A Girl Named Florida

I was partially through Leonard Mlodinow’s entertaining The Drunkard’s Walk (How Randomness Rules Our Lives) when the author’s solution to an intriguing problem didn’t sit quite right with me.

Part one goes something like this:

Let us suppose that a distant cousin has two children. You know one or both are girls, and you are trying to remember which it is – one or both? In a family with two children, what are the chances, if one of the children is a girl, that both children are girls?

The intuitive, and incorrect, notion is to figure that we know one of the children is a girl, and we know the chances of the other being a girl is 50 percent, so the probability that both are girls is 50 percent. Mlodinow dispenses with this reasoning:

Although the statement of the problem says that one child is a girl, it doesn’t say which one, and that changes things…The new information – one of the children is a girl – means that we are eliminating from consideration the possibility that both children are boys….That leaves only 3 outcomes in the sample space: (girl, boy), (boy, girl), and (girl, girl).

Since all three of these outcomes are equally likely, the chances of two girls (girl, girl) is 1 in 3, or 33 percent. So far, so good. A few chapters later, he offers a twist.

The variant is this: in a family with two children, what are the chances, if one of the children is a girl named Florida, that both children are girls?…I picked (Florida) rather carefully, because part of the riddle is the question, what, if anything, about the name Florida affects the odds?…are the chances of two girls still 1 in 3?…The fact that one of the girls is named Florida changes the chances to 1 in 2.

What. The. Heck. Why would it matter if we knew her name? Every girl has a name! What if we were looking for Allisons or Bridgets? Even the New York Times reviewer had trouble believing it.

The author proceeds with his explanation, offering the statistic that only about 1 in 1 million girls are named Florida.

Since our original sample space should be a list of all the possibilities, is this case it is a list of both gender and name. Denoting “girl-name-Florida” by girl-F and “girl-not-named-Florida” by girl-NF we write the sample space (boy, girl-F), (girl-F, boy), (girl-NF, girl-F), and girlF, girl-NF)I am skipping the steps in which he prunes (boy, boy) because we know there is at least one girl, and (girl-F, girl-F) as being irrelevantly unlikely which are, to a very good approximation, equally likely. Since 2 of the 4, or half of the elements in the sample space are families with two girls, the answer is not 1 in 3 – as it was in the two-daughter problem – but 1 in 2.

Still lost?

Imagine that we gather into a very large room 75 million families that have two children, at least one of whom is a girl. As the two-daughter problem taught us, there will be about 25 million two-girl families in that room and 50 million one-girl families (25 million in which the girl is the older child and an equal number in which she is the younger). Next comes the pruning: we ask that only the families that include a girl named Florida remain. Since Florida is a 1 in 1 million name, about 50 of the 50 million one-girl families will remain. And of the 25 million two-girl families, 50 of them will also get to stay, 25 because their firstborn is named Florida and another 25 because their younger girl has that name. It’s as if the girls are lottery tickets and the girls named Florida are the winning tickets. Although there are twice as many one-girl families as two-girl families, the two-girl families each have two tickets, so the one-girl families and the two-girl families will be about equally represented among the winners.

I reread that paragraph ten times before I started to understand, but I couldn’t shake the fact that the “1 in a million” chance wasn’t factored in anywhere – the rate of two-girl families had simply changed from 1/3 to 1/2. What if the chance of a girl being named Florida was 1 in 1,000? 1 in 10? 1 in 2?

The “1 in 2″ thinking set me on the right path. Let’s plug the assumption that 50% percent of girls are named Florida into his lottery numbers above. Of the 25 million two-girl families, 25 million will get to stay, 12.5 million because their firstborn is named Florida and 12.5 million because their younger girl has that name.

Notice anything wrong? Of course you do. All 25 million two-girl families won’t have a girl named Florida. It’s like saying that if there’s a 50% chance of rain on Friday and a 50% chance of rain on Saturday then we’re 100% in for a rainy weekend. You can’t add simply add probabilities; you have to approach it another way: the chance of neither girl being named Florida is 25% (.5 x .5), therefore the chance of at least one Florida is 75%, not 100%. Mlodinow does mention that we should assume parents won’t give their kids the same name, which breaks the common “independant” clause of simple statistics. For instance if the oldest is named Florida, the chance that their second child will be named Florida is now zero. Think of it as sampling without replacement. After thinking on it, I realized that this doesn’t affect the calculations at all since we don’t care about the total number of Floridas, just the number of families with a Florida. If a family names their oldest child Florida, we don’t care what they name their second child. Florida or not, we’re counting that family anyway. When Googling this problem this was a huge source of controversy, but my stance is that it can be safely ignored.

The logic is more subtle but no less important when dealing with a 1 in 1 million chance. The chance that if one of the children is a girl named Florida, that both children are girls, ranges from 1/3 at near-zero Florida rates to 1/2 at 100% Florida rate. (If all girls are named Florida, all 25 million two-girl and 50 million one-girl families will remain.)

