# Let’s play a little game of “Baron Rothschild”, from Rocky Humbert

January 31, 2012 |

Let's play a little game — it's called “Baron Rothschild” — who once said “I made my fortune by selling too early” (a comment also made by Bernard Baruch)… Suppose that the dealer lays cards down, one after another. Each is an annual market return. At any time, you can call out “Baron Rothschild” and go to a defensive position, or you can gamble and get the entire market return the dealer shows next. The gain cards read, say, 15%, 20%, 25% and 30%. If you're defensive, you lag the market by 10% when the market return is a gain, but you get, say, 5% if the market return is a loss. There is one -20% loss card. Once it appears, the game ends and everyone counts their dough, compounded. It turns out that if the loss comes anytime before the 5th card, you're almost always ensured to beat or tie the dealer by immediately blurting out “Baron Rothschild” even before the first card is shown. For example,

20%, 20%, 20%, 5% beats 30%, 30%, 30%, -20%
15%, 15%, 15%, 5% beats 25%, 25%, 25%, -20%
20%, 10%, 5%, 5% beats 30%, 20%, 15%, -20%
5%, 5%, 5%, 5% ties 15%, 15%, 15%, -20%

You can easily prove to yourself that even for a six-year market cycle, you still generally win even if you call out “Baron Rothschild” after year two. It just doesn't pay to risk the big loss. The point of this isn't that investors should always take a defensive stance — some market conditions are associated with very strong return/risk profiles that warrant substantial exposure to market fluctuations. The point is that the avoidance of significant losses is generally worth accepting even long periods of defensiveness. Because of the mathematics of compounding, large losses have a disproportionate effect on cumulative returns. Remember that historically, most bear markets have not averaged 20%, but approach 30% or more. A 30% loss takes an 80% gain and turns it into a 26% gain. It's difficult to recover from such losses, which is why the recent bull market has not even put the market ahead of Treasury bills since 2000 or even 1998. So again, the point is that the avoidance of significant losses is typically worthwhile even if, like Baron Rothschild, one is defensive "too soon." With regard to present stock market conditions, it would take a correction of only about 10% in the S&P 500 to put the market behind Treasury bills for the most recent 3-year period. That's not an empty statistic given rich valuations, unusual bullishness, overbought conditions, rising yield trends, and a market long overdue for such a correction. Given the average return/risk profile those conditions have historically produced, it makes sense to call out "Baron Rothschild" even if we allow for the possibility of a further advance, in this particular instance, before the market inevitably corrects.

1) Let's assume that one's goal is to beat some passive index (it doesn't have to be stocks; it could be the Yen or Natgas) over an X month period. And let's further assume that one is willing to engage in "selling early." And lastly, let's assume that "selling early" is sometimes the "right" thing to do due to the essay above. As a statistical matter, what is the likely minimum value for X … that permits the speculator to beat his passive index?

2) Let's assume that one's goal is to beat a passive index (again, it doesn't have to be stocks) over an X month period. And let's further assume that one is willing to exit the market "early," but also "buy early." Obviously, if one exits, re-entering is a necessary thing to do. As a statistical matter, what is the likely minimum value for X … such that the speculator can beat his passive index?

3) As a purely statistical matter, which should be better/worse : Buying early and selling early? Or, buying late and selling late ? And, again, what is the minimum X month performance period where either strategy has a chance to beat the passive benchmark.

## William Weaver writes:

1. Disposition Effect

2. Great essay and the observation of defensive over aggressive is very good but I can't agree with purely taking profits unless there is a reason to exit. Assuming sufficient liquidity, in my humble opinion, it might not be bad to tighten stops (volatility historically has fallen as equities rise - though high levels in the late 1990's - so stops based on standard deviation should tighten anyway) allowing one to lock in profits but continue to profit from any trend that develops or continues. This seems to be a prominent trait of the most successful traders I've met; allowing profits to run by controlling for risk instead of picking a top.

3. The saying "There is nothing wrong with taking small profits" is a great way to lose everything if you don't also control for losses. In this essay there is only an early exit for profits.

