Friday, October 26, 2012

The Yankees' A Rod Problem: Sunk costs and investing

As any baseball fan knows, the New York Yankees have an A Rod problem. Just in case you have no idea what I am talking about, A Rod is Alex Rodriguez, the third baseman for the New York Yankees, signed in December 2007 to a one of the richest sports contracts in history. The Yankees, dazzled by the the numbers that A Rod posted in 2007 and by the possibility that he could become baseball's home run king (with 500 home runs, he seemed to be on a path to beating Barry Bond's record of 762 home runs), signed the then 33-year old to a ten-year contract worth $275 million (with numerous bonus clauses for breaking home run records). The five years since have not measured up to expectations, with the disappointment building to a crescendo in the 2012 post-season, when A Rod's anemic hitting led to his being benched in the last two games against the Detroit Tigers. Now, the Yankees owe $114 million over the next 5 years to a 38-year old third baseman, who is susceptible to injuries and has seem to have lost his home run power  and his capacity to hit right handed pitching.  

What should the Yankees do with A Rod? If they follow financial first principles, the contractual commitment of $114 million that they have already entered into should not be part of the calculus in any decision that they make now. Thus, if they feel that A Rod, based upon his current skill level (and age), is worth only $3 million a year for the next 5 years, they should be willing to consider trading him to another team (assuming he okays the trade) that will offer even a little bit more (say $3.1 million/year) in return, and eat the rest of the contract (about hundred million). Will they do it? I don't think so, because any such deal be an explicit admission that they made a horrendous mistake five years ago. Instead, what you are most likely to see is A Rod at third base for the Yankees, to start the next season, with everyone hoping and praying that he discovered the fountain of youth (at least a legal version of it) in the off season.

The financial principle I was referencing is of course the one of sunk costs and anyone who has taken a basic corporate finance class knows the rule. A cost that you have already incurred or are contractually committed to incur should be ignored in your decision making. That rule, though, is easier enunciated than put into practice and here is a simple exercise to see why:

1A. Assume that you are the manager of a business that is in ongoing development of a new product that will require spending an additional $100 million to bring to completion. Assume that you have just learned that a competitor has come up with a superior product at a lower cost and will be bring it to 
the market at the same time as you will. Would you spend the $100 million?
a) Yes
b) No

1B. Now assume that the same facts as in the prior case but also assume that you know that you have already spent $ 900 million on developing this product. Would you spend the additional $100 million?
a) Yes
b) No

For most of you, I am sure that the answer would have been an easy "No" for 1A, since spending an extra $ 100 million on a product that will not compete seems pointless. For some of you, though, was it more difficult to say "No" to 1B? If so, you are not alone since 80% of managers in an experiment that asked exactly these questions were swayed by the sunk costs into investing in a doomed project. Interestingly, there have also been follow up studies that find that if decision makers were responsible for incurring the sunk costs in the first place, they are even more likely to be swayed by those costs.  In behavioral finance, the capacity of sunk costs to affect decisions falls under what is termed the "Concorde fallacy", named after the ill-fated supersonic jet that the British and French governments poured billions of dollars into, even in the face of clear evidence that it would never be a commercial success, partly because they had already spent so many billions in development.

If you are an investor, you may wonder what this post has to do with you. I think we are all susceptible to the sunk cost problem. To illustrate, let's try a different experiment:
2A. Assume that you are looking at a stock trading at $10/share and that you have valued the shares at $8/share. Would you buy the stock?
a) Yes
b) No

2B. Now assume that you are looking at the same stock trading at $10/share, but that it already part of your portfolio and you bought it at $50/share. If your value per share is $8, would you continue to hold the stock?
a) Yes
b) No

2C.  Now assume that you are looking at the same stock trading at $10/share, but that it already part of your portfolio and you bought it at $2/share. If your value per share is $8, would you continue to hold the stock?
a) Yes
b) No

I am sure that the answer that you gave to question 2A was an unequivocal "No" but was your answer different for 2B? And how about 2C?  (Remember that holding a stock in your portfolio is equivalent to buying the stock....) If the answers were different, why? After all, on an incremental basis, the choice is exactly the same, and an investor who would not buy the stock in 2A would have also sold the stock in 2B and 2C.

