Interview: Lars Kroijer (Part II) – On Having An Edge In The Markets

Please see earlier podcast Interview with Lars Kroijer Part I – on the importance of Global Diversification

And my earlier book review of Lars Kroijer’s Investing Demystified.

Lars_Kroijer

In this discussion with author Lars Kroijer we talk about the main assumption of his book Investing Demystified – which I happen to completely endorse – which is that ‘beating the market’ lies somewhere between highly unlikely and impossible. The goal for individuals should be, instead, to earn market returns. Common behaviors that most investors do, like

1.  Paying extra management fees to an active portfolio manager, or

2. Stock picking yourself in order to ‘beat the market’

is a fool’s game, and will ultimately prove unnecessarily costly.

Later in the interview I asked Kroijer to describe his earlier book, Money Mavericks.

 

Lars:                Everyone’s got sort of their angle. My angle is really to start with asking a question of the investor, which is; do you have edge? Are you able to beat the markets? I don’t even make that call for you but I try to illustrate it is incredibly hard to have edge, and that most people have no shot in hell whatsoever of attaining it. Incidentally, that means that people like you are I are not necessarily hypocrites because it’s entirely consistent with our former lives to say we worked in the financial markets; we’ve bought and sold products, and as well informed as anyone. So if we didn’t have edge, edge doesn’t exist.

You could say I’m a hedge-fund manager, and I sold edge for a living, and I certainly thought I had it. But that doesn’t mean that most people, or even that many people have it. I start with the premise in this book of saying do you have it. Then I go on to explain it’s really bloody hard to have it. If you don’t have it, which most people don’t, what should you do?

Essentially, this is a book written for my mom. It kind of is. You wouldn’t believe, but as a former hedge-fund manager, every time I talk to my mom, who’s a retired schoolteacher, she’d always say which stock should I buy. I’d say mom, you could buy an index. And she’s like no, no. Then she’d say stuff like Dansker bonds have done so well, I should be buying it. And I’d be like no, don’t do that. She’s certainly not alone in that position.

Michael:          I completely agree with you, and when I think about how your book lays out four simple rules, starting with the one that you should be exposed to the broadest, most global index portfolio, and I have not done that, in terms of I am US-centric and small-caps centric, so I don’t have the broadest exposure. On the other hand, there is no gap between what you advocate, in terms of can you beat the market, and the way in which I invest, which is always I assume from the get-go ‑‑ and this is why that part of it resonated with me ‑‑ so clearly I, like you, say you can’t beat the market. The goal should not be to beat the market. The goal is to expose yourself to the appropriate allocation to risky markets, appropriate to your own personal situation. And then get the market return.

Lars:                You want to capture the equity-risk premium.

Michael:          The entire finance-marketing machine is about can you beat the market. Beating the market is a complete fool’s game. I think it’s particularly interesting, the other reason I wanted to talk to you, is because you’ve worked in the hedge-fund world, you’ve been a hedge-fund manager, an advisor to hedge funds. I worked on Wall Street. I founded my own fund, and it’s all about that theory that you can, in a sense, have an edge in the market. Yet, the more you know about how it actually works, the more extremely bright people, with the highest powered computing power and the most cutting-edge ideas ‑‑ and you think about the power they had, and we had, and the chances of any retail investor or in fact any of those investors themselves beating the market, or as you say, having edge, is just impossible.

Lars:                Add to that they’re at a huge cost disadvantage, informational disadvantage, analytical disadvantage. It’s so unlikely, and this is why always start with you’ve got to convince people they can’t. That’s actually probably the toughest thing. You’re fighting not only against conventional wisdom, but you’re also fighting this almost innate thing we have, that you somehow have to actively do something. You somehow have to pick Google or whatever.

You have to have a view, and you’re smart, you’re educated, doing something to improve your retirement income, or whatever you’re doing. What you and I are advocating is essentially do nothing. Admit you can’t. I think that rubs a lot of people the wrong way.

Michael:          You need to bring humility to the situation. I cannot do better than the market. I can do the market but I can’t do better. It’s a very hard, humble approach, but in my opinion and in your opinion it’s the correct approach.

Lars:                Yeah. And I also think we’re extremely guilty of selective memory. We remember our winners. That adds to the feeling. It’s a bit like when you ask guys whether they’re an above-average driver. 90% will say they’re above average.

If you ask stock pickers whether they do better than average, 90% of stock pickers would say yes, even more than that. I think there’s a lot of that, a huge degree of selective memory. It’s a shame because I think it really hurts people in the long run.

Michael:          It makes conversations along the lines of what you mentioned with your mother conversations with me and other friends and retail investors in stocks ‑‑ hey, I’ve got this great new stock. I’m such a bummer when I talk to them because I say really? I don’t know what to say.

