Before getting into the details of bear market mathematics, I want you to ask yourself a question: “How much downside are you capable of experiencing in an investment (as a percentage) before you will panic and sell everything?”
Go ahead – give it a few seconds of thought! ( and be honest to yourself! no one is listening)
In my experience two things usually happen whenever I have asked this question
- Most people consciously overestimate the percentage figure for the possible loss in investment value that is acceptable to them.
- at the same time they subconsciously underestimate the absolute value that their selected percentage figure will represent in an actual investment portfolio.
For example, many people comfortably say that they can tolerate a 30% decline in investment value before they start to worry (the word panic is probably more accurate). However, if you were to ask the same person how much decline can they tolerate in a hypothetical million dollar portfolio, then their answer usually is 100 – 200K! (actually it depends on the individual’s net worth but I am just giving an example).
Just by giving an absolute figure to the investment portfolio the risk tolerance reduces considerably, and the implied percentages are drastically different than the stated one. In fact, if I asked the question again by increasing the portfolio amounts to greater levels, the absolute amounts keep getting lower.
Risk tolerance seems to decrease exponentially as the absolute amounts at risk increase. This is not a scientific study but something I have observed repeatedly overtime (maybe someone should do a study on this!).
Logically it makes some sense as the utility values of large absolute amounts is high and most people find it easier to think in those terms rather than a vague percentage which treats a 30% loss on $100 the same as a $3mil loss on $10 mil.
However, when speaking on investment portfolios, all our assumptions are based on the percentage figures of risk tolerance and as such it ignores the behavioral psychology that comes into play when bear markets strike.
So this is the first part: People overestimate their risk tolerance repeatedly and as such are unprepared to face true bear markets.
The second issue, which unfortunately only a small number of people realize, is that a 50% loss on an investment followed by a 50% gain on it is still going to result in a net loss. The math is simple enough:
- assuming you start with a $100 investment
- The value drops by 50% so now its worth $50
- The investment recovers and goes up by 50%, but now the starting point is $50 since that’s what it is worth now
- a 50% gain on $50 is $25 so the final value is $75
- You are still down 25% from your initial investment. You actually need a 100% return on an investment that has gone down by 50%, just to get back to par.
But this is the easy part! While the example above may be well known to a small group, an even smaller number of people realize is that as your initial drawdown (drop in value) keeps on getting higher, the required returns to just get back to par (starting value) keep rising exponentially.
Here’s how the required return chart looks like for various drawdown levels. How to read the data/chart above: The investment drawdown % figures are represented by the blue line with the data points overlapping it. The corresponding required return % figures (just to get back to the starting value of 100) are plotted on the y axis.
You can see that at 50% drawdown the required return value is 100% and beyond that it keeps rising exponentially. A 90% loss for example requires a 900% gain to get back to 100.
I have only plotted up to 90% drawdown, as above those levels, the required return figures are literally going off the chart! The data is in the table above the graph for reference.
If you ask me, this is by far, the scariest chart I have ever seen in finance and it never fails to remind me the importance of buying things that have limited downside and also to cut my loss if and when I am wrong!
Second part: Most people don’t realize how much of an issue a deep drawdown on an investment is. An investment that goes down 70 – 80% has a huge uphill climb to make for you to get back to par. This is why its critically important to buy things that do not have huge downsides.
The mathematics of a bear market
Let me give you a scenario with the following conditions:
- There is a stock X that is going to fall by 90% over the next one year and thereafter it will triple in value.
- Lets now assume that you will be traveling during the few days it will be down 90% (from the top) and as such you will not be able to do the trade. By the time you return from your trip the price would have rebounded 3 times from the bottom.
- You are a prudent risk manager and have given a standing instruction to your broker for a stop loss order for any investment that falls below 30% of its value.
- You will be able to invest in X on date D just before you travel, by then the price will be down 80% and you know it will fall down to 90% and recover quickly thereafter.
Would you invest in X on date D? (Having read the above section, I am sure you would not decide to invest in it right now.) Read the conditions again if you want to.
A large percentage of people say yes to this “opportunity” where we are investing when know exactly how the future plays out. And it is the same large percentage of people who would not make a dime on the investment X (instead will take a loss), even though it really is a great investment.
This is what happens:
Let’s say X starts at $100 today and as mentioned and by date D its trading 80% down, i.e. at $20. Due to your trip, you are happy to buy it at $20 as you expect it to bounce back by the time you return.
Note that at 80% down from the starting value is $20 but at 90% down the value is $10! This is an additional 50% drop from your purchase price of $20!
The gap between 80% and 90% drawdown is an additional 50% drop from 80%.
And since you had given a standing instruction for cutting all trades at 30% loss, your broker would have sold X at $14 (30% down from $20), so you would have made a 30% loss instead of a possible 50% gain had you held it all the way through. (3x return from $10 means X is at $30 after your trip i.e. a 50% gain over your cost of $20)
Of course, in reality, we would only know condition 3 beforehand, as all other values in the example above will be unknown. Also, condition 3 won’t really be exercised by a broker but your own psychology when you see that your new investment that you just bought dropped 50% in a matter of days (you won’t always be on a trip without access to your trading account!). The natural tendency of straight line extrapolation of recent events will make you question your beliefs and all signs will point to the investment going to 0.
This means if you are not capable of handling the downside (volatility) while ensuring that it is not so huge that it becomes an impossibility to recover from, you are probably going to end up losing money on investments that eventually become great.
This is exactly why value investing, while so easy to understand, is so difficult to practice. Most people don’t understand the impact of buying something at the wrong price when the downside is high, and then the psychological aspects of maximum acceptable drawdowns come into play.
Nowadays it has become fashionable for everyone to consider themselves a value investor and they start to see “value” when a particular investment is down 10-15% whereas downsides of 70 – 80% are not uncommon in individual stocks and sometimes even across entire indices/sectors.
Finally : Protecting the downside is the most important thing about investing since getting that wrong will usually make even great investment ideas worthless. The conundrum is that once you have estimated the downside to be less at a given point, you have to ignore all future downside (volatility) from then on (as the scenario above demonstrated).
As a value investor, it is important to buy low but it is even more important to have the patience to hold on when the cheap asset goes down further. This of course is much easier said than done, as behavioral psychology indicates that people have different thresholds for psychological pain and also that the pain of losing a certain amount of money is twice as much as gaining an equal amount of profit (loss aversion).
So…did you think value investing was going to be easy?
Charlie Munger on investing: “It’s not supposed to be easy. Anyone who finds it easy is stupid.” as quoted in Howard Marks “Its not easy”