Investing at the speed of light

Okay, so we all know about Einstein’s theory of relativity, right? One of the results of relativity is that time slows down as speed approaches the speed of light. But how can we use this to improve our returns when investing?

I’ve been thinking about this for a while, and I think I have it figured out, but it is a bit complicated.

Buying a bond is the same as receiving a series of inflows; the price is based on the present value of those inflows. If time slowed down, those inflows would be further in the future, and thus worth less. So a bond will decrease in value as you approach the speed of light. Obviously buying a bond is not the right plan then.

But what about shorting a bond? Yeah, that could work! Find someone who is about to travel at something approaching the speed of light. Ask him what bonds he owns. Short those bonds. Then, when he is on his journey and his bonds are worth less, buy them from him to cover your short.

I will leave the method of communicating with him while he is traveling at the speed of light up to you to figure out.


Apparently there is a new flu strain to watch out for. The CDC announced several cases of H1Enron have been confirmed in Houston.

Symptoms include:

• Fever
• Off balance sheet liabilities
• Runny nose
• Special Purpose Vehicles
• Sore throat
• Over-leveraged capital structure
• Headache
• 401(k) declines
• Fatigue
• Poor corporate governance

Those who are at risk for infection should wash their hands frequently and consult with their local auditor.

Okay, so this isn’t really about finances, but it is nerdy, so I thought you all would appreciate it.

Grocery Store Gift Cards

A few weeks ago I mentioned a local grocery store that lets you save money on your gas budget by buying your groceries there.

This store has just upped the ante a little bit. The gas program is still going on, but they have also added a gift card program. Here’s how it works:
If you buy a $250 gift card they will add $20 to the balance, giving you a $270 gift card for $250.
If you buy a $300 gift card, they will add $30.

We asked how this integrates with the gas program, and they said that no gas points are given when the gift card is purchased, but points are given like normal when the money on the card is actually spent.

Our grocery budget is about $600 a month for a family of five, including non-grocery things bought at the grocery store (toiletries, etc.). My wife also gets her prescriptions there, since they are the same price as everywhere else, but we get the points.

So, this is all upside to us. Our plan is to buy two $300 gift cards every month, and use them for that month’s groceries. Since we spend that much every month anyway, this has basically no cost to us, but gets us an extra $60 to use for groceries.

One question that arises is what to do when the promotion ends. It is one thing to prepay your monthly grocery bill to get the rebate, since you would spend that much that month anyway. But what about when the program is about to expire — how many months worth of groceries do you prepay? It is not worth paying credit card interest just to save on groceries, but we also want to maximize the rebate we get. We haven’t decided what we will do yet, and there may also be limits on how much you can do at one time, but I think it would be worth prepaying at least a few months to get the 10% rebate.

What about you? Anyone else have a grocery store with this type of program? Are you planning to take advantage of it?

What is a “risk-free” investment, anyway?

Have you ever heard someone say that an investment was “risk-free?” What does this mean?

The Capital Asset Pricing Model (CAPM) considers a Treasury bill to be risk-free. A T-bill is a short term investment in the U. S. Government, and since the government has never reneged on its debt, this investment is supposed to be risk free.

But is it really?

Ignoring the possibility of the government defaulting on its debts, a T-bill is STILL not risk free. Default risk is just one of many risks to consider with any investment. Here are some other risks to consider:

Inflation risk — the risk that the return on the investment is below inflation, and thus you are actually losing purchasing power.
Reinvestment risk — The risk that periodic cash flows (such as interest or dividend payments) will have to be reinvested at a lower rate than is currently available.
Market risk — the risk that the investment’s market value declines.
Currency risk — for foreign investments, the risk that changes in foreign exchange rates decrease your return.
Liquidity risk — the risk that the market is not liquid enough to allow you to cash out an investment.

This is just a quick summary, there are many other risks to consider as well. But, the point is that calling A T-Bill “risk-free” is really not accurate. It may be default risk-free, but it is not completely risk-free. In fact, there is no investment in anything that is risk-free. All investments require a balance between the various potential risks, but none are completely risk-free.

You might say this is just semantics, but I would disagree. I have met many people with their entire 401(k) invested in T-Bills. When asked why, they say “Because they are risk-free.” These people don’t realize that inflation risk is probably a bigger concern than default risk for their portfolio.

The logic of gift card rebates

In my last post on credit cards, I discussed using them for the rewards and rebates.