Lars:                The alternative is to say you don’t know what you’re talking about, which is not an all together pleasant thing to say. It’s not how you make friends. Certainly not when you’re moving to a new town, like you did.

Michael:          I’ve written about this on my site before, but essentially when somebody talks about individual stocks, to me what I’m hearing is I went to Vegas. I put money on 32 and 17 on the roulette wheel. Look how I did. I just don’t know how to respond to that. That’s fabulous, you hit 17 once. I don’t know what to say.

Lars:                This is conventional wisdom because to most other people that person will sound smart and educated. They will say here’s why I found this brilliant stock and here’s why it’s going to do great. Most people in the room will consider that person really smart, educated, and someone who’s got it. They’ll sound clever about something we all care about, namely our savings. And you think if I could only have that, I’d want that. It’s tough to go against that.

This is why I think the biggest part of this book is if I could get people to question that. Maybe even accept they can’t beat the market. Then that would be the greatest accomplishment. I think a lot of the rest follows. I haven’t come up with any particularly brilliant theory here. It’s sort of academic theory implemented in the real world and that’s pretty straightforward.

Michael:          It cuts against the grain of what I call on my site “Financial Infotainment Industrial Complex,” which is there’s a lot of people invested in the idea that markets can be beaten, that individual investors can play a role.

Lars:                Think of how many people would lose their jobs?

Michael:          Yeah, it’s an entire machine around this idea. It’s very hard to fight against that. It’s very boring to fight against that. I joked about it in my review; your book is purposefully hey, I have some boring news for you. Here’s the way to get the returns on the market and sleep better at night.

Lars:                I sort of compared going to the dentist. You really ought to do it once in a while and think about it. I completely agree with you. I mentioned in the book ‑‑ when I thought about writing this book, it was one of these things that slowly took form, but there’s this ad up for one of these direct-trading platform websites. And there was a guy who was embraced by a very attractive, scantily dressed woman. He was wearing Top Gun sunglasses, with a fighter jet in the background. It said something like “Take control of your stock market picks.”

I thought fuck; are you kidding me? Really? Whoever falls for that, I’d love to sell them something.

Michael:          Oh yeah, they’d be a great mark.

Lars:                You also hear a lot about the quick trading sort of high-turnover platforms. It’s something like 85-90% of the people on there will lose money. You have a lot of these companies, their clients, 85-90% will lose money.

It’s almost akin to gambling. You can argue is it gambling, which is a regulated industry in a lot of countries, for good reason, because it costs you a lot of money. And I think certain parts of this circus is the same. But it’s very tough to regulate, and I’m not saying you should. But it could cost a lot of people a lot of money.

I feel very strongly about this. I’m not saying edge doesn’t exist. I’m saying it’s really hard to have it. And you’ve got to be clear in your head why you do, and what your edge is.

Michael:          I have not read [Kroijer’s previous book] Money Mavericks but give me a preview so when I do read it, what am I going to get?

Lars:                It’s a very different book. Money Mavericks is essentially the book of how someone with my background, a regular kid from Denmark ends up starting and running a hedge fund in London, and all the trials and tribulations, humiliations and all that you go through in that process. I thought when I wrote it lots of things have been written about hedge funds, and a lot of it’s wrong. Namely this whole idea that we’ll all drive Ferraris and date Playboy Bunnies and do lots of cocaine.

I thought very little was written from a first-hand perspective, someone who’s actually set up a fund and gone through the fund raising and trying to put together a team. And the humbling failures, and successes, so I thought let me try to write that. I did. I found myself enjoying the process of writing it, which I guess was part of the reason I did it. But then it got published, and it ended up doing really well.

I was actually kind of pleased about that because I thought it’s very nonsensationalist. We didn’t make billions, we didn’t lose billions. No one defrauded us and we didn’t defraud anyone. So those are the four things you normally think about when you think of hedge funds.

Michael:          If you’re trying to sell books, yes.

Lars:                Yeah, so this is none of that. It’s just a story of some guy starting a hedge fund, how it all worked out, all the little anecdotes. I was really pleased that resonated. In fact, the best feedback I got was from people in the industry who were like yeah, that’s exactly what it was like. I’m sure you would appreciate it because you’d have lived a lot of it. Begging for money.

Michael:          No, that’s my second [imaginary] book. My first [imaginary] book is personal finance. My second book is gonna be that experience, your books in reverse.

Lars:                I think you’d enjoy it. That resonates with a lot of people, including what you also would’ve experienced, this whole undertone of anyone can start a hedge fund; I’m going to quit my job and raise 50 million dollars. I’m going to build a track record and then raise another couple of hundred million. Then I’m going to be rich and happy. The number of times I’ve heard some version of that makes me want to puke. When you’re actually doing it you realize how incredibly hard it is.

Michael:          Very stressful.

Lars:                It impacts your health, your life, your family, all of that. Then that’s before you try to make or lose money.