Odds a girl is named Florida # One-girl families with Florida # Two-girl families with Florida % Two-girl families
1 in 1,000,000 50 <50 49.9999875%
1 in 1,000 50,000 49,975 49.987%
1 in 10 5,000,000 4,750,000 48.7179%
1 in 2 25,000,000 18,750,000 42.85%
9 in 10 45,000,000 24.750,000 35.48%
10 in 10 50,000,000 25,000,000 33.3%

The answer isn’t 50%, it’s 49.9999875%

This is important not because of the extremely small difference in value, but because the author doesn’t adequately explain that the solution exists on a continuum based of the rate of girls-named-Florida, but instead makes it sound as though the rate jumps from exactly 1/3 to exactly 1/2, which is not the case. The percent of two-girl families asymptotically approaches 1/2 at near-zero Florida rates but will never hit it. While I think the author understands this, while searching for further discussions online it’s clear that not everyone does.

Jolly Blogger took a stab at it in one comment thread.

Holy crap, I’ve just skimmed most of the comments, but I think you guys are over thinking this. Work through it just like the first problem.

Here are all of the possibilities for two children if we allow three “types” (B-boy, F-girl named Florida, G-girl not named Florida): BB, BF, BG GB, GF, GG FB, FF, FG

The problem says we need at least one F, which leaves us with: BF, GF, FB, FG, FF

We need to make one assumption: that Florida is a rare name, and the probability of two Floridas in one family is nearly zero, so now we have four equally likely possibilities: BF, GF, FB, FG

Two of these are 2 girls, so the probability is 2/4 or 1/2.

It may be more accurate to say the probability is ever so slightly greater than 1/2… and assuming nothing about the probability of the name Florida, we can say the probability of two girls lies somewhere between 1/2 and 3/5.

So close and yet so far. (It’s slightly less than 1/2, not slightly more.) His error lies here: “we have four equally likely possibilities: BF, GF, FB, FG”. At near-zero Florida rates, those options are close to (but not exactly) equally likely. However, as you raise the rate of Floridas you will see “BF” and “FB” becoming more likely than “GF” and “GB”. I ran 100 million computer simulations of two-child families and threw out families without a girl named Florida:

Odds a girl is named Florida BF GF FB FG
1 in 1,000,000 ~25% ~25% ~25% ~25%
1 in 1,000 24.9% 25.2% 25.0% 24.9%
1 in 10 25.15% 24.84%% 25.14% 24.87%
1 in 2 33.33%% 16.66% 33.34% 16.66%
9 in 10 45.46% 4.54% 45.45% 4.55%
10 in 10 50% 0% 50% 0%

As the Florida rate rises, the chances of GF and GB drop. At 100%, there’s no such thing as GF or GB – all girls are named Florida.

Are we out of the woods yet?


My second beef with the author is that, after presenting us the solution to this mind-bender, he doesn’t explain why the seemingly irrelevant rarity of a girls name affects the probabilities above.

It took me a while to wrap my head around it, but let me present a scenario that will help. Florida State is playing Miami in a basketball game and it’s tied with one second left. Florida State is on the free throw line. What are the chances that FSU will win the game assuming they have one, or two, free throws left? First of all, we’ll need to know the free throw percentage of the player about to shoot. If it’s 98%, the surprising revelation is you don’t really care whether he has 1 or 2 shots. FSU is almost certain to win. With 1 shot, the team’s chance of winning is 98%, and with 2 shots it nudges up to 99.996% – just a 2% rise.

What if he’s a 60% shooter? Then the chances of a win are 60% with one free throw and 84% with 2 shots – a 40% rise! See where I’m going with this? As the shooting percent falls, it’s more and more important to get that second shot. Indeed, a 10% shooter will benefit 90% by taking two shots instead of one. Remember, we’re not concerned with the number of shots made, just that he makes at least one.

Back to Mladinov’s “lottery” theory. As the rate of girls named Florida falls, families with two children benefit disproportionally more than families with one child when looking for a girl named FloridaOr any independent rare condition – it could be a name, disease, or IQ, just like a poor basketball shooter benefits from having two free throws more than a great shooter. The rate of benefit of the extra lotto ticket will approach 100% as Florida rate approaches zero, which is why the ratio of two-girl families climbs if you know that one of their girls has the 1 in 1 million name.

So there you have it.


Boycott the oil boycotts

$3.62. That’s the price for a gallon of regular unleaded gas at the station down from my house. This means that if I drive my 13 mpg truck to the Hardee’s 10 miles away, I will spend more on gas for the round trip than I will on their delicious delicious Thickburger.

^ Patties now almost 70% meat

“But Jake,” you might be saying, “whatever is your point?” Alas, I won’t answer, because my name isn’t Jake.

But if it was, I’d point out that there are several plans floating around the interwebs purporting to “stick it the the man” and lower gas prices for good, so that we can get back to worrying about important things such as Prince William’s wedding. Unfortunately, it’s not that simple. Here’s why.

