Mathematiques Roadshow

Antique Drawer knobI don’t think it’s very normal of me, at the tender young age of 28, to enjoy the Antiques Roadshow as much as I do. I tend to explain that I like it for very much the same reasons that I like books like Salt; namely, that in the examination of the most arbitrary of things, you can reveal the history of the whole damned world. Me being me, of course, a not-insignificant contribution to my enjoyment is made by the people-watching aspect of it.¬† People are shy or proud or hopeful or confused about the things they bring in, but they are always invested, and that gives the show some (albeit subtle) dramatic tension that predates reality TV.

There is an undercurrent of innumeracy in the show, though, that I find distracting. In the end it’s not enough to wean me – if people are happy in their numerical misunderstanding, so be it; I would hope never to be the one subtracting happiness from the world. But it creates a sort of dissonance for me when I’m watching, to know that their notions of appreciation, even the appraisers and experts, is sort of… out of whack.

Take this dialogue from today’s show in Louisiana, utterly typical of the roadshow:

<Octogenarian Southern Belle> Ah bawught this decayntuh in 1950 from an antique dealuh who told me it was Tiffany. That’s all ah know about it.
<Sotheby’s Dude> I see, and do you mind telling me how much you paid for it?
<OSB> Ah paid $200 dolluhs. He wanted $225 but I could only afford $200.
<SD> $200 was a lot of money back then. Well let me tell you about this decanter.

… time passes …

<SD> So you paid $200 for this originally. Well what would you say if I told you that on today’s market, this decanter would sell for $5-6000?
<OSB> Really? Well that’s amazing, thank y’all so much.
<SD> My pleasure. A pretty good investment, wouldn’t you say?

Poppycock, says I.

First off it bears mentioning, of course, that Ms. OSB is an absolute doll. As I have already said, if this interaction brings her joy, and more importantly if the decanter has brought her joy over the last 56 years, well then truly that is all that matters. And if Sotheby’s Dude hadn’t dropped the investment line at the end, all would be well in the world. Since he has, let’s do a bit of math (hooray!)

For $200 to become $6000, it has to increase in value thirtyfold. Let’s pretend, because, perversely, it makes the math easier, that she sells it for $6400, such that it has actually increased 32-fold. Saying that it has multiplied its value 32-fold is the same has saying it has doubled in value 5 times (2*2*2*2*2 = 32, look it up.) To double in value 5 times over 55 years (let’s pretend the show was recorded last year) means doubling once every 11 years. Everyone with me so far?

There’s a rule of thumb in compound growth calculations called the Rule of 72 which is really sort of magical. Notationally, 72 = nr, where n is the number of growth periods, and r is the growth rate, but that is all rather obtuse and anyhow it’s not nearly as precise as that equals-sign implies. In English, and when dealing with monetary things, there are two neat things the rule of 72 does. If you know the growth rate, say 10%, dividing 72 by that number tells you how many years it takes to double your money. 72/10 = 7.2, so it takes a little over 7 years to double your money in an account paying 10% interest. Less than 10 years, of course, since compound interest makes those last years particularly exciting. Doing the hard math gets you something more like 7.27254, but the rule of 72 got us pretty close.

The other neat thing the rule of 72 can do is that if you know the time it took for a value to double, dividing 72 by that can tell you what the annual growth rate was. OSB’s Tiffany decanter doubled in value every 11 years. 72/11 = 6.545% annual return. The harder math (in this case, the 11th root of 2) gives us a real number closer to 6.50%. 6.5% growth, over arguably the longest period of virtually uninterrupted economic growth in the history of civilization. According to my read of NYU’s numbers, US stocks in the period 1950-2005 grew at a rate of about 11.56% annually. Almost double the growth rate OSB experienced, but of course in the world of compound interest, everything multiplies. Instead of doubling once every 11 years her $200, invested in stock, would be doubling every 6.33 years. Instead of doubling 5 times, it would have doubled about 8.7 times in 55 years. And instead of growing thirty- or even thirty-two-fold, it would have grown…

410-fold, and change. Best I can figure it, her $200 would be worth $82,149.92 today. A damned sight better than six grand, no?

Buy antiques because you love the history they represent, or because they have sentimental value, or because they are neat to look at. Maybe even buy them because in the back of your mind you suspect they might be worth more than you paid. But if you want something you can leave your kids that will be worth oodles more than you paid for it, buy an index fund.

And don’t get me started on investment wine.

[Photo courtesy of allilinin]

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