4. His analysis of the equity premium to Treasuries is very insightful but I will leave that to the list for independent testing.

5. Every trader is different and must play to their own personality. For me, when trading intraday (which I am new to and still not the biggest fan of but am coming along) I will take off part of a position when anything changes, and this helps manage risk (leads to a larger percentage of profitable days). But will wait for long term momentum to reverse before exiting the last half as this is where the majority of my monthly profits come from. This way I can be a wuss and still profit.

6. Read The Disposition Effect if you have not and are interested in any type of trading/speculation. (To add to things to do to become a successful speculator: know, understand and be able to identify behavioral biases both in your own trading, and in the market).

## Leo Jia writes:

I don't fully understand Rocky's 3 questions at the end. Guess they are meant for some real speculations, rather than for the Baron Rothschild Game, right?

If so, then I take Will's approach as described in his Point 2, except that I don't exit on instant stops, but on closing prices of certain intervals (30 minutes for instance for position trades) if the means of the intervals trigger my stops. My feelings about instant stops are that 1) they tend to have more execution errors (due to price chasing), and 2) either they get triggered more often or I have to set them wider (meaning more losses). I don't have concrete results about this and would love to hear other opinions.

I can't see how the game closely resembles trading. From what I understand about it, there seem to be many more winning cards than losing ones. So a strategy of simply selling on random cards gives one an easy edge to beat the dealer (though not necessarily achieving the best result). Am I missing something there?

Turning to writings from 100 years ago, a friend found this book in his attic in Montana and gave it to me: Fourteen Methods of Operating in the Stock Market.

The first article in this book was A Specialist in Panics, which has been discussed on the List before. This method is to buy when there is a panic.

There was another article by H.M.P. Eckhardt, "Plan for Taking Advantage of the Primary Movements". He advised buying during steep market declines, as the Specialist in Panics did, but also suggested selling if a rapid rise brought profits equal to the interest the investor could have earned over three or four years. Mr. Eckhardt surmised that, with his money already having earned its keep for at least three years, the investor would probably get a chance to put it back to work in less than three years when another panic occurred.

For these sorts of techniques, Rocky's X is the length of a business cycle, which is unknowable in advance, but would normally be at least 48 months.

## Alston Mabry writes:

Let's say you start at January, 2004 (arbitrarily chosen start date, but not cherry-picked, i.e., not compared to other possible start dates), and you go to January 2012. You have \$100 a month to invest. You can buy the SPY and/or hold cash. You have a total of 97 months and thus, \$9700 to invest. If you buy the SPY every month (using adjusted monthly close), you wind up with:

\$11,451.37

But being a clever speculator and wanting to buy the dips, you come up with a plan: You will let your monthly cash accrue until SPY has a large drop as measured by the monthly adjclose-adjclose; each time the SPY has such a drop, you will put half your current cash into SPY at the monthly close. To decide how large the drop will be, you compute the standard deviation of the previous 12 monthly % changes, and then your buying trigger is a drop of a certain number of SDs. Your speculator friends like the plan, but disagree on the size of the drop, so each of you chooses a different number of SDs as a trigger: 0.5, 1, 1.5, 2, 2.5, 3, and the real doom-n-gloomer at 4.

The results, showing the size of the drop in SDs required to trigger a buy-in, the final value of the portfolio, and the average cash position during the entire period:

SD / final value / avg cash
0.5  \$11,522.13    \$543.03
1.0  \$11,328.42    \$737.77
1.5  \$10,885.80  \$1,351.02
2.0  \$10,884.15  \$2,083.36
2.5  \$10,655.96  \$2,711.34
3.0  \$11,005.72  \$3,704.12
4.0   \$9,700.00  \$4,900.00

You, of course, chose 0.5 SDs as your trigger and so come out with the biggest gain. But your friend who chose 3 SDs says that he *could* have used his larger cash position to invest in Treasuries and thus have beaten you. You say, "Coulda, woulda, shoulda."

Mr Gloom-n-Doom cheated and bought the TLT every month and wound up with \$14,465.56.