Scheme #1: Participating in a one-day boycott of gasoline will lower gas prices.

The premise of these chain emails, often typed in capital letters and with poor diction, is that if everyone in the US declined to purchase gas on the same day, billions of dollars would be taken out of Big Oil’s pockets and they would tremble before the power of the common man and justice would prevail and “Jersey Shore” would be canceled. Or something.

^ No punch line necessary.

The problem with this plan, which anyone over the age of conception should easily discern, is that it doesn’t affect overall consumption but simply shifts purchases to the previous or subsequent day. Exxon will make $2 billion less on Thursday and $2 billion more on Friday.

Scheme #2: Participating in an extended boycott of selected gas companies will lower oil prices.

Sample email: “For the rest of this year, DON’T purchase ANY gasoline from the two biggest companies (which now are one), EXXON and MOBIL. If they are not selling any gas, they will be inclined to reduce their prices. If they reduce their prices, the other companies will have to follow suit.

The reason it won’t work is simple. It doesn’t affect demand, just shifts it to a different company.

Economics Prof. Pat Welch of St. Louis University says any boycott of “bad guy” gasoline in favor of “good guy” brands would have some unintended (and unhappy) results.

Welch says the law of supply and demand is set in stone. “To meet the sudden demand,” he says, “the good guys would have to buy gasoline wholesale from the bad guys, who are suddenly stuck with unwanted gasoline.”

So motorists would end up…paying more for it, because they’d be buying it at fewer stations.

And yes, oil companies do buy and sell from one another. Mike Right of AAA Missouri says, “If a company has a station that can be served more economically by a competitor’s refinery, they’ll do it.”

Oil is extraordinarily fungible.Fungible: a good or a commodity whose individual units are capable of mutual substitution. At the Shell station, you would never know that you were pumping Exxon gas into your tank. The gas is interchangeable, just like those socialite darlings Paris Hilton, Jamie Ramada, and Mildred Motel Six.

Scheme #3: Consumers’ buying only a few gallons of gas at a time will bring down the price of gasoline.

You can read the full, slightly disturbing email, but the premise is that if drivers didn’t fill up their tanks every time they stopped for gas, but instead only bought a few gallons at a time, the reduction in purchases would create a glut of unsold gas that would clog up the supply chain from dealerships to tank farms to refineries to tankers. In order to avoid being overwhelmed with unsold product, the gasoline industry would have to drop their prices in order to clear out the surplus and free up storage capacity for incoming supplies.

The problem is that this notion simply shifts motorists from driving with full tanks to half-full tanksNotice I didn’t say half-empty. I’m an optimist and will result in motorists stopping more often for small refills instead of one large refill.

Scheme #4: Signing a petition to the president will meaningfully lower gas prices.

Gasoline and Diesel Prices

PETITION FOR PRES. BUSH Presidential Petition. Please do NOT let this petition stop and lose all these names. If you do not want to sign it, please forward it to everyone you know.

To add your name, click on “forward”. You will be able to add your name at the bottom of the list and then forward it to your friends. Or, if necessary you can copy and paste and then add your name po the bottom of the list.


E-MAIL ADDRESS: President@WhiteHouse.gov Thank you very much.


I’m betting that the president is aware of current oil prices. There’s also not much the President or Congress can do to significantly affect them, at least in the short term.

Econ 101 teaches us that prices are a function of supply and demand. In all of the plans above, neither factor is being affected. I can’t stress this enough. If you receive a chain email promising to lower prices at the pump, ask yourself whether the plan will result in a long-term increase in supply or a long-term decrease in demand. If the answer to both is “No”, you can safely delete the mail and return to your normal internet procrastination involving pictures of cats and funny Youtube videos.

Do effective actions exist? Sure. You most likely can’t affect the supply-side, so affect the demand side. Get a vehicle with higher gas mileage, such as a smaller car or motorcycle.I just bought a used motorcycle that was leaking oil, so I took it to a dealer who told me I needed a new O-ring. Isn’t the phrase “o-ring” redundant? Discuss. Carpool. Take public transportation.

These actions aren’t as sexy as boycotts. But, in the end, aren’t they the same thing?

Postscript: If you get any emails containing sketchy “facts”, such as the asserting that our president is a Muslim, the moon landing didn’t happen, or peanut butter and chocolate aren’t delicious together, please do the world a favor and do a quick search on Snopes.com to check the validity of the content before forwarding to your entire contact list.


Anatomy of a Craiglist scam

I recently posted a laptop for sale on Craigslist, which apparently is internet code for, “Please scam me from Nigeria.” While most people are savvy enough to see through these shenanigans, it’s worth breaking down. Here’s a play-by-play.

March 29, 8:20 pm: I post my laptop for sale for $550 on Greenville Craigslist.

