Investing With a Klunky Time Machine

You have the use of a time machine of limited functionality to aid in your investment.

In particular, you can only use it once to make a single round trip to Wall Street of the last market day of 1926. You will arrive at 6AM local time and return to 2006 after 12 hours.

When you arrive, you will find an irrevocable trust consisting of an envelope with your name on it and containing $10,000 in cash. The trust will be broken and distributed to you on the last day of 2006.

The only possible action that you can take in 1926 is to use all or part of the $10,000 to buy a predecessor to an S&P500 index fund. No other options are possible.

What percentage of the $10,000 will you use to buy the index fund?

Answer: 100%

Stocks in general will far outperform cash over the 80 years involved on an absolute basis.

Same problem, except that your grandfather, born in 1905, will have exactly one opportunity to sell all or part of the index fund for cash at some future date of his choosing. The resultant cash will remain in the trust for your benefit. There is no possibility of you leaving any message, information or instructions for your grandfather.

Would your percentage allocation to the index fund change? Why or why not?

Same two problems as above, except that government bonds are an additional allocation option. If any are chosen, they will be automatically rolled over upon maturity. How do the results change?

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I have to confess that the

I have to confess that the last few posts of fanciful econobabble from Don have been somewhat interesting. I might become an economist yet!

I note that the option to

I note that the option to use "part or all" of the funds in the two different questions are both distractions, assuming that history plays out deterministically. Allocating assets into different categories makes sense to lower risk. In both of the questions, we have perfect foreknowledge, so there is zero risk. The question is a simple one of looking historical stock values.

Without actually doing the lookup, I would say (a) invest 100% of the case in the S&P; (b) hold the S&P till around the middle of July 2000 then sell 100%.

Of course, if the experiment was to run arbitrarilly far into the future, one should not sell the index in 2000, but hold it.

Stocks in general will far

Stocks in general will far outperform cash over the 80 years involved on an absolute basis.

The key words in that sentence are "in general." Life, and the real world, are not general but specific.

Kip, "Stocks in general will

Kip,

"Stocks in general will far outperform cash over the 80 years involved on an absolute basis."

The key words in that sentence are “in general.” Life, and the real world, are not general but specific.

In this case, it's like saying that, in general, water tends to run downhill.

When holding a diversified bundle of stock, you have millions of people trying their best to make you rich, not because they care anything about you, but because you benefit from their actions in their own self interest.

When holding money, OTOH, everyone who can directly impact the value of your holding is trying to make it worth less. Nothing personal, but your well being figures very little in theirs. Since 1926, the dollar has lost in excess of 90% of its purchasing power. This is roughly a price inflation rate of 3%. This would very likely be considered a successful targeting of inflation for the next 80 years by new Fed Chairman B.

Even under a gold standard, all the prospectors, miners and explorers will make you worse off to the extent they succeed in their quests to make themselves better off.

Regards, Don

In this case, it's like

In this case, it's like saying that, in general, water tends to run downhill.

Well, stocks follow a random walk with a very minor positive bias.

So actually you have it backwards: the correct analogy would be as if you were arguing (incorrectly) that water follows a random walk with a minor downhill trendline.

But water does not randomly flow uphill and neither do stocks nor indices invariably move upward. Gravity is a law of physics and stock returns are a probability distribution. That's my whole point.

TJIC's comments about

TJIC's comments about determinism and risk are correct, but I think he misunderstands Don's experiment. You don't get to determine when to sell the index fund for cash - your grandfather does, and you cannot give him any advice or information (like "sell before the dot-com bubble bursts").

Given that, it now makes sense to talk about only allocating a part of your endowment to the index fund. You are trying to assess the risk that your grandfather will unwisely sell the index fund sometime before 2000. I honestly can't begin to calculate the right ratio here... it depends not only on the kind of financial acumen my grandfather had, but also complexly on the differential return between his choosing to sell at various points in time and for various amounts. All of that guesswork then has to be weighed against my risk tolerance - how willing am I to risk losing X to gain Y, which of course depends not just on the degree of risk but also the size of X and Y *and* the value of X and Y to me (gaining $1M means less to me if I'm already worth $1B than if I'm flat broke).

But this is Don... so I suspect a trick.

The worst case would probably be if Grampa held the "index fund" from '26 through the crash of '29 and then sold at the market bottom. Our stake would be reduced by however much the market fell from '26 to '29, whereas it would still be $10,000 if we never put any of it in stocks to begin with.

So I'm guessing (without searching for the data, as I'm sure Don has) that stocks actually *rose* from '26 to the market bottom in '29. The "crash" was so devastating because the market had run up so dramatically in a relatively short period beforehand. If the bubble didn't start inflating until after our broken time machine dropped us off on New Year's Eve 1926, then after the market crashed in 1929 our "index fund" may well have been in the black, not the red.

Which means even if you assume that Grampa is going to make the worst possible choice for us, we're still better off putting it all in stocks instead of leaving any of it in cash.

Do I get the cookie?

the best return would have

the best return would have been to purchase hardwood forest land. its had an unbelievable track record for a long time.

Your machine is useless: no

Your machine is useless: no such fund that existed in 1926 or successor fund survived until 2000.

Here are my back of the

Here are my back of the envelope numbers.

Using the data from freelunch.com for the Dow Jones Industrial Average:

Year Value
1926 157.2
2005 10,717.5

The return factor is:

(10,717.5 - 157.2)/157.2) = 67.177

The annualized rate of return is:

(67.177 ^ (1/79))-1 = 5.47%

Either way, $100,000 * 1.0547^79 or $100,000 * 67.177 = $6.7 million at the end of 2005.

Factoring an 3% inflation factor of 9.33 ((1+3%)^79), (67.177 - 9.33) * $100,000 = an inflation adjusted $5.7 million at the end of 2005. Now this $1M difference is too high because of the mitigating compounding factor not taken into consideration. Let's just take half away for a new inflation adjusted amount of $6.4M.

Assuming that the cash only option does not earn interest in a bank and the the bills do not have any neusmatic value in 2005, the cash would be worth $10,718 ($100,000/9.33).

The math may not be totally right but $6.4 million is a lot bigger than $10,718.