Decision focused learning and portfolio selection

One of the more interesting papers on portfolio management links prediction with optimization. Rather than a two-step process, the authors focus on how optimization should be managed alongside prediction. The paper, “Return Prediction for Mean-Variance Portfolio Selection: How Decision-Focused Learning Shapes Forecasting Models”, provides insights on how decision-focused learning (DFL) can be used to improve overall portfolio returns. 

The usual process for building a portfolio is through mean-variance optimization. This process is two-staged. It is a predict-then-optimize method. In the first stage, a set of expected returns is generated, and in the second stage, the optimization selects the set of assets that maximizes return subject to a set of constraints. The problem with MVO has been studied extensively. The issue is that if the expected returns are poorly defined, the MVO will choose the “best" returns, yet the portfolio may be optimized on the forecast errors. The classic answer from Markowitz is that estimating expected returns is the investor’s job, not the optimizer’s.

The DFL framework will integrate the prediction and optimization to improve the outcomes. The issue is whether the MSE of forecasts for each asset is treated independently and equally or integrated with asset correlations. With DFL, the optimization accounts for prediction errors when finding the weights via a loss or regret function.

It is found that DFL identifies fewer assets than a standard MVO and exhibits a bias toward positively returning assets, given the optimization for a long-only portfolio. Still, it offers a better way to optimize a portfolio.

Asset allocation is always about the stock-bond correlation

The primary asset allocation decision is based on the relationship between stocks and bonds. If the correlation is negative, there is a significant benefit to holding bonds. If the correlation is rising and positive, the bond diversification benefit is limited, and it is time to consider other alternatives. The trend is not favorable to bonds. The long-term trend is higher, though the recent trend has returned to negative territory.

Buffered ETF - the product of 2026?

 

For better or worse, the top ETF product for 2026 may be the buffered ETF. At a very general level, a buffered ETF, is one that provides downside protection versus some referenced index. That is, there is a buffer on the losses associated with the ETF. However, in exchange for this protection, the investor wil give-up some of the upside. The market has grown from approximately $5 billion in 2020 to a $90 billion AUM as of the end of 2025.

This type of protection can be achieved by managing the portfolio. There is a cost with having the ETF provide you protection, yet there always seems to be a need for these products. First, the mechanism for offering this protection is systematic and removes emotion from any allocation decision. Second, the timing of the protection is well-defined. Yet the payoff structure is complex and comprises multiple option positions. There are parts of the distribution that are protected or buffered, parts that are exposed to risk, and an upside portion that is capped. The folks at Alpha Architect provide a good overview of the problem. 

Realize that if you want protection from downside risk, there is no free lunch. If you move to cash, you lose the upside. If you buy derivatives, there is a cost. If you allocate to alternatives, you are at the mercy of their return profile. Choose your protection wisely.

The 60/40 stock/bond mix can result in periods of no return

 

Still spending time on the 6/40 stock bond mix. The reason is simple - it is the benchmark for asset allocation. Yes, it works; however, investors should be aware that there are extended periods of flat returns. You can have lost decades of no performance. The challenge is finding alternatives during these flat periods, especially when real yields are negative. Can alternative investments do the trick? The core solution is to find positive real returns with low correlation to equities. Trend-following can do it, but the core returns do not match the periods of lost decades. The challenge is finding the right mix at the right time, with clear rules for triggering a switch in asset allocation.

The need for diversifiers - Not coming from bonds

 

HSBC generated a helpful chart on the correlaiton when inflation is higher than 2.5%. The Fed will not, or cannot, get inflation back to 2%, so we expect the stock-bond correlation to remain positive. This means that there should be an active search for diversifiers. It is unlikely that any hedge fund strategy beyond managed futures will generate negative correlation. Still, there is an opportunity to find strategies with low correlation and higher risk-adjusted returns than a bond portfolio. 

TPA - Total Portfolio Approach - Is this a fad?

