Tracking Error In The S&P 500 And Your Wealth

As recently as 2015, Macy’s traded at a price of $76 per share while having trailing annual profits of $1.6 billion. It had almost $2 billion in cash, a fully funded pension, online sales growing at a clip of 15% annualized, and appeared to have recovered from the worst of the Great Recession when the price of the stock was punished down to $7 per share. 

However, Macy’s management observed that nearly all of its peers were repurchasing large chunks of stock with its cash flows, even borrowing money at low-interest rates to do so. As Warren Buffett said during his 1992 speech at Notre Dame’s business school, the dumbest reason to undertake an action is because your peers are doing so.

And Macy’s decisions, particularly in relation to its liquidity reserves, bears that out. Macy’s took on a total $4.6 billion in debt, with over $1 billion if it due within the next year, and the $2 billion cash pile has been reduced to $300 million. What does Macy’s have to show for it? A share count that reduced from 546 million to $300 million. Meanwhile, the company’s net profit of $820 million has been converted to unspecified losses, straining the $300 million cash reserves and putting the company in a position to require funds from a lender, be it the federal government or private industry.

Amid this, the S&P 500 Index just announced that Macy’s (which is now valued at a market cap of $1 billion but was once valued as high as $17 billion) will be replaced with Carrier Global Corporation, the $17 billion air conditioning giant that was spun off from United Technologies about a week ago. 

Due to the daily volatility and sharp movements of stocks in the S&P 500, this move highlights some of the discretionary decisions that are involved in implementing a stock market index as well as executing an index fund that is designed to follow those indices.

In the case of the S&P 500 Index, Standard & Poor’s makes decisions every quarter about the companies that are added and subtracted from the index (Macy’s last day in the S&P 500 Index was April 3, 2020) with Carrier entering the Index on April 6, 2020 in an amount equal to the divisor percentage that was previously allocated Macy’s. 

As for the index funds themselves, they like to give themselves maximum flexibility when it comes to implementing the change that the S&P 500 effectuated with the change in the index. 

For instance, the Vanguard S&P 500 Index Fund, which is one of, and often the, largest index fund in the world with $500 billion in assets under management, grants itself maximum flexibility for carrying out changes in the index. If you read the prospectus for Vanguard’s S&P 500 Index, you will see that Vanguard only obligates itself on page 8 of the Prospectus to have 80% or greater of its funds under management to track the index. In order words, Vanguard only guarantees that your index fund will be 0.8x of an index as a legal matter (and this isn’t picking on Vanguard, as it is prospectus-standard language for index funds). 

This statement is done for legal and pragmatic reasons. Of course the Vanguard S&P 500 tries its best to 100% resemble the underlying performance of the S&P 500, but it presumably wants to avoid legal liability for “tracking error” which occurs when there is a delay in the selling and purchasing of new assets for the index compared to the instant change that the S&P 500 creates.

For instance, the S&P 500 can see Macy’s stock at $4.81 on April 3, 2020 and just choose that termination price. Likewise, the S&P 500 can see the $16.92 price of Carrier and choose that as its entry price for performing calculations. 

For the index funds themselves, there is an act that must accompany the math. Macy’s, as the smallest component of the index, constituted 0.0015% of S&P 500 indices at the time of its exit from the fund. 

For a $500 billion fund like the Vanguard S&P 500, it must actually sell $7.5 million worth of Macy’s stock and acquire $7.5 million worth of Carrier. It cannot do so instantaneously without moving the market price of Macy’s. And every other index fund has to do the same thing. I called Vanguard and asked them about their index methodologies, but I was referred generally to the prospectus and was informed that index funds were carried out “as quickly and with as little market disruption as possible.” According to Standard & Poor’s, it takes the typical S&P 500 Index Fund 28.3 days to carry out the changes to an index.

This is why every index fund has some degree of tracking error. For instance, if you look at the Vanguard S&P 500’s actual ten-year performance, you will see that the Vanguard S&P 500 has returned 10.37% annually over the past ten years while the S&P 500 Index actually returned 10.53%. The 0.16% pre-tax, pre-fee difference can be explained by the tracking error of actually selling and acquiring the stocks that make up the index. 

The practical effect is that S&P 500 Index often shifts the benefits and risks of an underperforming stock’s recovery onto its smaller indices. In connection with the decision to remove Macy’s from the S&P 500 was also the decision to move Macy’s to the Small-Cap 600 Index. If Macy’s receives funding and quickly recovers to $20 per share, it is the owners of the Small-Cap 600 Index that will receive that benefit (and if Macy’s re-enters the S&P 500, the index holders will not have received the benefit of the stock appreciation along the way). On the other hand, if the coronavirus pandemic lingers and Macy’s is not able to shore up financing, then the Small-Cap 600 Index owners will suffer the final losses that precede the bankruptcy. 

The reason that this remains largely an academic point is because the companies that enter and exit the index are normally such a small part of the index. For instance, with Macy’s only accounting for 0.0015% at the time of exit, even if investors were to miss out on Macy’s rising ten-fold in a recovery, it would only amount to 0.015% of the index at the end of the comparison (and that is assuming the price of all other stocks stayed at current levels and didn’t raise as well, which is unlikely). And if Macy’s were to go bankrupt while in the S&P 500, it would only result in a .0015% loss of wealth. 

Over the course of a lifetime, a tracking error in an index is small but not nothing. For someone who starts with $10,000, invests $500 per month, and does so for 50 years, the index would suggest a total of $2,161,918 in pre-tax wealth. For someone who actually receives a career 0.16% haircut as reflected by the Vanguard S&P 500 Index over the prior ten-year period, the index fund would result in $2,018,187. These little additions and subtractions to the index over a lifetime, as well as the actual real-world execution of following them, would cost this hypothetical investor around $143,000 over the course of an investing lifetime.

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