Case #22: The Missing Returns

The city was dark, cold and wet.  Like a dredged up stiff in a cement overcoat.  Only smellier.  The alleyway below my window was lit by the flickering neon light of the local dive.  A dive that attracted every goon, hood and heel the way a plump kid at summer camp draws mosquitoes.

I had just polished off another bottle of Jack, my steadiest of companions, when she walked through the door.
 

She was tall and mysterious and drew your attention like a Nazi commandant.  If Nazi commandants wore red silk dresses and high heels.  Which some of them probably did.  No judgment here.  Except that they're Nazis, of course.

Uh...where was I?

She wore her flowing blonde hair off to one side like Veronica Lake. 

Not that Veronica Lake was a Nazi commandant.

In any case, I could tell she spelled trouble.  I don't know how she spelled trouble.  I never asked.  I assume just like the rest of us.  Of course, she might have been Albanian and used an umlaut or something strange like that.  I didn't ask about that either.

She parted her full, red lips and spoke in a deep, breathy voice.

"I want to hire you, Mr. Deadwood."

I looked her in the eye, trying to figure out her angle.  Dames like her don't just show up in my corner of the city.  I got up from my chair and walked around my desk.  I wanted to face her.  Confront her.  Let her know just who she was messing with.  Or rather, with whom she was messing.  No, that still sounds awkward.  Anyway, she beat me to the punch.

"Is that a gun in your pocket, or are you just glad to see me?"

I knew the game.  She wasn't the first commandant in a dress and high heels to walk into my life and she wouldn't be the last.

"Neither.  It's a half eaten sandwich from...last Thursday?  Yeah, Thursday."

She gave me a knowing glance and helped herself to my chair.  And my scotch.  She then started talking about her finances.  How her numbers didn't jive, how she didn't know where to turn.  I wasn't interested.

"Lady, I think you're confused.  Can't you read the shingle over the door?  I'm a dick."

"You can say that again."

"A detective.  Private eye.  Gumshoe.  Sleuth.  I'm no financial accountant."

She tried to stare me down.  Hide her desperation.  But a single tear cracked her steely veneer.  I wasn't moved.  Life in the big city had made me tough.  Tough as a nickel steak.  But I was also broke.  Broke as the plate I threw across a restaurant after losing a filling on a nickel steak.  I decided to take the case.

"What do you charge?"

"Twenty clams and a herd."

"Heard of what?"

"I mean a pack of Camels."

"Of course I've heard of a pack of camels.  What of it?"

"Forget it.  Gimme twenty clams and a bottle of Jack."

"An empty bottle?  What, for the camels?"

 

She was trying to confuse me.  It was working.  I didn't trust her, but I wanted to know where this was going.  I pulled up a chair and prepared for a long evening.  I was all in.

She said that about ten years ago, she had socked away ten grand for early retirement, and since the internet hadn't been invented yet, she couldn't use any of the excellent online tools that didn't exist.  So she built herself her own model using empirically based assumptions about stock market returns.  The returns over the last ten years were true to her prediction, but somehow her nest egg was substantially smaller than it should have been.  Seven grand smaller.  That's a whole lot of Jack.

"Let me see this model of yours."

She opened her patent leather clutch and pulled out a huge sheet which she spread across my desk.  There were numbers upon numbers laid out in a grid.  I had never seen anything like it before.

"Listen, lady, what are you trying to pull here?"

"I'm telling you, Deadwood, this is my model.  This is how I project my finances."

We spent hours poring over her model.  She told me how the number at the bottom of one column was the same as the number at the top of the next column, and in between there were assumptions for investment returns, inflation and taxes.  She said her assumptions had all been spot on, but her holdings were over 25% lower than they should have been.  She was sure some rat at the bank was sampling her lettuce and she wanted him iced.

"Now, let's you and I get something straight.  I'm not some hired goon with a hair trigger sandwich.  I'm here to find your money, that's all.  If you want to rub someone out, that's your business, see?"

"I said I wanted some ice.  For my drink, you lugnut."

 
I leaned back in my chair and closed my eyes.  This case was complicated, and I was beat after the three day bender I was on.  And that's when it hit me.  Square in the face like a cold drink.  In fact, it was a cold drink.

"Say, mister, what's the big idea?  I'm not paying you to sleep!"

I wiped the scotch off my face and danced a little jig until the ice fell out of my shirt.

"I wasn't sleeping, see?  I was resting my eyes.   I do that these days.  Sometimes, twice a day."

I took another look at the sheet spread on my desk.  My suspicions grew stronger.