 

I am trying to understand the relatively new concept of the Total Portfolio Approach (TPA), which is being embraced by many large pension funds and endowments. Now, we know the foundations of SAA (Strategic Asset Allocation) and TAA (Tactical Asset Allocation), but there does not seem to be a clear definition of TPA.

SAA is structured around an investment committee allocating capital to major asset classes based on expected returns for each class. This is a long-term perspective, and in the short run, it will be applied for the year. TAA is a short-term. Both of these involve a top-down process in which the focus is on identifying asset classes and then making assumptions about future returns, volatility, and correlations to determine a set of portfolio weights. The allocations are then given to specific investment groups that aim to beat the benchmarks for each asset class. The investment committee monitors the performance and the weight for each asset class. The foundations of this approach are modern portfolio theory, with a focus on diversification. 

The reality is that many endowments have not been able to beat their SAA portfolio benchmarks, and the benchmarks themselves have not been effective because the underlying return and risk assumptions have proved ineffective. The process does not seem to work, so there is room for an alternative approach.

The new approach is the total portfolio approach, which still embraces diversification and modern portfolio theory. It also embraces the idea that allocations should be more flexible, drawing on the principles of tactical asset allocation. Still, there is no new theory behind the concept.

There is a belief that allocations should be more flexible and that endowment portfolios should not be siloed into fixed asset-class weights. There is a shift in investment staff to compete for capital across all asset classes. It argues that siloed thinking will not be effective for generating alpha or for adjusting to a dynamic market environment. TPA is more of an approach to managing the portfolio and not setting goals. The objective is to maximize surplus (assets - liabilities), subject to a downside or volatility constraint on surplus risk. 

This all sounds good, but it is not clear that there is a single acceptable definition of the concept. Hence, TPA may be in the eyes of the beholder.

The good and bad over the last 30 years

 

No region or asset class will always dominate the markets. Even the US stocks will underperform, as seen between 2000 and 2010. This is the core lesson of asset diversification. As shown in the table, the 60/40 mix will give you the median return. It will never outperform, nor will investors live to regret it. Should investors move out of their US exposure? Timing is never easy, so the most straightforward approach would be to use a trend-relative model to help. Money will flow toward better opportunities, but diversification remains the best approach to balancing risks in an uncertain world. 

The 60/40 plus portfolio still works

 

There has been a lot of bashing of the classic 60/40 stock-bond mix amid bonds' poorer performance. It provides a nice base middle ground for any portfolio discussion. If there is a market shock, it will rebound better than moving to cash and trying to time the addition of risk exposure.

Yes, using the 60/40 as a base anchors thinking, but it can serve as a good beginning for any portfolio construction.

Can investors do better? Yes, adding alternatives provides for a better return without adding volatility. The advantage of starting with the 60/40 blend is that it allows for a careful review of how to add new strategies to the portfolio. There is no major switching from risk-on to risk-off.

The search for divesification

The ongoing issue with alternative investing has persisted for the last few decades. Can you find a better diversifier than traditional assets? The long-term trend has been for further market integration, so the demand for alternatives has been strong. You just do not get the benefit from international equity investors or holding fixed income.

While the trend toward traditional asset diversification is declining, there is an ebb and flow to this diversification. There is less diversification gain during a crisis, but there are periods when holding a diversified portfolio reduces risk; nevertheless, the demand for alternatives will be strong as long as market integration continues. 

Managers outperform mid and small cap benchmarks

The SPIVA report from S&P provides a good measure of the quality of alpha generation from long-only equity managers. The numbers are usually not very good. Managers usually underperform the large cap benchmark. Managers typically do better than mid- and small-cap benchmarks, although they still generally fail to beat the corresponding benchmarks. For 2025, equity managers are performing much better than the benchmarks by a much wider margin. 