Michael:          You actually have to do it, get a return that people are happy with, and they’re happy to stick with you. Does your fund exist still?

Lars:                No, it’s just my own money. I had incredibly fortuitous timing. I returned all capital in early ’08. But no skill, it was for mainly my own reasons, sanity, health, and family. I’ve been lucky.

Michael:          As we always say better lucky than good. That’s more important.

Lars:                For me there was a big part of that. I thought let’s quit while you’re ahead. To be honest, I have yet to wake up one day where I miss it. I get to wake up one morning where I wish I was heading to Mayfair to turn on to Bloomberg and be at it.

 

Please see related podcast Interview with Lars Kroijer Part I – on the importance of Global Diversification

Please see related book review on Investing Demystified by Lars Kroijer

 

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Rage Against the Machine – Oil & Gas News Coverage Version

Morning News Rant

Do you find yourself eating your morning granola, hunched over the financial news, stopping in the middle of a paragraph, feeling your eyes glaze over as your BS-meter tilts red in 0.6 seconds, and then looking up at the window to start mumbling like a deranged person to yourself about the absurdity of that business story?

Reading the newspaper and getting upset
Grumpy investor reading the news!

You do?

What a coincidence, because so do I!  That’s so weird!  It’s like we’re twins!

Well, ok, not so weird, because you read Bankers Anonymous and you understand that’s one of our conditions – the daily, and perhaps hourly frustration with the Financial Infotainment Industrial Complex’s faulty depiction of events that affect our lives.

Why do I bring up our common condition today?

I’ll tell you why.

Oil and Gas Drilling
The Natural Gas Revolution in South Texas

I live in South Texas, where the development of fracking fields is in the process of revolutionizing energy production in the US.  I believe the consequences of this process, for everything from renewable energy, to regional job creation, to potential environment liability, to geopolitical and Middle Eastern politics cannot be exaggerated.

As a result, I read what I can about business developments in my regional back yard, both in the local paper – The San Antonio Express News – and the Wall Street Journal.

The local paper’s coverage has its flaws[1], but I want to pick a fight with a story today in the Wall Street Journal.  I have found that of the two papers, only the Wall Street Journal covers the Eagle Ford Shale stories from the perspective of national and international public and private equity firms, and I appreciate this, since it’s missing from my local paper.

I should also say my following rant pertains not particularly to the oil and gas or fracking industry, but rather practically any industry covered by the Financial Infotainment Industrial Complex.

The part of the story where my BS-meter hit red

The WSJ story describes the sale of Texas shale-driller GeoSouthern Energy Corp to Devon Energy Corp for $6 Billion, the largest acquisition of the year in the US in the oil and gas industry.  (Pretty important news, which at least 24 hours after the announcement, the local paper still hasn’t touched.  But I digress.)

What gets my goat is a quote buried in the middle of the story by “Wells Fargo energy analyst” David Tameron.  Tameron says:

If you are private[2] right now and you can sell yourself, you do.  If I’m a buyer and there are a lot of people who want out the door, it’s a good time to be buying.

 

Maybe this quote was taken out of context, and if so, I apologize to David Tameron, Wells Fargo energy analyst, for what I’m about to say.

My interpretation of Tameron

I interpret Tameron’s statement as:

“If you’re selling an oil drilling company, it’s a good time to do that.  Also, if you’re buying an oil drilling company, it’s a good time to do that.”

This is an absurd ‘analysis,’ by David Tameron, Wells Fargo Energy Analyst.

Tameron’s statement goes unchallenged by the Wall Street Journal as the self-serving, churn-inducing statement that it really is.

In the real investing world – not currently occupied by either David Tameron, Wells Fargo Energy Analyst, or the Wall Street Journal reporter on this story – there are attractive times to invest $6 Billion in an oil and gas drilling company, and there are less attractive times.

Most of the time, for real investors, we can not be sure whether it’s an attractive time, or not, to be making a $6 Billion investment in an oil and gas drilling company.  Because it really depends on a lot of unknowable future factors, not least of which are the future input costs and output costs for oil and gas, both of which are volatile.

Some time in the future, we may eventually know whether it was a good time to be a buyer of GeoSouthern Energy Corp for $6 Billion, or not.  The answer may even change a few times in the future, again, because markets fluctuate.

From an investor’s perspective

What I do know, however, is that it’s not simultaneously a good time to buy and a good time to sell.

Wait, I need to be more specific.  For investors in the transaction, it is not simultaneously both a good time to buy and a good time to sell.  From an investor’s perspective, it will end up being a good time for one side, and a bad time for another side, some time in the future.

From the brokers’ and the Financial Infotainment Industrial Complex’s perspective

But the investor’s perspective is not shared by brokers or the Financial Infotainment Industrial Complex.

For financial intermediaries (brokers) who buy and sell companies – or stocks, or bonds, or currencies, or real estate – its always simultaneously a good time to buy and sell the same thing, since this is how they make money.