"What assumption did you use for your stock market return?"

"We went over that already.  Ten percent."

"That's not what I mean.  What does the ten percent represent?"

"That's the average annual return of the stock market over the previous 50 years.  I used it as my assumption for the last ten.  And it's been true to form.  The average annual return has been almost exactly ten percent."

I had it.  Once again, I had smoked out the culprit.  Oregon Deadwood, Private Eye.

"Glamour, you're like every two bit chump that waltzes through here.  No one is dipping into your wad.  You've confused Average Annual Return with Compound Annual Growth Rate."

"Bu...but...what do you mean?"

"Percentages are asymmetric, see?  If you drive your Studebaker five miles in one direction and then five miles in the reverse direction, you end up right back where you started.  If you have five ounces of gin in your tumbler, drink three ounces, and then add three ounces, you're back to five.  Miles and ounces are units, and unit changes are symmetrical."

I pulled out the chalkboard left behind by the last client who strolled in.  Don't ask.  Let's just say she had this whole Catholic school teacher thing going on and leave it at that.  No, seriously, leave it at that.

I started scribbling.

"Percentages behave differently.  If you start out with $100 and you lose 50%, you are down to $50.  If you then gain 50%, you only get back to $75.  That's because percentages are unitless fractions with a changing reference point.

"If you take the average of those changes, -50% and 50%, you get 0% in total.  So if you use the average annual return (AAR), you might think you should still have $100.  But you only have $75.  The average means nothing, see?  The AAR is playing you like a cheap violin!"

She slapped me in the face.  I guess I had it coming.  I took a swig of gin, flipped the board over, and began again.

"What matters is the compound annual growth rate (CAGR).  The CAGR is -13.4%.  That's much lower than 0% and it's the rate you would use to get to $75 over two years."

She slumped in my chair like a pile of dirty laundry.  She raised the back of her hand to her forehead.

"Stop it!  Stop it!  I'm telling you, mister, I can't take it anymore!"

She'd had enough.  But I wasn't done.  I erased the board and moved in for the kill.

"Now, the stock market fluctuates, but the difference between AAR and CAGR isn't generally as large as our example.  Over the last ten years, the AAR was 10.1% and the CAGR was 6.6%.

"Your misstep was using 10.1% instead of 6.6% in your model.  There's your missing 7 Gs.  No one stole from your stash, lady!  It was you all along!  You used the wrong percentage!"

"YOU CAD!!"

Slap!  Slap!  Slap!!

I grabbed her arm and wrestled it behind her back.  I didn't enjoy being slapped around.  Okay, maybe a little.  But not so much.

She fell to the floor in a heap and lay there weeping.  I pulled out my handkerchief and tossed it at her.

"You're a mess.  Wipe your face.  And the next time you decide to project your finances, be sure to subtract a couple points off any AAR assumption to arrive at a reasonable CAGR which is what a deterministic model implicitly uses.  If you don't, you'll substantially overestimate your projected net worth.  Subtract two points or you'll be sorry.  Do you hear me!?  Sorry, I say!"

She wiped her eyes and pulled her hair back from her face.  Half her face, anyway.  Because, you know, Veronica Lake.

"Stop bustin' my chops, Deadwood.  I hear you."

She stood and smoothed out her dress as she headed for the door.
 

"So long, Deadwood."

"Aren't you forgetting something?  You still owe me twenty bucks."

"Twenty bucks is a little steep, mister.  You didn't even get capped."

"There are private eyes and there are private eyes.  You could have gone with any two bit gumshoe, but you chose me.  I'm the biggest dick around."

"You can say that again."

She opened her clutch.  But instead of handing over my hard earned greenbacks, she pulled out a pearl handled Walther.  I reached for the sky.

"I'm hitting the road, mister.  Don't try to follow."

"Figures.  Lady, I knew the moment you came in."

"Knew what?"

"You spell trouble, see?"

"T-R-O-Ü-B-L-E"

"Not bad.  Now spell 'büreaücracy.'  That one always trips me üp."

"You've got a dictionary.  Figure it out yourself.  You do know how to use a dictionary, don't you?  You just pull it off the shelf...and blow."

"That doesn't make any sense."

"It does in Albanian."

 

She turned, and walked out the door and out of my life.  The seams on her gams still straight as a nun's ruler in a Catholic school.  And just as deadly.  I'm just saying.

I rolled away the chalkboard and stared out the window as the rain peppered the glass.  Left once more to my solitude, I returned to my native state.  A lone wolf in the big city.  Oregon Deadwood, Private Eye.