returns

Optimal Portfolio Weights

Zachary Bartsch6 Comments

All of us have assets. Together, they experience some average rate of return and the value of our assets changes over time. Maybe you have an idea of what assets you want to hold. But how much of your portfolio should be composed of each? As a matter of finance, we know that not only do the asset returns and volatilities differ, but that diversification can allow us to choose from a menu of risk & reward combinations. This post exemplifies the point.

1) Describe the Assets

I analyze 3 stocks from August 1, 2024 through August 1, 2025: SCHG (Schwab Growth ETF), XLU (Utility ETF), and BRK.B (Berkshire Hathaway). Over this period, each asset has an average return, a variance, and  co-variances of daily returns. The returns can be listed in their own matrix. The covariances are in a matrix with the variances on the diagonal.

The return of the portfolio that is composed of these three stocks is merely the weighted average of the returns. In particular, each return is weighted by the proportion of value that it initially composes in the portfolio. Since daily returns are somewhat correlated, the variance of the daily portfolio returns is not merely equal to the average weighted variances. Stock prices sometimes increase and decrease together, rather than independently.

Since the covariance matrix of returns and the covariance matrix are given, it’s just our job to determine the optimal weights. What does “optimal” mean? This is where financiers fall back onto the language of risk appetite. That’s hard to express in a vacuum. It’s easier, however, if we have a menu of options. Humans are pretty bad at identifying objective details about things. But we are really good at identifying differences between things. So, if we can create a menu of risk-reward combinations, then we’re better able to see how much a bit of reward costs us.

2) Create the Menu

In our simple example of three assets, we have three weights to determine. The weights must sum to one and we’ll limit ourselves to 1% increments. It turns out that this is a finite list. If our portfolio includes 0% SCHG, then the remaining two weights sum to 100%. There are 101 possible pairs that achieve that: (0%, 100%), (1%,99%), (2%,98%), etc. Then, we can increase the weight on SCHG to 1% for which there are 100 possible pairs of the remaining weights: (0%,99%), (1%, 98%), (2%, 97%), etc. We can iterate this process until the SCHG weight reaches 100%. The total number of weight combinations is 5,151. That means that there are 5,151 different possible portfolio returns and variances. The below figure plots each resulting variance-return pair in red.

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Why Low Returns Are Predicted for Stocks Over the Next Decade

Scott Buchanan2 Comments

I saw this scary-looking graphic of S&P 500 returns versus price/earnings (P/E) ratios a couple of days ago:

JPMorgan

The left-hand side shows that there is very little correlation between the current forward P/E ratio and the returns in the next year; as we have seen in the past few years, and canonically in say 1995-1999, market euphoria can commonly carry over from one year to the next. (See here for discussion of momentum effect in stock prices). So, on this basis, the current sky-high P/E should give us no concern about returns in the next year.

However, the right-hand side is sobering. It shows a very strong tendency for poor ten-year returns if the current P/E is high. In fact, this chart suggests a ten-year return of near zero, starting with the current market pricing. Various financial institutions are likewise forecasting a decade of muted returns [1].

The classic optimistic-but-naïve response to unwelcome facts like these is to argue, “But this time it’s different.” I am old enough to remember those claims circa 1999-2000 as P/E’s soared to ridiculous heights. Back then, it was “The internet will change EVERYTHING!”.  By that, the optimists meant that within a very few years, tech companies would find ways to make huge and ever-growing profits from the internet. Although the internet steadily became a more important part of life, the rapid, huge monetization did not happen, and so the stock market crashed in 2000 and took around ten years to recover.

A big reason for the lack of early monetization was the lack of exclusive “moats” around the early internet businesses. Pets.com was doomed from the start, because anyone could also slap together a competing site to sell dog food over the internet. The companies that are now reaping huge profits from the internet are those like Google and Meta (Facebook) and Amazon that have established quasi-monopolies in their niches.

The current mantra is, “Artificial intelligence will change EVERYTHING!” It is interesting to note that the same challenge to monetization is evident. ChatGPT cannot make a profit because customers are not willing to pay big for its chatbot, when there are multiple competing chatbots giving away their services for practically free. Again, no moat, at least at this level of AI. (If Zuck succeeds in developing agentic AI that can displace expensive software engineers, companies may pay Meta bigly for the glorious ability to lay off their employees).

My reaction to this dire ten-year prognostication is two-fold. First, I have a relatively high fraction of my portfolio in securities which simply pump out cash. I have written about these here and here. With these investments, I don’t much care what stock prices do, since I am not relying on some greater fool to pay me a higher price for my shares than I paid. All I care is that those dividends keep rolling in.

My other reaction is…this time it may be different (!), for the following reason: a huge fraction of the S&P 500 valuation is now occupied by the big tech companies. Unlike in 2000, these companies are actually making money, gobs of money, and more money every year. It is common, and indeed rational, to value (on a P/E basis) firms with growing profits more highly than firms with stagnant earnings. Yes, Nvidia has a really high P/E of 43, but its price to earnings-growth (PEG) ratio is about 1.2, which is actually pretty low for a growth company.

So, with a reasonable chunk of my portfolio, I will continue to party like it’s 1999.