And for members of the Financial Infotainment Industrial Complex, of which the Wall Street Journal is among the most important and sophisticated, it’s always simultaneously a good time to buy and to sell.  Because transactions create events, which in turn gives them something for them to talk about.  They are not investors but rather cheerleaders.

This Eagle Ford Shale example this morning – like the several or dozens of financial transactions a day we vaguely witness passing through the peripheral transom of our financial mindshare – just reminded me of the different incentives we have when compared to the united front of brokers and the Financial Infotainment Industrial Complex.

The Financial Infotainment Industrial Complex needs to churn a story every day, that’s how they get revenue.

And brokers – represented in this example by David Tameran, Wells Fargo energy analyst – need to try to churn a transaction every day.

As consumers (victims?) of the Financial Infotainment Industrial Complex we get hit with somebody else’s strong bias – the need to constantly churn transactions.

The truth that this does not help us think straight about investing – in fact it undermines our ability to think about investing – is rarely mentioned.

You and me, I guess we know this.  We are, somewhat, occasionally, immune.  But what about the rest of the folks out there, fed the disturbingly wrong, the self-servingly biased line, that it’s always simultaneously a good time to be buying and selling?

Sigh.  Time to finish my granola.



[1] Fine, since you asked, what’s wrong with the local paper?  The local paper only covers the Eagle Ford Shale with three themes. A) Fracking = Lots of Jobs!  B) We need to invest in the roads in south Texas that are being hurt by super-heavy truck traffic!  C) There are plucky wild-catters trying to make money here.  Of these, stories A and B are true as they go, and C is absolutely, totally, and completely misleading, since wildcatters comprise approximately 0.0001% of the activity in the Eagle Ford.  As far as the other potential stories of the Eagle Ford, the local paper does not cover them.  These might include: a) Environmental impacts b) The national and international businesses doing deals in South Texas, and their relationship to high-profile public and private equity firms c) Technological innovation in the fracking process in the past 10 years and d) the revolutionary impact of 90 years’ worth of affordable energy on our lives as well as on the renewable energy business.

[2] “private” in this sense meaning the fact that GeoSouthern Energy Corp is owned privately, it has no public shares outstanding.

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Part V – Discounted Cash Flows, using an annuity to learn the math

PiggyPlease see my earlier posts

Part I – Why don’t they teach this in school?

Part II – Compound Interest and Wealth

Part III – Compound Interest and Consumer Debt

Part IV – Discounted cash flows – an example using a pension buyout

Preamble

In the last post I used the example of a pension buyout to show how the discounted cash flows formula worked, and I argued that discounted cash flows are the key to all investing decisions.[1]  Everything else you get inundated with – from the Financial Infotainment Industrial Complex – is just a whole lot of hype, gimmicks, tricks and tips.[2]

Which makes it all the more odd that almost nobody outside of the financial industry has ever heard of discounted cash flows, never mind actually using the formula in their investment life.

So, allow me to peel back the curtain a bit more, using the example of an annuity investment.[3]

 

“Life’s but a walking shadow, a poor player
That struts and frets his hour upon the stage
And then is heard no more”

 

Another example using discounted cash flows, to value an annuity

Is that guaranteed monthly income annuity offered by an insurance company a good deal or not?  To answer the question you’d need to know how to discount cash flows to put yourself on an equal footing with your insurance company offering you the annuity.  Which I did on my site once before.[4]

Let me break down some of the numbers, by way of example, or possibly by way of inspiration to others who want to start calculating discounted cash flows in their own life.

I just went on my preferred insurance provider’s website[5] and asked for a quote on a 15-year fixed time-period annuity.  In exchange for a $100,000 lump sum from me, the insurance company offered me $641.15 per month, guaranteed, for the next 180 months.  The question I ask is whether that is an attractive investment for my $100,000?

To answer the question I’m going to use the discounted cash flows formula Present Value = Future Value/ (1+Yield/p)N.

I offer a bit more explanation of these variables in a footnote[6]

I can discount exactly 180 different future payments of $641.15, by dividing each of them by (1+ Yield/12)N.

For the first cash flow, N is 1.  For the second, N is 2.  For the 180th monthly payment, N is 180.

This looks like this table in my spreadsheet, which contains 180 rows of numbers and discounted cash flows formulas:

N Period Monthly Payment Formula: PV = FV/(1+Y/p)N
1 $641.15 =$641.15/(1+Y/12)1
2 $641.15 =$641.15/(1+Y/12)2
3 $641.15 =$641.15/(1+Y/12)3
$641.15 =$641.15/(1+Y/12)
180 $641.15 =$641.15/(1+Y/12)180

 

Once I have programmed a spreadsheet to calculate 180 individual discounted values for $641.15, I next program the spreadsheet to add up all 180 payments.[7]

Next I can input a value for Y, or Yield, to try to figure what kind of deal I’m offered by my annuity company.

