My Personal Comprehension Of Risk Versus Reward - Part II
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So let’s do this. We must remember: higher risk does not equal higher reward. Higher risk means there is potential for higher reward at the cost of potential pain. If, in comparison to stock B (which is trading at $10, has no risk, and will reward you nothing above inflation—sound like a Treasury bond?), stock A has a 60% chance of failure (i.e., chance of say defaulting) but a 40% chance of turning a profit, then, depending on what we feel the price might do should it turn a profit, we might want to speculate with stock A. Though this isn’t a mathematics blog, a probability distribution can be used to generally illustrate the risk of something with its associated reward—and most importantly, it will force us to acknowledge the risk of pain, or loss. In other words, it will help us think. What you’re about to see is precisely why so many of the buyers of speculative stocks fail: they incorrectly incorporate failure into the price of a speculative buy. Those that fail always assign the value too high. For this example, we’re going to assume that if the stock defaults the stock will go to $0 and if it turns a profit, it will double.
It turns out that the $10 price tag is already too high.
Given the level of risk of default, the stock should be trading at $8, even when considering that the stock will double if it turns a profit. Sound fishy? Think of it like this. Let’s pretend we had ten identical stocks like this. Let’s say we took $100 and bought one share of each. 60% of the stocks default, so we are left with $40 of our equity. But all of the rest turn a profit and their share prices double. Now, as expected, we have $80 in equity over our original ten purchases, or $8 per share. Another good thing about looking at it this way is that we are forced to properly assign something to every possible outcome. You can see from the picture that we have acknowledged 100% of the possibilities. This helps us prevent letting our optimism completely diminish at least a decent look at failure. We threw off the blinders.
How you can use this: 1) If you believe that the market is so efficient that this risk is already efficiently incorporated into the price, then the probabilities we assigned, and the prices at the outcome, are not perfect, or 2) If you believe that the market is not always so efficient, and you feel pretty good about your assigned values, you can be a little smug. You can avoid the stock.
We all know that many stocks that default don’t immediately drop to $0. Of course, those that turn a profit rarely double either. So maybe our example was doomed from the outset. So, let’s say the stock would, should it default, drop to only $3, but it will still double if it turns a profit. This sounds much more nice. Well, it turns out that it’s still overvalued. Not by as much, but still:
It should be trading at $9.80 per share. Still too low (and we’ve gone as a far as to say it will double if it turns a profit, a rather unlikely scenario; meaning its still-too-high stock price is actually more-too-high than we thought).
Next we’ll look at some ways to evaluate stocks more comprehensively and learn of a strategy that might incorporate real risks and their real rewards while disbanding perceived risks and rewards.
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