March 30, 10:53 am. Receive inquiry,

Are you sure its perfectly working condition am buying this item for
my fiancee i will love coming down to your place but my day to day
business will not allow me to do so Hope it is still in a good working
condition as said?.I will love to see the Pics.i will pay you $650 for
the item including the shipping, so get back to me with your pay pal
email address so that i can make the payment to your account ASAP.

Big, huge, gigantic red flags and alarm bells. He could’ve been a little subtler. Craigslist even auto-includes a warning saying “** CRAIGSLIST ADVISORY — AVOID SCAMS BY DEALING LOCALLY **”, but he must’ve thought the extra $100 for shipping would entice me. I’m sure it’s a scammer but am curious anyway. I respond with my email address telling him to send the payment.

There’s two possibilities here: he will either send me a fake PayPal email telling me a payment has been made, or he will actually send me a real payment from a hacked PayPal account in order to get me to send the laptop.In that case, once PayPal’s fraud department is alerted to the hack, the payment will be removed from my account.

March 30th, 12:34 pm: He writes,

Have made the payment check your PayPal box for the payment confirmation…

About this time, I receive the following email from “PayPal”:

At the bottom are shipping instructions,

Name: Badmus Yusuff
Address:Block 132 Flat 4 Jakande Estate Oke Afa
City: Isolo.
State:Lagos State.
Zip Code: 23401.
Country: Nigeria

I don’t have to check my PayPal account to know that there’s no money there. Just viewing the email information in Gmail reveals that the email actually came from customercareservicecentre@ukaccountant.net. He doesn’t even respect me enough to spoof PayPal’s email address. Tsk tsk.

He picked the wrong guy. I’m basically a rocket scientist. I invented alternating and direct current, and the ballpoint pen. I was born in a log cabin I built with my own two hands.

March 30, 1:26 pm: I want to see what he says, and write back,

Hello, it appears the PayPal payment didn’t go through correctly because I checked my account.

March 30th, 1:42 pm: He responds,

Thanks for getting back to me have already paid the money to your paypal account all you need to do now is get back to paypal with the tracking number so that your pending funds can be release to you…

So this is how he gets people to send packages without receiving payment. He claims that I have to send the package first and then enter the USPS tracking number into PayPal in order to “release” the payment. How dumb would I have to be, on a scale of 9 to 10?

March 30th, 2:31 pm: I write,

Ok I understand the payment will be released when I ship the item. I will begin to ship it. Before I do please confirm that you are a serious buyer by sending me a picture of your fiancee holding a newspaper. Then I can ship the item. Thank you.

March 30, 2:49 pm: He responds,

Thanks for getting back to me okay this is the one of my fiancee pic that is the only i can see for now so ahead with the shipment now and once you are back from the post office get back to me immediately.

He also attaches this picture. No joke.

March 30th, 2:52 pm: I respond,

Who is that? Are you a girl? I thought you were a guy so I expected a picture of a girl haha. But this picture doesn’t have a newspaper in it like I asked. Please send me a picture of a girl holding a watermelon, thank you.

Haven’t heard from him since.

A few hours later I get another inquiry from a different email address.

I am currently out of town on a vacation trip and i would have
loved to come over to your place to take a look at the package and
make the payment in cash but i can’t right now due to my vacation
trip.I want to get this package for my fiancee as a Birthday gift…



Spending on things vs. experiences

“How should I spend my money?” It’s as basic a question as “Paper or plastic?” or “Why is Criss Angel popular?”

^ I want to punch him in the face with my foot.

There are infinite ways to break expenses down, but one of the simplest is things vs. experiences. You can buy an iPod or go skydiving. You can have a new laptop or you can go to Hawaii. Surprisingly, study after study after study shows that people report feeling happier when they spend their money on experiences rather than objects.

“ ‘It’s better to go on a vacation than buy a new couch’ is basically the idea,” says Professor Dunn.

This revelation is surprising, because a vacation or cooking class doesn’t leave you with a tangible and lasting possession like buying a Playstation does. However, do this for me: reminisce back on your vacations and try to think about a few of them that you wish you hadn’t taken. Even if it rained the whole time and your hotel smelled like New Jersey and your airplane seatbuddy on the way back was Dr. Phil, you still remember that one sunset where the weather was perfect and your margarita was strong.

^ Dr. Phil = kinda creepy

On the other hand, your iPod/laptop/waterbed somehow doesn’t inspire the same daily feelings as that lovely vacation memory. We humans have something called “hedonic adaptation“, which means that we adapt very well to major positive or negative events or life changes, whether they be winning the lottery or the loss of a close family member. We are so adaptable to seemingly life-changing events that six months from now we won’t even notice our new Porsche or diamond tennis bracelet. Sad but true.

It turns out that this logic works in reverse for experiences – we usually remember the good parts and gloss over the memories of overaggressive TSA pat-downs and underwhelming seafood dinners.

(An additional point on this matter is that, while things are very rarely free, experiences often are. It doesn’t cost anything to go for a run or to throw rocks at trains.)