The problem is that investors seem to have different sets of rules, one for new or marginal investments, and one for existing investments. Rationally, your decision on whether to keep an investment in your portfolio should be based on whether that investment is cheap or expensive, given its price and value today, and not on what you originally paid for the investment or its value then.  (I know that taxes can create a real issue here, but this problem seems to persist even for tax exempt investors.) However, we are human and almost by definition, we are not rational, and behavioral finance chronicles the costs that we bear. In particular, there is significant evidence that investors sell winners too early and hold on to losing stocks much too long, using a mixture of rationalization and denial to to justify doing so.  Shefrin and Statman coined this the "disposition effect" and  Terrence O'Dean looked at the trading records of 10,000 investors in the 1980s to conclude that this irrationality cost them, on average, about 4.4% in annual returns. Behavioral economists attribute the disposition effect to a variety of factors including over confidence (that your original analysis was right and the market is wrong), mental accounting (a paper loss is less painful than a realized loss) and lack of self control (where you abandon rules that you set for yourself).

So, is there anything that we can do to minimize the disposition effect? I don't have the answer but here are some things that you could consider. I employ the first two in my portfolio and while I cannot quantify how much they have saved me, they have brought me peace of mind.
  1. Regular value audits: The easiest path to the disposition effect is denial, where we refuse to look at the investments that we already have in our portfolio because we are afraid of what we may find. In fact, think about how much time we spend trying to come up with new investments to add to our portfolios (it is always more fun to start anew) and how little time we spend on maintenance investing. One practice that I have instituted for myself is that I have to value every company that is already in my portfolio at least once a year. It forces to me to take a look at the company, as if it were a new investment, and decide whether it deserves to stay in my portfolio another year. Since I have about 40 stocks in my portfolio, it does require some discipline but I think it has been well worth the cost.
  2. A selling rationale: Even with these value audits, I (like most investors) find it difficult to let go of losers, since selling a stock that has gone down is an explicit admission that I made a mistake. So, I provide myself with cover, especially at year end. For every winner that I sell each year (and I do sell one or two that have become over valued, at least in my judgment), I look for a loser (which is also over valued, in my judgment) that I will unload to reduce my tax exposure. Thus, rather than having to admit that I made a mistake, I can pat myself on the back for a savvy tax trade. Delusional, I know, but it helps...
  3. Automated rules: If the first two suggestions don't work, there is a third option, which is to take control of the decision out of your hands. You can put in a stop loss order, specifying that a stock that drops more than X% from your original purchase price, it gets sold automatically. It is a bludgeon, because that stock may very have become a bargain, but you may be saving yourself some bad disposition effect losses.
  4. Decision making separation: If it is the unwillingness to admit to your own mistakes that lies at the heart of the "disposition effect", it may be alleviated (at least in part) if the person making the assessment of whether to hold or sell a losing stock is not the person who made the mistake of buying the stock in the first place. Perhaps, mutual fund managers should work in pairs, with one manager responsible for making new investment picks and the other in charge of monitoring existing investments. Impossible to do for individuals, you might say... but I am considering talking to my wife about splitting the investment management role in our family. She can be the stock picker and I could be the stock assessor or vice versa.... One of us gets to make judgments on the other's mistakes.. On second thoughts, scratch that idea..
So, as we watch the Yankees tackle their A Rod problem, it is worth remembering that we all have our own versions of the same problem: a reluctance to admit to our past "investing" mistakes and let sunk costs be sunk costs.


Avid said...

I learn so much from your posts, I sometimes wonder why people pay for business school.

Anonymous said...


You are assuming that the value of a stock can be determined. I am not so sure about that. For example, the valuation of Facebook stock varied widely at its IPO. Similarly, there are many buyers (undervalue) and sellers (overvalue) of Apple stocks.

So if one cannot be certain of the valuation of a stock, the acquisition and disposition rules may not be clear-cut.

I would advise against your automatic rule #3 in the current trading environment. A sell order triggered by a "flash" crash can be extremely costly to your wealth.

Anonymous said...

This is great stuff. Behavioral control is one of the greatest challenges for us humans, particularly in finance since loss of money hurts.

However tackling sunk cost fallacy is not easy. It is not easy to say with confidence that the competitor's product is in fact cheaper and superior.

In theory it works. But in practice there are whole load of factors which affect decision-making such as what if the competitor's product though thought to be cheaper and superior fails in terms of expectations. What if I chose (for theoretical reasons)to dump the idea of spending another 100m and later regreted only to find that it could have given a better npv with 100m extra. Market moods change and so do fortunes.