Why are managers doing better? The simple answer is that it is a better stock-picking environment, yet that does not tell what the characteristics are that are causing this better environment. We argue that the dispersion in the stock market is higher and the cross-correlation is lower in the associated indexes. If there is more equity dispersion, the choices that are made by managers will lead to added performance. The choices improve when there is less correlation between stocks

 

Prediction is not optimization

Many researchers and practitioners have questioned how the input parameters of MVO should be estimated. To this, Markowitz is said to have responded with wit and grace, “That’s your job, not mine.”

- Stephen C Sexauer and Laurence B Siegel. 2024. Harry Markowitz and the philosopher’s stone. Financial Analysts Journal

With the quant revolution, there have been significant advancements in the methods and types of optimization that can be used for portfolio management. However, the key to successful optimization remains the accurate predictions of expected return, volatility, and correlation. Optimization on the wrong inputs is a fool's errand. 

The machine learning explosion has to focus on system predictions across a large set of assets, which can then be used as inputs into a traditional optimizer. Before using an optimizer, focus on the input variables. 

Co-occurrence versus correlation- Still learning about diversification

 

There is a need to deepen our understanding of diversification, but is there a limit to how much we can extract given the basic principles of covariance and correlation? Some in finance are starting to discuss the concept of co-occurrence, which, in the case of asset management, measures the cumulative co-movement of asset pairs during a specific horizon. If, over a particular horizon, the cumulative returns converge to the other returns in the portfolio, you may not have the diversification expected. If we have two assets that, over a one-year horizon, generate similar returns, then you are not diversified. The paths are different, but the two assets end in the same place. 

You can measure the co-occurrence by multiplying the z-scores of two assets and dividing by the average of their squared z-scores. The co-occurrence will fall between -1 and 1, much like the correlation. If the z-score of an asset is zero, then the co-occurrence will be zero. If the z-scores are highly aligned for the tested time period, the co-occurrence will tend toward 1. The determinant of the co-occurrence is the joint informativeness of the two variables, which is essential because the correlation of any two assets is the weighted average of the informativeness with the co-occurrence. So, the co-occurrence tells us something about correlation when we align the return horizon, which we do not do with traditional correlation measures. 

Correlation is useful, but we also want to see how assets move over longer horizons to determine whether there is a pattern of behavior that tells us whether performance diverges or is similar. 

Robo-advisors - keep the rules simple

 

More investors are using robo-advisors to get investment advice. Relative to doing it yourself, the robo-advisor may be an improvement. Is this better than a financial advisor is a different question and remains to be answered. We know that the robo-advisor is cheaper, so the investor is receiving net savings versus the standard fees that are usually charged. 

Do you get more sophisticated advice? A recent study shows that the advice given is rather simple and focuses on only a few factors - what is your horizon, goal, and loss reaction are the top three. These simple rules are driven a lot of client money and will tie the movement of savings to a limited set of variables. See "What drives robo-advice?"

Knowing the inflation and growth regime is critical for equity and bond investing

 

Picking stocks and bonds is a critical part of investing, yet make no mistake, the inflation and growth environment do matter. It is critical to know what is the macro regime. Now it is hard to say what is the current regime relative to past history since you are living in the current; nevertheless, if you can formulate a view on the current regime, you can provide meaningful policy tilts for the benefit of your overall portfolio. When inflation is high, avoid bonds. When growth is high, hold stocks. This does not have to be complex, but a regime view is critical. Charts are from the UBS data yearbook 

End of summer and investors are satisfied

The summer is not officially over, but Labor Day usually marks the end. Schools start and vacations are over. It is looks like we have had a good summer with the Fed likely to lower rates, inflation manageable, and still no recession. The markets seem to have rationalized albeit it is still a large cap world. Small caps have done well this summer even with a give-back in August. The Mega caps in information technology and communications eaves have started to rationalize although they still dominate the markets. Growth stocks have slowed their ascent, but there is a rotation to low volatility and high dividend stocks. Bonds have done well this summer. Overall, the markets are preparing for the Fed cuts, assuming inflation has been tamed, and see continued potential gains but with a focus on getting more defensive. 