[1] Here is a blurb from the Llama 3.1 chatbot offered for free in my Brave browser, summarizing the muted market outlook:

Financial institutions are forecasting lower stock market returns over the next decade compared to recent historical performance. According to Schwab’s 2025 Long-Term Capital Market Expectations, U.S. large cap equities are expected to deliver annualized returns of 6% over the next decade, while international developed market equities are projected to slightly outperform at 7.1%.1 However, Goldman Sachs predicts a more modest outlook, with the S&P 500 expected to return around 3% annually over the next decade, within a range of –1% and 7%.42 Vanguard’s forecasts also indicate a decline in expected returns, with U.S. equities falling to a range of 2.8% to 4.8% annually. These forecasts suggest that investors may face a period of lower returns compared to the past decade’s 13% annualized total return.

Keeping Receipts

Zachary Bartsch1 Comment

Online shopping is convenient and even the norm for many items. Going to the store sounds like a time-consuming labor or an exceptional outing. My family, for example, lives in a suburban location that doesn’t have well-priced grocery home delivery. Shipping only works for some non-perishables. So, for many items we order online and do ‘drive-up pick-up’. We don’t even need to go into the store for many items. And reordering the same items repeatedly is a breeze.

We are also accustomed to the ability to return things. If your blender breaks on your first smoothie, then no worries – you can return it. If the chocolate cookies don’t taste like chocolate? Return it – satisfaction guaranteed. You can buy three pairs of shoes in different sizes and then keep the ones you want at the original sale price. Return the others.

For me, besides the time saved and convenience, a major factor in my decision to make purchases online is the documentation. I don’t need to save the receipt in a shoe box, Ziploc, or file drawer – the online retailer keeps an archive of all my purchases. Often this includes the date, amount, and shipping details including delivery date. There’s a super convenient digital paper trail.

If I need to contact a seller in order to exercise a warranty, then I have their contact information. I don’t need to retain the product packaging or investigate the brand at a future inopportune time. For example, I recently bought a Little Tykes water table for my kids. As I was assembling it on Christmas Eve I realized that I was missing a small part. I was able to work around it. But I was also able to immediately contact the manufacturer with a copy of my invoice. I emailed the date of purchase, the product model number, and the instruction manual had conveniently included part numbers. They were able to ship me the parts after a single email. Online shopping, and the resulting trail of evidence, makes the process much more practical than keeping paper records in a likely unorganized fashion.

There are other benefits to the paper trail. Back before widespread online shopping, retailers would often offer rebates as a sales strategy. In the year 2004, I bought a computer hard drive for $120 before a $40 mail-in rebate. The retailer (or manufacturer, I can’t remember) was hoping that people saw the post-rebate price and then failed to redeem it. And that often happened.  You needed to fill out a rebate form on an index card, cut the UPC bar code of the product packaging, and then mail them with your receipt to the company rebate department in a stamped envelope. If you dragged your feet, then you’d probably lose an important piece of the crucial combination and lose out on your $40 rebate. If the items were lost in the mail, then you were shucks-out-of-luck. Now, rebates have gone the way of the dodo since receipts are automatically retained and retrievable.

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Will the Huge Corporate Spending on AI Pay Off?

Scott Buchanan2 Comments

Last Tuesday I posted on the topic, “Tech Stocks Sag as Analysists Question How Much Money Firms Will Actually Make from AI”. Here I try to dig a little deeper into the question of whether there will be a reasonable return on the billions of dollars that tech firms are investing into this area.

Cloud providers like Microsoft, Amazon, and Google are building buying expensive GPU chips (mainly from Nvidia) and installing them in power-hungry data centers. This hardware is being cranked to train large language models on a world’s-worth of existing information. Will it pay off?

Obviously, we can dream up all sorts of applications for these large language models (LLMs), but the question is much potential downstream customers are willing to pay for these capabilities. I don’t have the capability for an expert appraisal, so I will just post some excerpts here.

Up until two months ago, it seemed there was little concern about the returns on this investment.  The only worry seemed to be not investing enough. This attitude was exemplified by Sundar Pichai of Alphabet (Google). During the Q2 earnings call, he was asked what the return on Gen AI investment capex would be. Instead of answering the question directly, he said:

I think the one way I think about it is when we go through a curve like this, the risk of under-investing is dramatically greater than the risk of over-investing for us here, even in scenarios where if it turns out that we are over investing. [my emphasis]

Part of the dynamic here is FOMO among the tech titans, as they compete for the internet search business:

The entire Gen AI capex boom started when Microsoft invested in OpenAI in late 2022 to directly challenge Google Search.

Naturally, Alphabet was forced to develop its own Gen AI LLM product to defend its core business – Search. Meta joined in the Gen AI capex race, together with Amazon, in fear of not being left out – which led to a massive Gen AI capex boom.

Nvidia has reportedly estimated that for every dollar spent on their GPU chips, “the big cloud service providers could generate $5 in GPU instant hosting over a span of four years. And API providers could generate seven bucks over that same timeframe.” Sounds like a great cornucopia for the big tech companies who are pouring tens of billions of dollars into this. What could possibly go wrong?