So all said in theory it works but it is tougher in practice because of the expectations game. We cannot predict things in advance.

Gooza said...

I guess because not all professors are that keen on sharing their thoughts and experience in a public blog. But I'm biased....

Anonymous said...

Dear Professor,

I'm Dung, I come from Viet Nam.I'm learning Finance Master degree in Viet Nam. And I'm researching about Operating Cash Flow subject. My teacher told me that I should find some books that were written from you. I didn't find any book about operating cash flow at bookstores in Viet Nam. Could you please help me to give name of books that relating to operating cash flow.
Thanks Professor so much.

Anonymous said...

I generally do an yearly or semi-annual update of investments and projects value. This means that we recalculate npv, irr, payback, ... and on this base we make decisions. Besides, the competitive scenario must be judged on a case by case basis and factored in the calculation (e.g. Top line). Sunk costs are sunk and as such are not factored in financial plans.

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Anonymous said...

Great read - thank you.

Anonymous said...

crescendo (noun) a steady increase in force or intensity

Using it as a synonym for "climax" is sloppy, even if it becomes condoned.

The article was excellent otherwise.

capitalistic said...

The sunk cost should be the initial contract at time 0, not necessarily the remaining contract. The Yankees generated revenue from A. Rod, although his production as eroded. A sunk cost would be signing an athlete, and the athlete experiencing a season ending injury.
Just my opinion

Aswath Damodaran said...

Sundry responses... Good point on "crescendo".. Should have used "climax". And on the question of "sunk costs", you are right. The A Rod problem is a variation of the sunk cost problem which is the "non incremental cost" problem, i.e., a cost that you are going to incur no matter what decision you make on A Rod...

Ryan said...

How would a value audit work with real assets though. I understand that in financial markets, value is almost real time but for example real estate which is not traded as frequently would the same concept apply?

Eric from London said...

I enjoyed reading your post. As a fan of Munger, Mauboussin, Montier and Kahneman, I am pleased that behavioural finance is now becoming more mainstream.

One of the issues other comments have alluded to is the uncertainty of future outcomes. There is a chance that A Rod is in a temporary slump (Buffett, Bolton and other fund mangers have them too) and can come back. Therefore there is option value that one also needs to consider as well as the simple expected value of the outcome.

Investors who have allocated a portion of their wealth to equities should understand that investing is an opportunity cost game rather than an absolute return game. If you want to be in the market, then you should find stocks with higher upside than other stocks you have in your portfolio, independently of whether the incumbent holdings are in the red or black. Psychologically, it will be easier to make portfolio changes if you think of replacing those 'losers' with 'winners', rather than thinking of biting the bullet on the 'losers'. The best fund managers determine a target price at the time of investment and revise it periodically so that they will be aware of the expected return profile of each stock they hold.

David Merkel said...

Professor, have you considered yet another sell rule? I rule I have run across over the years is called the "economic sell rule" by some.

"When you find something something significantly better than what you have, swap for the better asset." Bond traders do this all the time. Stock managers don't. It makes life simpler, because relative binary comparisons are easier for humans to make: "I like this better than that."

Here's my implementation of this rule:


KevinM said...

I agree with earlier comments, the problem with applying the sunk cost concept to equities is that the real value is unknown, only suspected. One buys a stock thinking it is undervalued. At that moment of purchase we have bet against the market - it was wrong to sell to us solow. When the market disagrees, but other available information stays the same, the market is merely becoming "more wrong".

Bond values are less inferrence and more calculation, so the concept is better applicable.

Ugh! I can't prove I'm non-robotic!

MikeJake said...

Actually, I would argue that the Yankees are regarding the remainder of A-Rod's contract as a sunk cost.

The greatest advantage that MLB's big market teams have is that they can afford to eat bad contracts, which is why we're seeing them offer long term deals to players in their prime or nearing the end of their prime. If they give a guy an 8 year deal, he really only has to produce for 4 or 5 years at a top level (as measured by the Wins Above Replacement stat) for the contract to be worth it. This ability to offer extra years to older free agents is a significant competitive advantage for teams like the Yankees. For instance, every team in MLB probably would have been willing to sign Albert Pujols to a 5 year, $120 million deal. The Angels got him because they were willing to give him an extra 5 years, when he's not likely to be nearly as productive as he is now. But they knew that going in, so it's not like Pujols' inevitable decline in 4 or 5 years is going to come as a shock.