I compare the sum of all 180 values to my original $100,000 investment.  To come up with a comparable yield on the annuity, I input different values for yields into my spreadsheet.  For my purposes I can find the ‘yield’ through ‘iteration,’ basically trying different values until I match up the sum of discounted annuity payments to a final value of $100,000.

If I assume Y is 2%, as I’ve shown in the table below, it turns out the sum of all cash flows is too small and does not quite add up to $100,000.

N Period Monthly Payment Formula: PV = FV/(1+Y/p)N Calculation
1 $641.15 =$641.15/(1+0.02/12)1 $640.08
2 $641.15 =$641.15/(1+0.02/12)2 $639.02
3 $641.15 =$641.15/(1+0.02/12)3 $637.95
180 $641.15 =$641.15/(1+0.02/12)180 $475.09
TOTAL $115,407.00 $99,633.46 $99,633.46

 

If I instead assume Y is 1.5%, it turns out the sum of all cash flows is too large and adds up to more than $100,000.

N Period Monthly Payment Formula: PV = FV/(1+Y/p)N Calculation
1 $641.15 =$641.15/(1+0.015/12)1 $640.35
2 $641.15 =$641.15/(1+0.015/12)2 $639.55
3 $641.15 =$641.15/(1+0.015/12)3 $638.75
180 $641.15 =$641.15/(1+0.015/12)180 $512.04
TOTAL $115,407.00 $103,287.51 $103,287.51

 

 

So I keep trying to find, using my spreadsheet, the value that makes all 180 discounted payments of $641.15 equal to $100,000.  Once I find that, I know what kind of yield, or return, my insurance company offers me on my annuity investment

It turns out, through iteration, that 1.92% is the yield I get by investing $100,000 today and receiving $641.15 per month guaranteed for the next 15 years.

The fact that 1.92% is an absolutely pathetic return is not surprising, nor notable.  As I’ve written before, insurance companies are in the business of buying money cheaply and selling money expensively, and retail annuities are the ultimate source of cheap money for them.

What is notable is that we, as consumers, have no way of evaluating the return on an annuity if we can’t do discounted cash flows.

Which is why I say, ask not what you can do with your insurance company.  Ask what your insurance company is doing to you.

Just like credit card companies do not want you to know that the average American household, carrying the average credit card balance, at an average interest rate, will pay $2.6 million over 40 years because of compound interest[8], similarly, insurance companies can build massive skyscrapers in major cities because they know how to use the discounted cash flow formula to get money cheaply.

And you don’t.

Please see earlier posts

Part I – Why don’t they teach this in school?,

Part II – Compound Interest and Wealth

Part III – Compound Interest and Consumer Debt

Part IV – Discounted cash flows – Pension Buyout Example

Part VI – Conclusion, or why everyone needs to know this math for the good of society

and Video Posts

Video Post: Compound Interest Metaphor – The Rainbow Bridge

Video Post: Time Value of Money Explained

 

 

Be Rational Get Real


[1] Put it this way, if you’re an individual (I will exempt broker-dealers, HFT and many professional investors from this next statement because they are often doing something different) and you’re not employing a discounted cash flows formula, you’re gambling, not investing.  Which is to say, 99.5% (and I rounded down to be conservative) of us are gambling when we purchase an individual stock.

[2] Are the Chinese buying it?  Is your gym-budding selling? Will baby-boomer demographic trends boost this?  Is Bill Ackman short the stock?  Is it a breakthrough miracle drug?  Will nano-technology make it obsolete?  All hype.

[3] I’m using an annuity to illustrate the use of the discounted cash flow formula because it’s easier to talk about the straight math of future annuity cash flows than it is to talk about modeling future stock dividends and profits.  That involves a longer conversation about equities actually just being a series of future cash flows, which most people will not want to wrap their head around at this time.

[4] By the way, I just re-read my piece on annuities from six months ago.  You should go read it.  It’s good.

[5] I mentioned USAA before in my piece on annuities, because their customer service is awesome.  I have no relationship to them other than as a customer and I just like them.  I assume their quote is standard for an annuity provider, neither better nor worse than the competition.  As I wrote you before, USAA, you should totally make me your President Palmer, peddling life insurance for you.  Call me, maybe.

[6] This time with the formula I’ve introduced the variable p, which is the number of times per year that money gets compounded.  In the case of monthly payments, p is 12, because I have to take into account compounding 12 times per year.  N remains the number associated with each payment, from 1 to 180 in our example, unique to each monthly payment.  Yield, also known as Discount Rate, is the variable I’m going to solve for, to figure out whether the investment is a good deal or not.