So, that’s the recommendation based on my research. Skip the new couch. Go to Hawaii.


Credit Card “Rewards”, or, Why I’m Mean to Future Sam

Most credit cards offer a rewards plan in which you can earn points, airline miles, cash back, or other incentives when you make a purchase. For instance, with my Visa card I’ve chosen to earn alpaca feed and WNBA tickets, but that’s just me.

^ Me

These rewards may seem like free money, but I found a study called “Always Leave Home Without It” (PDF here) which found,

In studies involving genuine transactions of potentially high value we show that willingness-to-pay can be increased when customers are instructed to use a credit card rather than cash. The effect may be large (up to 100%)…

Saying that we spend more with credit cards than with cash is like saying that golden retriever puppies are cuter than dung beetles, but I didn’t realize the effect was so large. This “credit card premium” persists across such transactions as department store purchases, restaurant tips, and tickets to sporting events. A separate NPR interview stated that “When McDonald’s started allowing credit card purchases, the average purchase went from $4.50 up to $7.00″, a 55% increase in spending and, presumably, pants size. These numbers make a puny 2% cash-back plan seem useless, like explaining why anyone would wear Crocs or believe in the Axe Effect.

^ Classy

When we use a credit card, we spend more because we don’t experience the pain of payment right away. I’ve noticed this myself. I’ll stick an extra six-pack of beer or a juicy ribeye into my shopping cart at Publix because, hey, I’m not paying for it…Future Sam is. And, you know, screw him.

For all our intellectual sophisticationK-Fed and jorts notwithstanding, we still have an ancient section of our brain called the amygdala, commonly known as the “lizard brain”, which only wants to do four things: fight, flight, fornicate, or feast. It has no concept of the future and doesn’t care about your your rising LDL cholesterol or the fact that your 401(k) balance is tanking like it’s Tiananmen Square.I immediately regret that joke

Our lives are already a constant struggle between short-term pleasure and long-term planning, and credit cards make it far too easy to give in to the former.

I’ve decided to use cash or debit cards instead of credit cards for any purchase I can. Should you join me? Do bears do unspeakable things in the woods?


Why I’m dumb and you are, too

In my review of the book “The Four Pillars Of Investing”, I touched on the author’s comments on the psychology of investing, and how investors repeatedly make the same mistakes, much like Charlie Sheen.

^ When I die I want Charlie Sheen’s life to flash before my eyes.

I’m going to go over a few more of these mistakes today, in the belief that just knowing about the existence of common biases can make us less likely to fall prey to them. I went through Wikipedia’s list of cognitive biases and identified those common to investing.

Anchoring – the common human tendency to rely too heavily, or “anchor,” on one trait or piece of information when making decisions.
This is like dating a girl who is hot, crazy, rude and kicks puppies. You can keep going back to the fact that she’s hot, but is that going to un-slash your tires? No. Look at the whole package.

If you’re researching a stock that pays a 10% dividend, tread carefully my friend. Don’t salivate at that “guaranteed” 10% return because it may be a mirage (a.k.a. dividend trap). Look at the payout ratio (the percentage of earnings a company pays out in dividends) to make sure they can keep up the dividend. Look for a history of steady dividend increases. Make sure the company didn’t just hire Homer Simpson. Don’t fixate on that 10% yield.

Hindsight bias – filtering memory of past events through present knowledge, so that those events look more predictable than they actually were; also known as the “I-knew-it-all-along effect.”

What’s that? You knew that technology stocks were going to crash in 2000? No, Miss Cleo, you didn’t. If you did you would’ve shorted eBioDigiUnderwearDotCom stock and you’d be in Fiji right now wearing lobster and eating diamonds. Investors have a tendency to remember their past thoughts through a historical filter in which they know the final result, biasing what they recall. The only true test is if their current beliefs, as denoted by actual monetary investments, are correct going forward.

Confirmation bias – the tendency to search for or interpret information in a way that confirms one’s preconceptions.
These people are a hallmark audience of online stock message boards. A common mistake of new investors is to buy a relatively un-researched stock for a quick short-term pop, which fails to materialize, whereupon the person trawls for company information online to justify holding it for long-term investment. Any forum post by 123Sexxi4U is taken seriously if they’ve mentioned the stock in a positive light, and warning signs such as bad fundamentals are ignored. To do effective research you must take both positive and negative factors seriously. Besides, 123Sexxi4U is probably this guy:

Authority bias – the tendency to value an ambiguous stimulus according to the opinion of someone who is seen as an authority on the topic.

This is the reason that market pundits have jobs. Financial news outlets may report that markets rose because the Fed lowered rates (making it cheaper for companies to acquire capital) or raised rates (signaling a strong economy and fear of inflation). See the problem? That newscast or blog post was written by a person who has written thousands of similar stories in the past and who just wants to get home by 5:00 to watch his kid play Tee Ball. Take the advice of financial authorities with a large grain of salt.

