INFORMS Open Forum

Hello Bruce - Very interesting and practical research problem. 

The challenges you're facing with different models giving divergent recommendations really resonate with ongoing discussions in the Explainable AI (XAI) space.

I'm attaching two papers that you might find helpful:
The absorption and multiplication of uncertainty in machine-learning-driven finance
Deep learning applications in investment portfolio management: a systematic literature review

I would be happy to discuss it further if you are exploring possible similar directions.

Best - Sirine

Can you be more specific about what you mean by "rank the securities for selling"? In my understanding, your problem statement induces an optimization problem; but somehow, the methods you describe sound to me like you make a prediction first (and then-I'm speculating now-optimize the portfolio "heuristically" by selecting the asset with worst predicted performance to be sold?).

Gregor, thanks for the comment.  And Seline, thanks too! 

The securities have different coupon (income) rates, different market prices, different maturities, and different ratings (quality as judged by an external rating agency, somewhat reflected in the interest rate or current price). The bonds may also be tax-free nationally and/or at the state level, depending on whether they are issued by the same state in which you live.

In addition, as bonds approach a call date, their price converges to 100% of their face value.  

Now suppose you had to raise X dollars in cash.  You could offer some of the securities for sale at something close to the market price, enough to get you X in cash. 

So if you rank the securities by which ones should be sold first, you could just start selling 1,2, and so on till you reach the amount X. 

So my optimization so far uses the different features to produce a ranking, the order in which they should be sold.  

It would be nice if there was an unsupervised algorithm that could produce such a ranking.  But, for instance, a random forest regression can't do that.  Instead as a surrogate I generate a preliminary ranking based on the number of days till maturity.  Obviously, that is the order in which the securities would return cash to you absent any other predictors. 

Then I can run a random forest regression (or any other regression routine) of rank on the other features to produce a predicted rank. Sorting predicted rank first to last produces an integer order or rank in which they could be sold.

Clearly you'd think a cash holding might come first, since it's available now without a sale.

Securities very close to maturity or prerefunded perhaps ought to come next, though there are others which are worth more than their face value, because they have interest rates higher than the current interest rates; certain corporate bonds would be an example.  

Trouble is, when I run my random forests or regressions with different parameters, I get quite different rankings, and they aren't very intuitive.  

Sirine Taleb pointed out that there might be a case for an explainable AI (XAI) solution.  I'm currently looking at SHAP to create 'explanations' for the high-ranking items. (I've done some work with cooperative games in the past.)   Apparently SHAP and LIME differ mostly in the kernels (weights) employed in the calculation.

I'm learning a lot about what's possible with R.  But I'm not sure even the explanations will improve on a bad optimization.

I think there's a hole in my thinking because I'm using my surrogate rank as a target variable.  But the algorithms I've tried need something to fit to.  

Any suggestions are gratefully received.

Can you be more specific about what you mean by "rank the securities for selling"? In my understanding, your problem statement induces an optimization problem; but somehow, the methods you describe sound to me like you make a prediction first (and then-I'm speculating now-optimize the portfolio "heuristically" by selecting the asset with worst predicted performance to be sold?).

I fear that I still don't quite get what you want to achieve: if I understand you correctly, you regress time-to-maturity on some other features (like credit rating, the spread between price and face values, etc.), and then use the prediction from that model to obtain a new ranking. Is that correct?

If so, I have another question, and a comment:

• Why should the ranking based on the prediction produce better results than that based on the original metric (time-to-maturity)? My understanding is that you always have that quantity available for all your assets (so, technically, no need to predict it), and that the only difference between the actual value and its prediction is essentially noise, isn't it?
• I'm speculating now, but I could imagine that predicting time-to-maturity from other properties is delicate, in that few features have true explanatory power, at least not linearly: For example, a high price-to-value ratio is indicative for a long time to maturity, but not vice-versa. Other features might indeed induce multicollinearity issues: For example, low credit ratings might correlate with shorter overall term of bonds in general, and thus produce lower times to maturity on average; if, at the same time, you include the overall term as a feature directly, you might run into statistical (and numerical) problems. Now with regard to your observation that different algorithms produce vastly different rankings-I could imagine that this is a consequence of their very different handling of such challenging setups.

Gregor, thanks for the comment.  And Seline, thanks too! 

The securities have different coupon (income) rates, different market prices, different maturities, and different ratings (quality as judged by an external rating agency, somewhat reflected in the interest rate or current price). The bonds may also be tax-free nationally and/or at the state level, depending on whether they are issued by the same state in which you live.

In addition, as bonds approach a call date, their price converges to 100% of their face value.  

Now suppose you had to raise X dollars in cash.  You could offer some of the securities for sale at something close to the market price, enough to get you X in cash. 

So if you rank the securities by which ones should be sold first, you could just start selling 1,2, and so on till you reach the amount X. 

So my optimization so far uses the different features to produce a ranking, the order in which they should be sold.  

It would be nice if there was an unsupervised algorithm that could produce such a ranking.  But, for instance, a random forest regression can't do that.  Instead as a surrogate I generate a preliminary ranking based on the number of days till maturity.  Obviously, that is the order in which the securities would return cash to you absent any other predictors. 

Then I can run a random forest regression (or any other regression routine) of rank on the other features to produce a predicted rank. Sorting predicted rank first to last produces an integer order or rank in which they could be sold.

