vendredi 17 janvier 2020

Ode to Risk



Ode to Risk

Why should we invest in the company vs lending the company? In other word why should we invest in equity vs bonds?

First let’s concede that not everyone is built to withstand high level of volatility. It is far better to stay invested in a low return fund than to change strategy when things goes bad and reinvest after the market recovery. You must not be half convince of the below, but totally convince and go back to this article or to your saved thinking on the matter at the next crash to prevent you doing a yoyo.

Personally, I am convinced after research that the best way is to be 100% in equity. Here are my arguments.  

High level argument

Companies are concerned to maintain good credit level in order to have lower interest rate to pay for the future loan in order to be able to take on more profitable project. In case of bankruptcy, bonds gets repaid first and equity holders are often left with nothing. Thus bonds are safer than equity. Also, bonds have known interest rate when issued thus repayment fluctuates less than the value of the company.

However, no company would start borrowing at a rate of return higher than the project rate of return. If they did, they would get bankrupt. Thus rate of return of equity must be greater or equal over the long term than the borrowing (bonds rate). As an owner we can thus expect to receive more than the lender.

By spreading the risk throughout the entire market, you are no longer concern of any one company but to the overall risk. In a diverse index funds, bonds & Equity are protected against a catastrophic event. At this level though, there are still lot of fluctuation for equity.

In-detail argument (no withdrawal)

Why should you accept the risks that equity offers vs bonds? I have compare the return over various period (data : S&P500 and Moody AAA corporate bonds over 1968 to 2015) over various allocation.
Since the market is indifferent of investing a thousand dollar or a million, I simplified the return as a multiplier of a 1 unit of fund. The Tab 1, looks at the return (constant $) without withdrawal. The more the cell is blackened, the more the results are likely to occur. Thus we can see at time 0, all funds are at 1x (ie 1,000). After 30 years, Tab 1.a reports 2x-10.5x (ie 2,000-10,500) vs Tab 1.c which reports 3.5x-20x (ie 3,500-20,000)















First, let’s concede that we do see some drop below 0.5x in the 0 to 5 years range in the 100/0 allocation that we do not see in the 50/50 allocation. If we continue our analysis, we get the summary table


Let’s first compare what happens in the 50/50 allocation vs the 100/0 allocation:
  • Let’s admit that the worst after 10 years is substantially rosier in the 50/50 than the 100/0 (0.91x vs 0.67x). However, note that this reflect a single series of event in the past 100 years. Also note that the difference is 73%.
  • The worst 25% percentile of the 50/50 allocation are always similar or worse than the worst 25% percentile of a 100/0 allocation (After 1 year, 0.99x vs 0.96x). This is in-line with the fact that only about ¼ of the years returned negative return over the last 100 years.
    • This means that you can expect only better result or about in 75% of the case with a 100/0 allocation than a 50/50 allocation.
  • The worst 50/50 is the same as the worst 100/0 after 23 years of investing at 1.5x. This is highly interesting for the most conservative folks out there. After 20+ years, you are just losing money by having a lower allocation.
    • In other words, you are certain (based on historical results) to have a lower results with a 50/50 allocation after 20 years. Thus you are trading an uncertain gain for a certain loss going for a 50/50 allocation.
  • At 30 years, the average 50/50 is worse than the worst 25% of 100/0 (5.47x vs 5.78x). If you fear the worst 25%, than be happy to know that you would beat on average of 100/0 beat it after 30 years.
    • I have an easy time to concede that we want to minimize our lost. However, it makes no sense to aim for it.
  • At 30 years, we see that the best 75% of 50/50 is a little underneath the worst 25% of 100/0 (6.58x vs 5.78x). We could be tempted to think that the upside (75%) of a 50/50 is enough rosy. However, it is almost the same as the worst (25%) of a 100/0.
    • In other word, if I’m unlucky, I will do more than a lucky conservative (50/50) would make.

Perhaps a in between method would produce better results, however they are similar
  • It’s easy to see that the worst of 100/0 is lower most of the time than the 75/25. However, please note the size. Having 74% vs 64% is a difference of 10%. In other words, 100,000$ over a million. If the size difference was bigger I might concede this, but at this level, it is not enough significant. Can’t you take a 10% cut in your spending for a year?
  • At the worst 25%, they are always similar or worse in the 75/25 than the 100/0 scenario.
  • At 22 years, the worst 75/25 match the worst 100/0 at 1.5x.
  • At 30 years, the best 75% of 75/25 is the same as average of 100/0.

In-detail argument (withdrawal)

You may raise objection that sequence of return risk or withdrawal will more than offset any gains without withdrawal. Let’s look at what happens if we adjust for a simple withdrawal strategy. Let’s withdraw 4% of the current fund and guarantee at least 75% of all previous withdrawal. This would be similar/or better than a SWR of 4% with a 3% floor. See the Tab 2 for the results.





First, let’s concede that we do see some drop below 0.5x in the 0-15 years range in the 100% Equity allocation that we do not see in the 50%/50% allocation. However, if we continue our analysis of it we get the summary table



When we compare these, we quickly see that results are well below the no withdrawal strategy. Indeed, we see the ugly head of sequence of risk. The 10-20 years worse years are more disappointing than before or after.
  • We can see the difference of the worse between 50/50 to 100/0 is only 15%. However, after 10 years, the difference of the average is 22%.
    • Thus you would lose more on average for a lower pain in the short term.
  • At 7 years, all allocations are having similar worst 25% (0.9x). This means that on most case (75%) if would be advantageous to be in 100/0 after 7 years.
  • At 22 years, all allocation are having similar worst (0.63x). It would be thus just advantageous to be in 100/0 than the other allocation.
  • At 30 years, you are sacrificing more than 1x (ie your entire initial withdrawal) with going with a 50/50 rather than a 100/0.

Finally, we can go back at the question: if there’s a drop, how long does it take for us to earn back our money? The answer can be found in an expansion of Table 1. At the 14 years mark the worse real $ 50/50 would finally be over the 1x mark. The inflation is a major culprit for this. However, let’s remind us that 50/50 means that we are 50% in equity. Thus a 50% drop would still means a 25% in a 50/50 scenario. For a 75/25 allocation we need to wait 17 years so that worse hit the 1x. However, the 100/0 allocation hit the mark after 18 years, 4 years after the 50/50.

If you withdraw with the simple strategy of 4% of current fund (guaranteed 75%), the stats are worse. Only the 100/0 crosses the in the money point for the worst case scenario at the 30 years mark. The others do not have the luxury of getting even.

As my ode to risk, I hope I was able to convey the reason I think that a heavy equity allocation is superior to a 50/50 or even a 75/25 equity allocation. In the end, I would summarize my analysis as,
  • Low derisking gain going at a 50/50 for a major loss often.
  • Gain of a low equity is only felt in the worst scenario. Even then as time passed, the worst of 100/0 is better than all the other allocation.
  • The worst 25%  results are better in a 100/0 almost all the time. All better odd returns better results in a 100/0. 
  • After 30 years you would always lose out using a lower allocation.



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