^ How great was Tee Ball?

Disregard of regression toward the mean – the tendency to expect extreme performance to continue.
There’s an old scam in which a man receives a letter in the mail advising him to watch a certain volatile stock for the next week. The stock shoots up 15% and the man receives another letter telling him a second stock is going to fall in the following week. That stock falls 20%. This goes on for eight weeks, with each pick turning out to be absurdly profitable. By the end, the man is convinced of the validity of the service and pays thousands of dollars for weekly stock picks, which turn out to be a bust and the man loses his home and car. Also he gets the flu.

What happened? The scammers bought 256,000 addresses and mailed 256,000 letters, half of which said to buy a certain volatile stock the following week and half of which advised to sell it. The 128,000 receiving incorrect forecasts never got a letter again, and the 128,000 people receiving correct first-week results would get another letter, half of which said to buy a second stock and half to sell. After eight weeks, there were 1,000 “lucky” people who had gotten incredibly accurate picks in the mail and who couldn’t wait to buy the worthless future picks.

There was nothing special about these 1,000 in comparison to the other 255,000, and no reason to think that they would be that lucky in the future. Past performance doesn’t guarantee them future results – their returns will revert to the mean.

This is a common mistake when reviewing mutual funds. Kiplinger’s usually lists mutual funds by sector and then ranks them according to how well they’ve done in the past year. The top funds look enticing, but remember that those rankings have virtually no bearing on future results and both the best- and worst-performing funds will probably revert to the mean for their sector.

Escalation of commitment – the phenomenon where people justify increased investment in a decision, based on the cumulative prior investment, despite new evidence suggesting that the decision was probably wrong

The year is 2000 and you’ve just purchased some Enron stock, which is turning out to be as good an investment as an XFL franchise.

From Wikipedia,

In August 2000, Enron’s stock price hit its highest value of $90. At this point Enron executives, who possessed the inside information on the hidden losses, began to sell their stock. At the same time, the general public and Enron’s investors were told to buy the stock. Executives told the investors that the stock would continue to climb until it reached possibly the $130 to $140 range, while secretly unloading their shares.

And you know what? Individual investors continued to purchase stock as it fell. Lesson #1 is that Enron executive were assholes. Lesson #2 is cut your losses. It’s easy to rationalize this sort of doubling-down as dollar cost averaging, which reduces the average cost-per-share. However, while this is almost always a good idea when investing in the market as a whole, it is almost always a bad idea when increasing your investment in a single stock.

Normalcy bias – the refusal to plan for, or react to, a disaster which has never happened before

I’m looking at you, 2008 Wall Street. You were correct at the time – up until then, house prices had never fallen in recorded history. Banks and investment firms hung their hat on that fact and made outrageous home loans that the occupant could never pay, believing that they would be bailed out by rising home prices. I have on good authorityi.e., I made it up that at one point they accidentally financed a $4.5 million home in the Hamptons to the Geico gecko.

We all know how that story turned out. A small correction in the housing market set off a spiraling series of foreclosures and short sales. Just because something has never happened doesn’t mean it cannot happen. See Nassim Nicholas Taleb’s excellent book “The Black Swan” for more info on the fat tails of probability distribution. (Not to be confused with Natalie Portman’s movie.)

Clustering illusion – the tendency to see patterns where actually none exist.

There’s a school of thought which relies on stock charts to predict future prices (called technical analysis) which is particularly susceptible to this illusion. I honestly don’t know whether it works or not, but keep in mind that humans can find patterns in absolutely anything, from spins of a roulette wheel to star constellations on the sky. Be careful.

You may be reading this smirking at all those dumb investors wandering around with the wool pulled over their eyes. If so, you’ve fallen for the bias blind spot – the tendency to see oneself as less biased than other people.

Enough of all this negativity. If you’ve gotten this far, you’re either more intelligent than the average investor, or you’re bored and wasting time at work. Either way, congratulations.


Diving into peer-to-peer lending with Prosper and LendingClub

I’ve already stated my opinion that the stock market won’t continue to make 10% per year (largely due to historically low dividend yields), so I’ve been looking for new places to invest. In the peer-to-peer spirit that made Napster and Skype famous, I checked out two leading P2P lending services available right now: LendingClub and Prosper. (Kiva.org works much the same way, but investors make interest-free micro-loans to entrepreneurs across the world and can only recoup their initial investment.)

^ Prosper claims its lenders net 10.1% returns, after write-offs and fees, and LendingClub claims a similar 9.67%.

The concept is simple. Each site is a marketplace in which prospective borrowers post loan requests under such titles as “Engagement Ring Loan $13,000″ and “Consolidating some Debt!!” and “SF teacher needs a Vespa!”Apparently many borrowers assume exclamation points connote a distinct eagerness to responsibly make loan payments. Lenders deposit money into their accounts then scour through the website, browsing the notes like an old lady at a fish market. Once they find an attractive listing they can enter an amount to invest ($25 minimum) and click a button to electronically transfer the money. After a loan is funded, the borrower’s payment is automatically withdrawn from their bank account each month and is deposited back into the lender’s account.