[7] Those of you reading this who have spreadsheet experience will note that it’s very simple to create 180 nearly identical rows of formulas simply by a click-and-drag of a single formula.  Similarly, adding up 180 different discounted cash flows is as easy as typing “=sum()” into a spreadsheet cell and referencing the correct cells.  Out pops the answer.

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Part IV – Discounted Cash Flows – Golden parachute or silk umbrella?

golden-parachutePlease see earlier posts Part I – Why don’t they teach this math in school?

Part II – Compound Interest and Wealth

Part III – Compound Interest and Consumer Debt

Preamble

In the last two posts I wrote about how, using the compound interest formula, you can compute precisely how large your money will grow over time, using compound interest.  If you assume a particular growth rate (aka yield, or rate of return) and you know how frequently your money compounds (monthly, quarterly, yearly) you can model into the future what your money will become.

This post is about the reverse process, called discounted cash flows, and is – in my humble opinion – the most important piece of math for investing in anything.  The discounted cash flows formula is what you need to know in order to decide to invest in something today that will have some future value.

Despite what the Financial Infotainment Industrial Complex wants you to believe about the reasons to buy something, evaluating the true value of an investment depends on you knowing how to discount future cash flows.  The rest is just hype, spin, sales and marketing.

And all our yesterdays have lighted fools
The way to dusty death. Out, out, brief candle!

What about discounted cash flows?

First, let’s say what the formula is as, again, the Financial Infotainment Industrial Complex does not want you to know this stuff.

The discounted cash flows formula uses the exact same variables as compound interest, but ‘in reverse,’ solving for “Present Value” instead of “Future Value”

Present Value = Future Value/ (1+Yield)N

Where:

Future Value is the known amount coming to you at some point in the future.

Yield is the growth rate of money, also known as the discount rate.

N is the number of times money gets compounded.

Present Value is generally what you’re solving for when you use this formula.

Most importantly when you figure out how to discount cash flows, a whole series of financial and macroeconomic questions become clearer.

An example of a pension buyout showing the value of discounting cash flows

The discounted cash flow formula is what you’d need to use, for example, if your company offered you a lump sum buyout instead of a life-time pension, as GM did to many workers in 2012, and as many companies frequently do to get rid of their future pension obligations.  Let’s say they offer you a $500,000 buyout.  Sounds like a big enough number to induce many people to take a buyout.

Is the lump sum offer a good deal?  How would you know?

If you could set up a spreadsheet to discount cash flows, you’d know precisely what kind of deal it is.

You could add up the value of all of your future monthly pension payments, properly discounted by the formula above, and you could compare that to the amount GM’s pension department offered you.

Let’s say you would normally receive a $36,000 per year pension for the rest of your life, and you expect to live for another 20 years, here’s what you would do.

You might want to know the Discount rate, or Yield, on GM bonds to gauge the risk of the future pension, or you might want to just assume the government guarantees your pension, so you’d input a lower yield.  Let’s assume low, government guaranteed risk for this example and use a 2% yield to reflect government risk and moderate inflation.[1]

Next year’s payment I’d calculate by the formula Present Value = $36,000 / (1+0.02)1, or $35,294.12

The following year’s pension payment I’d calculate as $36,000/(1+0.02)2, or $34,602.08

I can calculate all of these values easily in a spreadsheet, until I added up the 20th year’s amount, which is calculated as $36,000/(1+0.02)20, or $24,226.97

When I add up all 20 years the result is $588,651.60

Which one is bigger?

Of course you can input different assumptions about your remaining life, and the discount rate, and even the pension amount, but all of this is to show that you need this tool to level the playing field and make good decisions.

I guarantee you that GM’s financial officers know how to discount cash flows, and they’re negotiating from a position of extraordinary advantage against their retired workers who cannot discount cash flows.

So, again, blame the math teachers.  And the Financial Infotainment Industrial Complex.

Please see related posts

Part I – Why don’t they teach this in school?,

Part II – Compound Interest and Wealth

Part III – Compound Interest and Consumer Debt

Part V – Discounted cash flows – example of an annuity

Part VI – Conclusion and why everyone needs to know this math for the good of society

and Video Posts

Video Post: Compound Interest Metaphor – The Rainbow Bridge

Video Post: Time Value of Money Explained

Also see related post: Using Discounted Cash Flows to analyze Longevity Insurance

 

Silk umbrella


[1] Really you can input whatever assumptions you want to derive a discounted cash flow.  Please don’t start a fight with me about whether 2% is the right assumption.  I’m just trying to show a math technique, not debate the proper discount rate for GM pensions.

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Part III – Compound Interest and Consumer Debt

hPart III – Compound interest and Consumer Debt

Please see earlier posts Part I – Why don’t they teach this in school  And Part II – Compound interest and Wealth

So in the last post I wrote about the the incredible power of compound interest, and the possibility it suggests about wealth creation over time.

Unfortunately, there’s also bad news.