So ultimately, I think A-Rod will be playing in New York next season for baseball reasons, not because the Yankees will be paralyzed by the sheer amount of sunk costs they've incurred. Granted, the extension they gave him was a terrible decision on the merits. But A-Rod's WAR still rates him as an average starter (and keep in mind that "replacement" players are worse than "average" players, so to have an average player at a position is not a disaster), he was playing well before he fractured his hand, and the Yankees' only current alternative at 3rd Base is Eric Chavez, who is 34 and has been plagued by injuries throughout his career.

edgewood121 said...

I think over-simplifying this can inadvertently lead one into rational expectations, which may not hold up well against reality.

There are inferior products in the world that sell at higher prices because of excellent marketing. So to say there may exist a better product at a less price may not be enough information to make a responsible decision. What about market share? Lots of products sell very well in the number two or three slot in ranking and still are profitable to investors. It goes without saying, the size of the market is important as well.

Unknown said...

Could this sunk cost principle be in part a cause of certain highly asset intensive and cyclical industries with high barriers to exit to be long-run non-economic? For example, airline operators will commit to planes "Day 0" but arguably should fly to the extent that revenue > variable cost, and at least on a marginal basis aren't incented to park planes in the desert until past negative GAAP earnings? On add on uncapitalized commitments to labor, etc...

Arguably, in scenarios like that, one might want to appreciate and price this in before making the initial purchase decision (eg. if I decide to buy a share of Exxon today and it falls 20% tomorrow without meaningful incremental news, would I be a seller)? This is obviously a different scenario from that which you are suggesting, ie. review the company to ensure that the incremental news truly has limited bearing on intrinsic value.

Unknown said...
This comment has been removed by the author.
Unknown said...

Hello sir,
I feel the important thing about sunk costs is when it comes time to make a decision about the project or investment, you should NOT factor in the sunk costs in that decision.
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justbetter said...

I hope you and your family are okay in the storm

Sourcing and Procurement said...

Should sunk cost matters if you already owned a stock that is trading signfiicantly below what you paid for, but you think it is overvalued? For example, an investor bought AAPL at $200, should she buy more at the current price of ~$575 even though she believes it is overpriced?

Anonymous said...

Dear Sir,

I hope you and your dear ones are doing fine (post hurricane sandy).

Best Wishes,

Pranav Pratap Singh said...

Hope you have power and internet back again!

It might not be a bad idea for one person to decide at what price to buy and another to decide at what price to sell a stock. I get a feeling that some people are used to think like 'how bad can it get'. Many people who have extensive experience in debt/credit markets are used to thinking like that. But they find themselves at sea when prices go up and can't decide when to sell. Would there be some people who have a better feel of 'how good can it get' and take better decisions of when to sell?

Pranav Pratap Singh said...
This comment has been removed by the author.
Pranav Pratap Singh said...
This comment has been removed by the author.
Pranav Pratap Singh said...
This comment has been removed by the author.
Pranav Pratap Singh said...
This comment has been removed by the author.
Pranav Pratap Singh said...
This comment has been removed by the author.
Unknown said...


Very good commentary, but one line gave me a bit of a chuckle. In the suggestion for performing regular value audits you note: "Since I have about 40 stocks in my portfolio, it does require some discipline but I think it has been well worth the cost."

You think? This comment screams out that the sunk cost of the time commitment of performing the task may be blinding you to its utility. Now I too expect it is indeed worthwhile, but the phraseology in the context of the subject was curious.

Aswath Damodaran said...

You may find this to be an obvious part of any portfolio but remember that the mantra for many value investors is to "buy and hold forever".... Moreover, there is utility only if you do redo your valuations, rather than just look at what's happened to the price., right? So, I am glad we agree.

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Anonymous said...

I posted this in the facebook IPO post as we discussed drivers of value there. But thought this may be more appropriate here buy facebook fans

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Sunshine Coast Bookkeeping said...

Long-term commitment needs courage with full vision in the future before investing on something. Like Yankee's A Rod, the third baseman for the New York Yankees, signed his contract for number of years without thinking that anyone is susceptible to injuries and might not be a good player. It's a lesson for us to remember.

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