The identity of borrowers is kept anonymous, but they are required to post such information as their gross income and debt-to-income ratio. In addition, each service checks the borrower’s credit history and uses a proprietary calculation to assign a score (“A” or “AA” would be Michael Vick circa 2001, “G” would be Michael Vick in 2008.) This score is extraordinarily important as it sets the interest rate on the loan.

Here are the current rates for a 3-year LendingClub loan36-month loans are the standard, but LendingClub is pushing lenders to fund 60-month loans, explaining that “Borrowers with the same FICO score pay 2.22%-5.02% more in interest on a 60-month loan than on a 36-month loan.”:

 Score Interest Rate 
 A 6.62% 
 B 10.37% 
 C 13.43% 
 D 15.28% 
 E 17.14% 
 F 18.99% 
 G 20.85% 

The potential returns of those bottom rows make lenders salivate, but remember that they’re likely going to the type of people featured on peopleofwalmart.com, or to this guy:

^ Sneaks beers into work using his stomach

Last week I opened accounts at LendingClub and Prosper and deposited $500 into each one. This will be my experiment to see if P2P lending is a worthwhile investment strategy or a poisoned example of adverse selection, namely, that the borrower has an information advantage over the lender.

The deposit hit my LendingClub account two days ago. I began to browse the listings with a particular schadenfreude-laced interest. As one blogger explained it, “Folks go to P2P loans almost always because they can’t get money through conventional channels”. (Read a full criticism of P2P lending here, along with Prosper’s agitated response.

Many of the higher-interest-rate loan requests took on the self-pitying howls of a country song.

After missing one payment, over a year ago, our bank raised the rate to over 25%. Repeated attempts to lower the rate after a year of timely payments has been refused

I exited the listings and opted instead to use the site’s “Build A Portfolio” feature, in which I chose the expected return I wanted (12%) and they built a portfolio to match:

The site then auto-magically chose 20 notes for me to invest in at $25 each, with the aggregate risk of the portfolio calculated to net me 12% per year. I glanced through the recipients and learned that I’m helping most of them consolidate credit card debt, as well as assisting Matthew McConaughey in buying some clothing.

^ Never wears a shirt

The process was relatively painless, especially since I skipped individually vetting each loan. I’ll repeat it with Prosper next week. I’m really interested to see if this is a valid investment / diversification strategy, or if it’s one of those ideas that seems good at first but turns out terribly, like plastic surgery or Gatlinburg.


Diversification is the only free lunch

The economics phrase, “There ain’t no such thing as a free lunch” is so often-quoted that it has its own Wikipedia page. It also happens to be false.

There is a free lunch on Wall Street and it’s called diversification. Let’s take a fictional basket of 5 random stocks and a second basket of 500 stocks. According to the efficient market theory, their expected future returns will be equal to each other, and to the market as a whole.This is somewhat of an oversimplification and ignores such factors as industry and asset classification, but bear with me. However, due to the smaller sample size, the standard deviation of the returns from the first portfolio will be much higher than that of the second.I should mention that owning a large number of stocks does not, in and of itself, guarantee diversification. Imagine if you owned BP, Chevron, ConocoPhillips, ExxonMobile, etc.

You’ve already learned in my article “When the average isn’t the average” that high-volatility returns are the natural enemy of the intelligent investor, much like a balanced political viewpoint is the enemy of Bill O’Reilly.

^ Is to rational commentary what beef-a-roni is to fine dining

In other words, since our basket of 500 stocks will have the same expected return as the basket of 5 stocks, with a smaller standard deviationThere is a calculation for this ratio called the “Sharpe Ratio”, which measures the excess return (or risk premium) per unit of risk in an investment asset or a trading strategy, over the long term it is virtually guaranteed to outperform its smaller counterpart. (There are small additional transaction costs to such a strategy, which can be largely eliminated by buying ETFs or index-tracking mutual funds.)

There’s a reason for the saying, “don’t put all your eggs in one basket”. If diversification were an NFL team, it would go 36-0 and win the Super Bowl and date Alessandra Ambrosio and cure cancer with cold fusion and record a platinum album. I think you get my point.


Why the stock market won’t make 10% per year

It’s commonly quoted that “stocks make 10% per year”. Here’s why they will not continue to do so. Let’s start at the beginning.

Irving Fisher was an economics professor, presidential advisor, and financial commentator in the early 20th century, and his contributions to economic theory are unparalleled. He pioneered the “dividend discount model” (DDM), and, in general, was a brilliant man who belongs on Mt. Rushmore between George Washington and Mr. T.

The DDM holds that “any stock is ultimately worth no more than what it will provide investors in current and future dividends”.

