This is a concept in maths I have been trying and failing to get my head round in terms of how to use it with investment decisions, today I finally got it!
The maths is pretty simple,
If we have 2 outcomes we are considering,
ABC has a 90% chance of falling to $1 and a 10% chance of rising to $5 then the expected value of ABC shares is,
9/10*$1 + 1/10*$5
so, 90c + 50c = $1.40 so based on that if we can sell the shares for more than $1.40 we probably should.
Of course the assigning of the possible outcomes and their odds is completely arbitary, but it can help frame and inform a decision.
In this case its worth noting that changing the liklihood of outcome doesnt make a huge difference in expected value, if we decide the odds of it falling to $1 are 19/20 and the odds of it going to $5 only 1/20, the expected value changes to 19/20*$1 + 1/20*$5 or 95c + 25c = $1.20
Obviously its better to find assymetric risk the other way round if we can, so a business like KPT which is a high conviction holding of mine is a case in point. I would say there is a 1/10 chance of a negative outcome for the business and I would also suggest it would cause the price to fall to no less than $1.50 and the liklihood of a positive outcome I would rate at 9/10 with a likely value of at least $3.50.
So, 9/10*$3.50 + 1/10*$1.50 is $3.15 + 15c so $3.30
The following is quoted from How Not to Be Wrong, The Power of Mathematical Thinking, by Jordan Ellenberg,
“Similarly: suppose I make a $10 bet on a dog I think has a 10% chance of winning its race. If the dog wins, I get $100; if the dog loses, I get nothing. The expected value of the bet is then
(10% × $100) + (90% × $0)= $10.
But this is not, of course, what I expect to happen. Winning $10 is, in fact, not even a possible outcome of my bet, let alone the expected one. A better name might be “average value”—for what the expected value of the bet really measures is what I’d expect to happen if I made many such bets on many such dogs. Let’s say I laid down a thousand $10 bets like that. I’d probably win about a hundred of them (the Law of Large Numbers again!) and make $100 each time, totaling $10,000; so my thousand bets are returning, on average, $10 per bet. In the long run, you’re likely to come out about even.
Expected value is a great way to figure out the right price of an object, like a gamble on a dog, whose true value isn’t certain. If I pay $12 apiece for those tickets, I’m very[…]”
Excerpt From: Jordan Ellenberg. “How Not to Be Wrong.” iBooks. https://itunes.apple.com/us/book/how-not-to-be-wrong/id731080341?mt=11