This brings up an interesting question, which I have often wondered about. Why do rewards cards offer you a choice between, say, a $25 check and a $25 gift card to various stores?

Isn’t a $25 check always more useful than a $25 gift card? Even if you are going to buy something from Amazon, you are no worse off getting $25 in cash, versus getting a $25 Amazon card. And some credit card companies even offer a “statement credit” which is applied directly to your account, so you don’t even have to go cash the check, you just pay $25 less on your credit card.

Granted, if you carry a balance, and you SHOULDN’T, a statement credit may be worth less to you, because it doesn’t put money into your pocket. But if you pay off your balance every month, a statement credit is effectively the same as direct depositing the amount into your checking account.

But, even if you carry a balance, and don’t want a statement credit, a check is still better than a gift card, right? Unless you buy something for that exact amount, you still have to enter another form of payment for the difference, which is arguably as much of a hassle as physically depositing the check in the ATM.

So, if gift cards are never better, and are at best, equal to a check, why do they even offer them? Better yet, why do people select them? I am assuming here that the face amount is equivalent, which has been the case in all circumstances I have seen. If the gift card is for more than the check, that is a different argument.

If you routinely select the gift card over the check, please post in the comments and let us know why. Maybe there is something I am missing, and I would love to learn about it.

What is the next date in this series?

A few weeks ago, on March 3, everyone was excited about the date being a math problem. 3/3/2009 is the same as 3/3/09 if you ignore the first two digits of the year, and 3*3=9. Pretty cool, huh?

But here is a more interesting series:
October 3, 1000
February 10, 1024
April 5, 1024
June 4, 1296
November 3, 1331
December 3, 1728

What is the next date in this series?
How many such dates are there with four digit years (from 1000 AD to 9999 AD)?

As you can see above, some of these dates are only a few months apart. Others are many years apart. What is the longest gap between dates, again limited to four digit years?

Post your guess/answer in the comments and we’ll see who gets it right first. I know this is a little different than our normal number freaking, but I thought it was a fun puzzle.

Are credit card rebates worth it?

We use our credit card for everything. We have a rewards card that pays us 1% cash back for all purchases, so we pay everything we can with our card just to get the rewards.

However, this brings up some important issues that I would like to explore.

First, is earning rewards worth carrying a balance? You don’t really need to do much math to know that the answer is no. Any savings on rewards would be wiped out by interest payments, so you should not attempt this strategy if you will not be able to pay off your card in full each month.

In fact, we pay off our card twice a month (online), and I’ll get to the reason in a moment.

The second question, which is harder to answer is, “Will I spend more because I am using a credit card?” Many studies have shown that consumers spend more when using a credit card, because they don’t perceive it as money. According to this theory, only by paying in cash do you associate a purchase with money leaving your possession.

I see the point, but I humbly disagree. When I make a purchase with my credit card, I immediately enter into an excel spreadsheet that tracks my expenses. So, even though I used my card I am effectively treating it as cash.

Also, as I mentioned above, I pay off my balance twice a month online, so I know when I charge something the money is coming out of my account almost right away. There are two reasons I do this — one is to keep my outstanding balance low relative to my credit limit, which helps my credit score. The second is to help me mentally treat this as spending actual cash, which helps me to spend less.

So, if you are careful with your spending, and pay off your balance each month, I think using a credit card for the rebates can be a wise decision. This is especially true for recurring bills that you would be paying anyway, such as cable, phone, etc. Not only do you get the rewards, but you save money on stamps because you don’t have to mail them a check.

What about you? Do you use a credit card for the rewards? Do you have any tips or tricks to share?

Saving on gas by buying groceries?

One of our local grocery stores has started a new affiliate program with Sunoco. For every $10 you spend on groceries, you get $.01 per gallon off on your next gas purchase. In addition, they have specials every week that generate larger savings. For example, a gallon of milk saves you $.15 per gallon of gas this week. There is a cap of 20 gallons of gas per transaction, and if you buy less gas, the money does not roll over.

If you already shop at this store, it’s obvious that this is a great deal — you get something for doing what you are already doing. But if you don’t shop there, should you? As always, it depends on the circumstances.

I live in a town that has four main grocery stores, although I am sure there are others as well. We don’t typically shop at the grocery store that has this promotion, so when the program started, we discussed whether to switch. Because my wife and I are both quantitatively inclined, we tend to remember how much things cost at our “regular” grocery store, so we decided to go to the new one and compare.