It was a good summer, now we must prepare for fall and winter. 

Should you prefer stocks or bonds? - Not an easy question

Inflation has come down and the bias form the market is that the Fed will cut rates in September and start the process of bringing down short rates. The advantage from holding cash will decline, so the question is whether those funds in cash should move into equities or bonds. 

If inflation is lower and growth is lower, the choice of seems to make sense, but the environment is not a given. Additionally, investors have to think about relative valuations. Stocks are, by some measures, expensive relative to bonds which tilts the decision in the direction of bonds.  The Sharpe ratio favors bonds, yet stocks will still do well, just less well than if the equity market is cheap. 

The bias seems to be in favor of bonds as the again the great diversifier; nevertheless, if the choice is expanded to alternatives choices like managed futures seem attractive. With trend-following you may be able to take advantage of adjustments in both stocks and bonds.

Why is the stock-bond correlation important?

 

Bonds have been the great diversifier relative to stocks, yet this relationship is subject to change and can move from negative to positive.  So, what does that mean for your asset allocation?

A switch from a -.5 to +.5 will double the volatility of a 60/40 stock/bond mix based on historical data. Think about it. You will see your portfolio can move from single to double digit risk while keeping the allocation the same. There will still be a diversification benefit from bonds, but you will have to live with more risk. Back to basics, the correlations across assets matter.

See the Fidelity working paper, "Liquid alternatives: The power of equity options-based strategies"

Volatility targetting is trend following for equities

 

Volatility targeting outperforms a buy and hold strategy, but why? Volatility targeting is the process of adjusting risk exposure or leverage to set a specific volatility level. Usually, managers set the leverage and allow the volatility to move.  

Volatility targeting works because there is a negative correlation between return direction and volatility which has been called the leverage effect. Volatility targeting will be negatively related to the magnitude of recent returns. Given this relationship, we can say that volatility targeting has a trend following effect. The relationship between volatility targeting and trend-following was explored more closely in recent research paper, see "Volatility Targeting is Trendy: How Trend Following Explains alpha in Volatility-Managed Strategies". The leverage effect is not present with bonds, commodity and currencies.  If you control for trend-following the alpha from volatility targeting will decline by about 2/3rds when tested against a portfolio of 14 stock indices. The volatility targeting link to trend-following does not occur with other asset classes. 

The big head fake - global diversification

 

It has often been said that diversification is the only free lunch in finance, yet the free lunch has not paid off with international investors. Forget about global investing and emerging markets, just put your equity investments and you can do no wrong.  In this case, the home bias for US investors has been justified.  The US market has grown at a 13.3% annual rate since 2009 while the MSCI EAFA only gained 5.9% and the MSCI EM grew 3.2%.  Earnings in the US have grown since 2010 under world of easy money. Valuations have declined since the GFC, but the contraction has been greater outside the US.  The US has been on significant expansion except for the COVID shock, but the rest of the world has not suffered from any severe contraction. 

Is this all about the magnificent seven and the tech?  They are a key contributor to the US performance. There are no comparable companies in other parts of the world, so going forward, less diversification is based on the view that there will be no reversal in the magnificent seven, the rest of the world will not catch-up to the US and the higher valuations in the US will continue. 

Why don't more investors use the equal-weighted index

 

I am surprised that more investors don't use the equal-weighted index. We know that a cap-weighted index is a closet momentum index. We know that a cap weighted will place excessive weight on the top performing names, yet there is a still this core bias. Investors may be stuck in their old ways, yet if we look at the equal-weighted performance it shows good performance versus many of the alternatives. There are rebalancing costs, yet it does diversify risks. Clearly, we know that an equal weighted avoids many of the issues with portfolio optimization, so this simple portfolio may be an effective way to max diversification and avoid any concentration bias.