Clearly you'd think a cash holding might come first, since it's available now without a sale.

Securities very close to maturity or prerefunded perhaps ought to come next, though there are others which are worth more than their face value, because they have interest rates higher than the current interest rates; certain corporate bonds would be an example.  

Trouble is, when I run my random forests or regressions with different parameters, I get quite different rankings, and they aren't very intuitive.  

Sirine Taleb pointed out that there might be a case for an explainable AI (XAI) solution.  I'm currently looking at SHAP to create 'explanations' for the high-ranking items. (I've done some work with cooperative games in the past.)   Apparently SHAP and LIME differ mostly in the kernels (weights) employed in the calculation.

I'm learning a lot about what's possible with R.  But I'm not sure even the explanations will improve on a bad optimization.

I think there's a hole in my thinking because I'm using my surrogate rank as a target variable.  But the algorithms I've tried need something to fit to.  

Any suggestions are gratefully received.

Can you be more specific about what you mean by "rank the securities for selling"? In my understanding, your problem statement induces an optimization problem; but somehow, the methods you describe sound to me like you make a prediction first (and then-I'm speculating now-optimize the portfolio "heuristically" by selecting the asset with worst predicted performance to be sold?).

Gregor, thanks for the comment.  And Seline, thanks too! 

The securities have different coupon (income) rates, different market prices, different maturities, and different ratings (quality as judged by an external rating agency, somewhat reflected in the interest rate or current price). The bonds may also be tax-free nationally and/or at the state level, depending on whether they are issued by the same state in which you live.

In addition, as bonds approach a call date, their price converges to 100% of their face value.  

Now suppose you had to raise X dollars in cash.  You could offer some of the securities for sale at something close to the market price, enough to get you X in cash. 

So if you rank the securities by which ones should be sold first, you could just start selling 1,2, and so on till you reach the amount X. 

So my optimization so far uses the different features to produce a ranking, the order in which they should be sold.  

It would be nice if there was an unsupervised algorithm that could produce such a ranking.  But, for instance, a random forest regression can't do that.  Instead as a surrogate I generate a preliminary ranking based on the number of days till maturity.  Obviously, that is the order in which the securities would return cash to you absent any other predictors. 

Then I can run a random forest regression (or any other regression routine) of rank on the other features to produce a predicted rank. Sorting predicted rank first to last produces an integer order or rank in which they could be sold.

Clearly you'd think a cash holding might come first, since it's available now without a sale.

Securities very close to maturity or prerefunded perhaps ought to come next, though there are others which are worth more than their face value, because they have interest rates higher than the current interest rates; certain corporate bonds would be an example.  

Trouble is, when I run my random forests or regressions with different parameters, I get quite different rankings, and they aren't very intuitive.  

Sirine Taleb pointed out that there might be a case for an explainable AI (XAI) solution.  I'm currently looking at SHAP to create 'explanations' for the high-ranking items. (I've done some work with cooperative games in the past.)   Apparently SHAP and LIME differ mostly in the kernels (weights) employed in the calculation.

I'm learning a lot about what's possible with R.  But I'm not sure even the explanations will improve on a bad optimization.

I think there's a hole in my thinking because I'm using my surrogate rank as a target variable.  But the algorithms I've tried need something to fit to.  

Any suggestions are gratefully received.

Can you be more specific about what you mean by "rank the securities for selling"? In my understanding, your problem statement induces an optimization problem; but somehow, the methods you describe sound to me like you make a prediction first (and then-I'm speculating now-optimize the portfolio "heuristically" by selecting the asset with worst predicted performance to be sold?).

Dear Professor Bruce Hartman,

This portfolio redemption problem, involving heterogeneous fixed income instruments under time-sensitive liquidity needs, requires more than statistical ranking methods. While techniques like regression or ensemble models offer initial heuristics, they often miss strategic interdependencies and trade-offs between long-term income preservation and short-term cash needs.

Here, collaboration between portfolio managers, advisors, and clients is essential. Joint decision-making enables shared understanding of preferences and constraints, aligning asset sales with broader investment goals.

Game theory also offers a powerful modeling framework. Cooperative models can structure collaboration, while non-cooperative models capture trade-offs between competing objectives (e.g., liquidity vs. opportunity cost). Mechanism design and bargaining approaches can support fair and efficient liquidation strategies. Integrating collaborative and game-theoretic approaches can yield more principled, adaptive, and transparent solutions-especially in urgent financial contexts.

For reference, we hereby include two of our recent studies, which may offer relevant insights or serve as illustrative examples for the issues discussed;

Özcan, İ., Sledzinski, J., Gök, S., Butlewski, M., & Weber, G. W., (2023). Mathematical encouragement of companies to cooperate by using cooperative games with fuzzy approach. Journal of Industrial and Management Optimization, 19(10).

Özcan, İ., Śledziński, J. D., Gök, S. Z. A., Meca, A., Weber, G. W., Butlewski, M., & Kocadag, E. (2025). A game theory perspective on strategic profit distribution in complex it projects. Journal of Industrial and Management Optimization, 21(2), 1503-1517.

With warm regards,

İsmail Özcan   (Contact person)
PhD
📧 ismailozcanmath@gmail.com

Gerhard-Wilhelm Weber
Faculty of Engineering Management, Poznan University of Technology
📧 gerhard.weber@put.poznan.pl