Here, P0 is the current stock price, D1 is the expected dividend, r is the required rate of return, and g is the expected dividend growth rate. Don’t be put off by the fancy equation, even South Carolina’s Miss Teen USA could understand it.

Well, maybe not.

If a stock pays a $1 dividend that will grow at 3% per year, and we require a 10% rate-of-return, the stock can be valued at $1 / (0.10 – 0.03), or about $14.30.

The real beauty is we can re-arrange this equation to what’s known as the “Gordon Equation”Named after, I’ll assume, NASCAR driver Jeff Gordon: Expected market return = dividend growth plus dividend yield. This is a stunningly simple yet powerful tool. During the 20th century, the average dividend yield was 4.5%, and compounded rate of dividend growth was also about 4.5%. This predicts an average market return of 9.0% per year, while the actual return was 9.89%. The difference comes from the fact that stocks became more expensive during this period – the dividend yield had fallen.

Now let’s use this formula to predict the future. The S&P 500 currently yields 1.68%. Long-term dividend growth rates are relatively stable, and there’s no reason to expect them to exceed the historical 4.5% rate I mentioned earlier.

Add these numbers together, and we get an expected long-term return of 6.2% per year. Ouch. Even using a very optimistic 6% dividend growth rate just gets us up to a 7.7% return. Note that this says nothing of day-to-day or even year-to-year returns, only over the very long term, and this not a perfect model. It is, however, absolutely something to be aware of as you plan your retirement.

These numbers are a bit disheartening. I feel dirty, as if I just kicked a baby poodle or ate at Taco Bell. So, to cheer us up, here’s a picture of Wilt Chamberlain and Andre the Giant holding up Arnold Schwarzenegger.


Time value of money

The time value of money is one of the most fundamental and important ideas in economics, so I figured it would be worth a short article explaining the concept.

A simple way to rephrase it is like this, “people would rather receive money now than receive the same amount of money in the future.” (It’s not a difficult concept, just an important one.) Future money is not worth as much as present-day money – we would rather get $100 today than $100 a year from now. To offset this preference, we can assign money an interest rate, where $100 today may be worth $103 or $105 or $110 in a year.

The really fun part comes when we realize that different people have different interest rate preferences. This is one of the basic concepts of capitalism. Some people have capital now and wish to invest it, other people need capital now and wish to borrow it. Joe Plumber might want to borrow money to buy a house today, so we’ll assign him a higher interest rate: $100 today is worth a lot to him, say, $106 a year from now. His personal interest rate is 6%. On the other side of the tracks, Prepster McCashBastard has extra trust fund payouts which he wishes to invest safely, so he will give up $100 today in order to have $102 a year from now: his personal interest rate is 2%.Banks, of course, operate as a middleman on both sides of this transaction – they borrow from Prepster at 2% and lend it to Joe at 6%. Pretty good deal.

Whenever there is a difference in interest rates between people or companies, present-day capital will flow from the lower interest rate to the higher interest rate, where it is valued more highly. This is as reliable a phenomenon as water flowing downhill, or Andy Rooney making absolutely no sense whatsoever.

^ Has been yelling at the kids on his lawnthey’re plastic gnomes since 1963, when John Wilkes Booth was president and the world was still black-and-white.

As a Finance major, much of my curriculum in school consisted of various ways of calculating the Net Present Value (NPV) of a future series of cash flows. This sounds complicated but simply entails discounting a future cash flow based on a given interest rate.

You can do it yourself in Excel. Type “=PV(0.06,1,100)” to see what $100 a year from now is worth to you today if your interest rate is 6%. Hint: it’s $94.34. Congratulations, you now have a Finance degree from Florida State.

With this nifty new information, we can do such interesting things as calculate the value of a winning lottery ticket. Lotteries in the United States usually offer the winner the choice of receiving an annuity (a fancy word for a series of payments) or a lump sum. The advertised “jackpot” amount refers to the sum of the annuity payments, in other words, a $20 million jackpot may pay out $1 million per year for 20 years. This is no chump change, but, as you learned above, it is worth much less than receiving all $20 million today. Let’s assume your personal interest rate is 6%Remember that this is the rate you discount future monies at – the higher the interest rate, the more you value money now rather than later.. Type this in Excel: “=PV(0.06,20,1000000)”. The result tells us that this particular series of payments is equivalent to receiving about $11.5 million today.

We can also approach this problem from the opposite side. What if, as an alternative to the 20-year annuity, the lottery offered you a lump sum of $9 million today? What interest rate does that imply? We can type in “=RATE(20,1000000,-9000000)” and discover that $9 million today is worth exactly the same as our million-per-year-for-20-years annuity at an interest rate of 9.20%. If your personal interest rate is higher than that, you should take the $9 million today. If it’s lower than that, take the annuity.

“Sam”, I’m sure you’re saying right now, “thank you for enlightening me on this important concept”. Trust me, it was my pleasure. I’m happy to do it, because my parents raised me as a gentleman. And a bear. My parents also raised me as a bear.