In late June, Goldman Sachs published a report titled, GEN AI: TOO MUCH SPEND,TOO LITTLE BENEFIT?.  This report included contributions from bulls and from bears. The leading Goldman skeptic is Jim Covello. He argues,

To earn an adequate return on the ~$1tn estimated cost of developing and running AI technology, it must be able to solve complex problems, which, he says, it isn’t built to do. He points out that truly life-changing inventions like the internet enabled low-cost solutions to disrupt high-cost solutions even in its infancy, unlike costly AI tech today. And he’s skeptical that AI’s costs will ever decline enough to make automating a large share of tasks affordable given the high starting point as well as the complexity of building critical inputs—like GPU chips—which may prevent competition. He’s also doubtful that AI will boost the valuation of companies that use the tech, as any efficiency gains would likely be competed away, and the path to actually boosting revenues is unclear.

MIT’s Daron Acemoglu is likewise skeptical:  He estimates that only a quarter of AI-exposed tasks will be cost-effective to automate within the next 10 years, implying that AI will impact less than 5% of all tasks. And he doesn’t take much comfort from history that shows technologies improving and becoming less costly over time, arguing that AI model advances likely won’t occur nearly as quickly—or be nearly as impressive—as many believe. He also questions whether AI adoption will create new tasks and products, saying these impacts are “not a law of nature.” So, he forecasts AI will increase US productivity by only 0.5% and GDP growth by only 0.9% cumulatively over the next decade.

Goldman economist Joseph Briggs is more optimistic:  He estimates that gen AI will ultimately automate 25% of all work tasks and raise US productivity by 9% and GDP growth by 6.1% cumulatively over the next decade. While Briggs acknowledges that automating many AI-exposed tasks isn’t cost-effective today, he argues that the large potential for cost savings and likelihood that costs will decline over the long run—as is often, if not always, the case with new technologies—should eventually lead to more AI automation. And, unlike Acemoglu, Briggs incorporates both the potential for labor reallocation and new task creation into his productivity estimates, consistent with the strong and long historical record of technological innovation driving new opportunities.

The Goldman report also cautioned that the U.S. and European power grids may not be prepared for the major extra power needed to run the new data centers.

Perhaps the earliest major cautionary voice was that of Sequoia’s David Cahn. Sequoia is a major venture capital firm. In September, 2023 Cahn offered a simple calculation estimating that for each dollar spent on (Nvidia) GPUs, and another dollar (mainly electricity) would need be spent by the cloud vendor in running the data center. To make this economical, the cloud vendor would need to pull in a total of about $4.00 in revenue. If vendors are installing roughly $50 billion in GPUs this year, then they need to pull in some $200 billion in revenues. But the projected AI revenues from Microsoft, Amazon, Google, etc., etc. were less than half that amount, leaving (as of Sept 2023) a $125 billion dollar shortfall.

As he put it, “During historical technology cycles, overbuilding of infrastructure has often incinerated capital, while at the same time unleashing future innovation by bringing down the marginal cost of new product development. We expect this pattern will repeat itself in AI.” This can be good for some of the end users, but not so good for the big tech firms rushing to spend here.

In his June, 2024 update, Cahn notes that now Nvidia yearly sales look to be more like $150 billion, which in turn requires the cloud vendors to pull in some  $600 billion in added revenues to make this spending worthwhile. Thus, the $125 billion shortfall is now more like a $500 billion (half a trillion!) shortfall. He notes further that the rapid improvement in chip power means that the value of those expensive chips being installed in 2024 will be a lot lower in 2025.

And here is a random cynical comment on a Seeking Alpha article: It was the perfect combination of years of Hollywood science fiction setting the table with regard to artificial intelligence and investors looking for something to replace the bitcoin and metaverse hype. So when ChatGPT put out answers that sounded human, people let their imaginations run wild. The fact that it consumes an incredible amount of processing power, that there is no actual artificial intelligence there, it cannot distinguish between truth and misinformation, and also no ROI other than the initial insane burst of chip sales – well, here we are and R2-D2 and C3PO are not reporting to work as promised.

All this makes a case that the huge spends by Microsoft, Amazon, Google, and the like may not pay off as hoped. Their share prices have steadily levitated since January 2023 due to the AI hype, and indeed have been almost entirely responsible for the rise in the overall S&P 500 index, but their prices have all cratered in the past month. Whether or not these tech titans make money here, it seems likely that Nvidia (selling picks and shovels to the gold miners) will continue to mint money. Also, some of the final end users of Gen AI will surely find lucrative applications. I wish I knew how to pick the winners from the losers here.

For instance, the software service company ServiceNow is finding value in Gen AI. According to Morgan Stanley analyst Keith Weiss, “Gen AI momentum is real and continues to build. Management noted that net-new ACV for the Pro Plus edition (the SKU that incorporates ServiceNow’s Gen AI capabilities) doubled [quarter-over-quarter] with Pro Plus delivering 11 deals over $1M including two deals over $5M. Furthermore, Pro Plus realized a 30% price uplift and average deal sizes are up over 3x versus comparable deals during the Pro adoption cycle.”