# Deep in the valley, how bleak things look — An analysis of Equity risk

As the all omniscience narrator of Bilbo knows, things are not as black as they appeared in the middle of the dark forest of Mirkwood.

*Actually, as I have told you, they were not far off the edge of the forest; and if Bilbo had had the sense to see it, the tree that he had climbed, though it was tall in itself, was standing near the bottom of a wide valley, so that from its top the trees seemed to swell up all round like the edges of a great bowl, and he could not expect to see how far the forest lasted. Still he did not see this, and he climbed down full of despair.*

Often we see statistics about average, standard deviation of the S&P500 over various length of time. Inevitably, the average between the period are similar and the standard deviation go down a bit by length. The issue I have with these types of statistics is that per definition it’s comparing point A to point B. Like Bilbo you could be comparing The highest peak (point A) to lowest point B. It’s rather inevitable to had these points. It’s rather fraudulent to do otherwise. However, given point analysis to these high/low doesn’t tell us some other very important factors, such as

- How would it compare to a reasonable expected interest increase?
- How long did it take to reach these highest peak (super fast increase or steady increase).
- How long did the bleak forest stretch? (how long for negative return and how long before return to equilibrium).

Let’s look at two of these stories: The 1929 crash and the 2008 crisis.

First let’s note your fund expected return throughout the years depending on the rate of return.

In other word, if you invest 100k in the super safe federal bonds, in 60 years you would ten have 130k. Instead if you are unlucky and only receive 5% return on equity, you would just under 2 millions. Current forecast average on equity would return 7.6 million and historical average over the last century (10%), of about 30.5 million.

Over a decade, the difference of interest rate unless you look at extremes is relatively small. It gives a quick sense of how things goes. A x1.1 would mean a loss decade, a x2 the average expected, a x4 beyond the wildest dream.

Now let’s look at the reason why we fear so much the equity world. The 1929 crash and the 2008 financial crisis.

#### The **Wall Street Crash of 1929**

Say that we are 35 years old and have inherited a Lump sum to invest (8.2k at 35). At the beginning of 1899, we though that a diversified portfolio mimicking as much as possible the recent S&P500 would be a good strategy. At 1899, the historical return were around 6%. At 7.5% interest, you would have expected the fund to be 50k at 60 and 72k at 65. After patiently waited for 65 we took our pension, at the onset of the slaughter. I’ve extended the scenario to include what would happen if we didn’t took a penny for the next years.

- How would it compare to a reasonable expected interest increase?

The first 25 years went about according to plan. At age 60 (1924), our fund would be just below average (46k vs expected 50k). However, at 65 (1929) our fund would be in the high sky area (161k vs expected 71k). In a matter of 4 years, we would have gone down to (60.7). At least the recent years have endure the most devastating deflation. Indeed, a dollar in 1929 was worth a dollar 30 cent at the beginning of 1933; the inverse of inflation (a dollar now is worth less next year). This would have mitigate our loss.

- How long did it take to reach these highest peak (super fast increase or steady increase).

The 1929 was reach super fast. In a matter of 5 years, the fund did 4x, or about 20 years worth of increase.

- How long did the bleak forest stretch? (how long for negative return and how long before return to equilibrium).

There’s no denying that 1929 was long and deep. It had 4 years of negative return and a decade later, you would have barely made even. The next decade would have however been ok (1939–1949 made x2). However, if we look things another way, at the worst of crisis (1933) we would still been better off than a 5% steady increase since start. It’s really a matter of perspective (short term or long term) to determine if we are in a crisis.

#### The Financial Crisis of 2008

Say that we are 35 years old and have inherited a Lump sum to invest (8.2k at 35). At the beginning of 1978, we though that a diversified portfolio mimicking as much as possible the S&P500 would be a good strategy. At 1978, the historical return were around 7.5%. At 7.5% interest, you would have expected the fund to be 50k at 60 and 72k at 65. After patiently waited for 65 we took our pension, at the onset of the slaughter. I’ve extended the scenario to include what would happen if we didn’t took a penny for the next years.

- How would it compare to a reasonable expected interest increase?

The first 10 years went like crazy good. Regardless of insane increase, we stick with the plan and man how much did it paid-off in the next decade. The fund went to an unbelievable 21.5x at age 55. Sadly the next 5 years experience the internet bubble and no interest were return. At age 60 (2003), our fund would be sky high at (176.3k vs expected 50k). Meh we said, that’s not nearly enough. Good call at 65 (2008) our fund would be in Nirvana (315.7k vs expected 71k). In a matter of 1 year, we would have gone down to (191.9k), but would have picked up in the next 3 years were we left off.

- How long did it take to reach these highest peak (super fast increase or steady increase).

The 2008 peak was reach at a steady super fast for 20yrs, then stagnated for 5 years, then super fast for 5 years.

- How long did the bleak forest stretch? (how long for negative return and how long before return to equilibrium).

2008 crisis was quick. Finish in a year, and return to equilibrium by 3 years.

What are the wisdom in these perspective?

- Well first, if we look at year to year change, change can be intense and quick. If we want to have a pension out of a fund, we need to have adequate reserve for these extreme situation.
- How long does the crisis can last? Well it can be long, but the latest crisis was over in just 3 years. Many new political features exist to reduce the length. In any case, we need to have the reserve that will last long.
- Did it rise out of nowhere? Yes and no. Yes, there was a rise. An heavenly increase, but this alone doesn’t always culminate with a fast decrease. However, it’s hard to say that a rise didn’t happen somewhere in the recent past. Perhaps it’s possible to have a reserve out of these extra return.
- If we look at our original expectation, equity had far outreach them. Even if we include the loss, past expectation were greater by much. Perhaps creating reserve above the extra return would enable us to shield us from the hard times.

Personally, these scenarios really demonstrate to me without any doubt of the soundness of equity. However, it raises some very important issue on how we look/disclose/review our fund. Looking at a single point estimate from a year to the next make the forest hides in the tree. If we are trying to get a pension out of our fund, we must try to find ways to make reserve for these bad times that will happens.