On the debt side of things, how much does your credit card company earn if you carry just an average of a $5,000 credit card balance, paying, say, 22% annual interest rate (compounding monthly) for the next 10 years?

In your mind you owe a balance of only $5,000, which is not a huge amount, especially for someone gainfully employed.  After all, $5,000 is just a quick Disney trip, or a moderately priced ski-trip, or that week in Hawaii.  You think to yourself, “how bad could it be?”

The answer, including the cost of monthly compounding[1], is $44,235, or about 9 times what it appears to cost you at face value.[2]

I hate to be the Scrooge, but the power of compound interest transformed that moderate credit card balance of $5,000 into an extraordinarily expensive purchase.[3]

 

Compound interest: Why the poor stay poor and the rich stay rich

To take another example, let’s think of compound interest on credit cards for the average American household.

Let’s say you are an average American household, and you carry an average balance of $15,956 in credit card debt.

Also, as an average American household, let’s assume you pay an average current rate of 12.83%.[4]

Finally, let’s assume you carry this average balance for 40 years, between ages 25 and 65.  How much did your credit card company make off of you and your extreme averageness?

Answer: $2,629,618.64[5]

So, in sum, your credit card company will earn from the average American household carrying a credit card balance for 40 years, $2.6 million. [6]

If you’re wondering why rich people tend to stay rich, and poor people tend to stay poor, may I offer you Exhibit A:

Compound Interest.

Now, your math teacher might not have done this demonstration for you in junior high, because he didn’t know about it.  Mostly, I forgive him.  Although not completely.

You can be damned sure, however, that credit cards companies know how to do this math.  THIS MATH IS THEIR ENTIRE BUSINESS MODEL.

Which same business model would work a lot less well if everyone knew how to figure this stuff out on his own.

Hence, my theory about the Financial Infotainment Industrial Complex suppressing the teaching of compound interest.  They don’t want you to learn how to figure out this math on your own.[7]

and Video Posts

[1] But importantly, excluding all late fees, overbalance fees or penalty rates of interest.

[2] We get this result using the same formula, although Yield is divided by 12 to account for monthly compounding, and the N reflects the number of compounding periods, which is 120 months.  So the math is: $5,000 * (1+.22/12)120

[3] Have you ever wanted to take a $45K vacation to Hawaii and pretend you’re a high roller?  Congratulations!  By carrying that $5K balance for 10 years, you did it!  You took a $45,000 Hawaiian vacation. You’re a high roller! Yay!

[4] All of these stats taken from this great site on credit card statistics, which cites all of its sources.

[5] We express this again dividing yield by 12 to account for monthly compounding, and raising it to the power of 480 months, the number of compounding periods.  Hence the math is $15,956 * (1+.1283/12)480

[6] I’m assuming for the purposes of this calculation that the debt balance stays constant for 40 years, but your household pays interest on the balance.  In calculating this result, please note I have framed the question in terms of “How much does the credit card company earn” off of your household carrying this average balance for 40 years.  Which is not the same question as “How much do you pay as a household?”  Embedded in my assumptions, and the compound interest formula, is the idea that the credit card company can continue to earn a fixed 12.83% on money you pay them.  Which I think is a fair way of analyzing how much money they can earn off your balance.  Since there are no shortages of other household credit card balances for the credit card company to fund at 12.83%, I believe this to be the most accurate way of calculating the credit card company’s earnings on your balance.

[7] Here’s where, for the sake of clarifying sarcasm on the internet – which sometimes doesn’t translate well on the electronic page – I should point out that I’m (mostly) kidding about the suppression of the compound interest formula.  Among the main reasons I started Bankers Anonymous was that the dim dialogue we have about finance as a society allows conspiracy theories to grow in darkness.  Just as pre-scientific societies depend on magic to explain mysterious phenomena, I think financially uninformed societies gravitate toward conspiracies to explain complex financial events.  As a former Wall Streeter who does not actually ascribe to conspiracy theories, I feel some obligation ‘to amuse and inform’ and thereby reduce the amount of conspiracy-mongering.  So, I don’t really think there’s a conspiracy here.  As far as you know.  Or maybe, that’s just what I want you to think.

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Part I – The Most Powerful Math in the Universe Goes Untaught

Einstein picture

On Teaching Compound Interest and Discounted Cash Flows

 

“The most powerful force in the universe is compound interest”

– Albert Einstein[1]

 

“Tomorrow and tomorrow and tomorrow,
Creeps in this petty pace from day to day
To the last syllable of recorded time”

 

This Spring I began teaching Personal Finance to a group of bright college students, and we recently wrapped up a section on compound interest and discounted cash flows.

What I’m trying to get across to these undergraduates is that all of the key financial choices they will make in their lives – all of their future decisions about consumer debt, retirement, insurance, purchasing a home, tax preparation, and investing – will be much, much better decisions if they deeply understand compound interest and discounted cash flows.

What are these concepts for?