Of the four chains in our area, this one is probably the second cheapest, but we shop at the one that is the cheapest, so switching would cost us money. But would we make more on the gas savings than we spent on groceries?

After a couple week test, I think we can safely answer yes, but with some additional commentary. We have changed from shopping at one store, to shopping at two. Simply put, $.01 per gallon for every $10 spent is not enough to cover the higher costs at the new store. So, we go to the new store and get the “specials” that get us extra points, and things that are cheaper here than at our regular store, and then buy everything else at our old store. This takes a little bit more effort, but it seems to be saving us quite a bit on gas. Last week my wife put 19 gallons in the car for $1.97!

One other thing we discovered is that the new store has a pharmacy and prescription purchases qualify for the program. We checked around, and for my wife’s prescription, everyone charges the same amount, so buying it at the new store saves us $.11 per gallon on gas, while not costing any more.

The last thing we discovered is how difficult it is to wait until your tank is almost empty to fill up. Since the discount is good on up to 20 gallons, and any unused amount does not roll over, you are wasting money if you fill up before you are almost empty (neither of our cars holds more than 20 gallons). But it is hard to drive around with a quarter of a tank and not get nervous about it, so that takes some getting used to.

This program has dramatically decreased our gas budget, from $250 per month last winter to $50-$75 per month now. Some of that is due to gas prices, but some is due to this program as well. I think this post should give you some ideas of how to analytically think about a program like this to see if it’s worth it.

Is Manhattan worth more than $24 in beads?

Yesterday I promised you an amazing example of the power of compound interest. Today, in my first post on investing, I will fulfill that promise. It is important to note that I did not create this example; I believe I first read about in one of John Paulos’ books, but it might have been somewhere else.

Growing up I’m sure you heard the story about how Manhattan was bought for $24 in beads in 1626. Sounds like a ripoff, doesn’t it? Manhattan must be worth more than $24, right?

Well, how much would that $24 be worth today, if it had been invested, rather than spent?

Let’s see, 1626 was 383 years ago. I don’t know what the various stock markets were returning at that time, but the average annual return during the 1900s in the United States was north of 10%. Let’s just call it 10%.

So, before you read on, formulate a guess in your head. How much would $24 grow to in 383 years, assuming a 10% annual return?

The image below is just a filler to help stop you from reading ahead — don’t move on until you have a guess.


The answer is $171 quadrillion, which is the same as $171,000 trillion. If you want to be more specific, the answer is $171,241,749,947,654,000 (this answer is probably not accurate as excel can’t really calculate accurately with that many digits). This post already showed you how big a trillion is, so imagine a number 171,000 times that size.

Obviously most people, except my friend Jon who claims to be immortal, don’t have a 383 year investing horizon. But, this example shows how a little bit of money, over a long time frame, can add up to a lot of money. Maybe setting aside $50 a month for your kids’ education or your retirement is a good idea after all!

How much is interest on a trillion dollars, anyway?

Yesterday I did some number freaking on the subject of one trillion dollars.

Today I want to expand that a little further, to show how truly massive that number is.

One of the things we discussed yesterday was that you could have spent $1 million every single day since Jesus was born, and still not have spent $1 trillion. That statement ignores the compounding of interest, however.

So, let’s add interest the equation. Pretend you were given $1 trillion on the date of Jesus’ birth, which we will say was 733,500 days ago. This money was put into a bank account that paid 6% per year. How much could you have withdrawn every day since then? Before you read on, please try to formulate a guess, so you can see how close you are.

I will even reproduce my little picture of $1 trillion so that you don’t accidentally read ahead.


Are you ready for the answer? It is $164,383,561.6438 per day! Interestingly enough, if you just round up to $164,383,561.65 you will end up running out of money after 400 years, and if you round down to $164,383,561.64 your nest egg will actually grow over time. That extra fraction of a penny makes a huge difference over 2000+ years.

What could you buy with $164 million per day? You could buy everyone in the country a $.50 newspaper and still have $10 million left every day.

You could sign A-Rod to a 6 year contract, every single day, and still have a couple million left.

You could pay the annual salary of any major league baseball team not named the Yankees, every single day.

The $164 million represents interest on the $1 trillion. But, even just the interest on the interest is $27,000 per day. So, if you took one day off from spending, and put that money in a separate account, and it earned interest at 6% per year, you could hire an entry level accountant for 6 months, with the interest on the interest every single day.

I think this is an amazing example of the power of compound interest, and tomorrow I will share an even better one with you.