages the daily weighted utility across the year.
• The document does not establish that this calculation represents utility from total portfolio wealth.
• A utility estimate may be incomplete when the investor’s non-stock wealth is unknown.

Tags

# Compute Utility From Portfolio Holdings Over Time


# Compute Utility From Portfolio Holdings Over Time












I have a dataset comprising daily stock holdings for individual investors over a one year-period. I only know about the individuals' investment in stocks. I have no information on any other wealth of the individuals. However, investors might rebalance their portfolios and buy or sell stocks increasing or decreasing their overall portfolio value.

Now, I want to compute the utility perceived from the portfolio wealth an investor holds over the time period of one year. How would you approach this task?

My approach (so far) shown with an example for one investor:

On day $t$, an investor holds $N_t$ assets in his portfolio. Each asset has a dollar value of $x_i$ with $i=1,\dots,N_t$. Let $w_i = x_i/\left( \sum_{i=1}^{N_t}x_i\right)$ denote the fraction asset $i$ has in the portfolio on day $t$. I would compute the weighted utility on day $t$ as:

$U_t = \sum_{i=1}^{N_t} w_i \cdot u(x_i),$

where $u(\cdot)$ may be any common utility function.

Since I want to evaluate over $T$ time periods, I would then compute an overall utility as:

$U = \frac{1}{T}\sum_{t=1}^T U_t$

Is this approach of intraday weighting of utility and averaging over time correct?

I haven't worked with utility computation so far and would be thankful for suggestions how to improve this approach or what pitfalls need to be considered.

Thanks!

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.