The compound interest formula tells these students, and any of us who use it, exactly how quickly, and to what ultimate size, money grows in the future.[2]

Discounted cash flows reverses the process, and tells us what the present value would be of any given cash flow or series of cash flows that occurs in the future.[3]

I’ve realized over the course of the last few weeks, however, that I’m trying to convince these students of the absolute centrality of an idea that 95% of them have never heard of before walking into my class.

Not only this, but also 95% of the people my students will meet in their life never have heard of compound interest and discounted cash flows, and therefore will not have the slightest idea how profoundly it affects their lives and their personal financial choices.

Picture me in front of the class jumping up and down and waving my arms wildly (metaphorically of course), trying to get them to believe me.

And yet, why should they believe me when I appear to be the first (and possibly insane) person to ever argue this case?

I’m afraid that after they leave my class, the Financial Infotainment Industrial Complex will never again reveal the importance of compound interest and discounted cash flows to personal finance decision-making.

Why isn’t this taught as a requirement of Junior High School Math?

I was a strong math student in junior high and high school.[4]  I received a solid foundation in algebra, geometry, trigonometry, and calculus.  Of these, algebra has frequently proved useful, but none of the others apply to my life or career.

Compound interest and discounted cash flows, however, dominated my professional life as a bond salesman and hedge fund investor, and I make use of insights from them in my personal financial life all the time.

And yet, nobody taught me compound interest or discounted cash flows in school.  I’d be willing to bet that almost all of you reading this didn’t get taught these concepts in school.  That knowledge had to wait until I started as a bond guy at Goldman.  This, despite the fact that you only need junior high school level math – basically algebra and the concept of ‘X raised to the power of Y’ – to understand and use compound interest and discounted cash flows.

The fact that school taught, and I spent years learning, complex but ultimately very niche mathematical skills, combined with the fact that nobody taught the essential mathematical skills of personal finance (and Wall Street finance for that matter) really gets up my nose when I think about it.

More than gets up my nose, it puts me in a suspicious frame of mind.

Why would these essential skills not be taught to every junior high school student, and then re-taught to every high school student, and then elaborated on for every college student?  Because that’s how important this stuff is.  And how relatively unimportant trigonometry, geometry and calculus skills are for most citizens.

I’ve only come up with a couple of possible explanations, as I explain below, but please chime in with your own theories.

1. Math teachers, as a group, do not understand the role of compound interest and discounted cash flows in personal finance.

I fear this is true.  I’ve become friends with a few of my high school math teachers as an adult and with one I’ve discussed the power of compound interest as a math concept and as a personal finance concept.  Later in his career, long after I took his class, he taught compound interest as part of his lessons on mathematics skills known as ‘sequences and series.’

In these later days he emphasized to his students that if he had really understood compound interest – as a young man – as well as he does now, his working and his retirement years would look totally different.  Could somebody please tell the Professional Math Teachers Association (or whoever is responsible for this stuff) that this is really the key concept, and I mean, for everything?

2. The Financial Infotainment Industrial Complex wants to keep us down.  I’m afraid I’m coming around more and more to this explanation.  Nothing else makes sense.

I mean, seriously folks, calculus: Not relevant (for most people.)  Compound interest: relevant (for everyone.)

 

Coming up next: Part II –  Compound interest and Wealth

Part III – Compound interest and Consumer Debt

Part IV – Discounted Cash Flows Formula

Part V – Discounted Cash Flows – another example, using annuities

Part VI – Conclusion, and why we need this math as a society

 

——Addendum by Michael to this post:

One of my high school math teachers (and my high school advisor!) responded to my post by pointing out that not only does he teach compound interest, but that its part of the math textbook he wrote.  How about that?  I can’t resist linking to his textbook on Amazon, as my way of atoning for casting aspersions on math teachers.

 

 

 


[1] Albert Einstein frequently gets credited with this wise statement.  A quick interwebs search suggests Einstein didn’t necessarily say this, as the first mention in print is found circa 1983.  But Einstein could have, and should have, because it’s true.

[2] To get started on your own learning journey on compound interest, I recommend beginning by watching a video here, with my favorite, Salman Khan.  If you enjoy that, continue the process with videos on present value #1, present value #2, and present value #3

[3] A nice place to start on discounted cash flows is Salman Khan’s video on present value #4 (and discounted cash flow).  Khan doesn’t go far enough on discounted cash flows, or as far as I’m going to go in this series of blog posts to follow, but he at least gets us started, which is more than I can say for almost anyone else available for free out there.

[4] I didn’t pursue math in college, beyond one statistics class required for my concentration, which was Social Studies.  Shout out to the 0.0005% of readers (I chose an arbitrary but statistically insignificant number) who will recognize my major and salute me for it, rather than assume I spent my college years doing what the rest of you did in Social Studies in middle school – memorizing state mascots.

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