Choice
How to choose between - Now and Later ?
Think about the last time you had to make a big decision in life
Should I take this job offer, or should I wait for a better one ?
Should I cash in my chips now, or stay in longer for a better hand ? Should I get out of the bet with the winnings I have now, or should I wait for the whole upside, whilst, accepting the risk that the game might turn and I might lose it all ?
Should I sell the stock and lock-in my current gains, or should I wait to get more gains, whilst, accepting that it might nosedive and I might look like a fuckin’ idiot ?
Should I sign the dotted line for this home in Hudson Yards, or should I wait for that dream home to open up in SoHo ?
On a more personal note …
Think of speed dating, but with a twist - you can say yes to anyone out of the ten people you meet, but you can only say yes to one person
Should I say yes to this person I feel an insane connection with right off the bat, or should I wait to find out who comes up next ? Once I pass on this person I feel a connection with, I cannot go back and change my decision - she gone
Its a true impossible choice
If the sure thing you have in hand now (x) is on an average higher than what you might get by waiting it out till the end (E(x)), then you’ll take your x and go home
But - what you might get later is a function of two things, how much will you get later (is it higher or lower than the sure thing you have in hand now i.e. x ?), and what is the likelihood of you getting that later ? which is what E(x) captures
x has no risk, for you already have it in hand, where as E(x) needs to take into account the average payout and the risk associated with getting that payout
You can either go out today and its beautiful and blue skies in Midtown Manhattan … or you can be more rested and go out tomorrow, and it might be - beautiful and blue skies
Yeah ?
In quant finance, we make this decision all the time, and really, you can apply it to any problem where you have two choices
is x < E(x) ?
So, let us do a very simple problem and you can apply the intuition to anything in life
Let us just consider spades in a deck of cards, so you have Ace, 2, 3 … 10, J, Q and K of spades. You can draw cards any number of times, but whenever you decide to stop, the value of that last card is what I’ll pay you
If the last card you draw is a nine, I’ll pay you $ 9
Its a truly randomized deck of spades, as in, the order of 13 cards can be anything, you are just as likely to get 10 as your first card, as you are likely to get 3
Say, you have drawn seven cards, and your eighth card is a 7, would you choose to stop and take the $ 7 as your payout ?
So, your x is 7
Well, and your E(x) ?
Your E(x) is what you are likely to get on average, based on what else is left in the deck
You have drawn eight cards, so you have five left. You know what you have drawn, so you also know - what cards are yet to be drawn in the deck
Perfect
So, assume, the five cards remaining in the deck are 6, 1, J, Q and 4. Would you take the $ 7 as your payout, and why ?
E(x) is essentially the likelihood of drawing each card from the deck, and the average payout for the rest of the cards
There is a 1/5th chance you’ll draw each card
E(x) = 1/5 * (6 + 1 + 11 + 12 + 4) = 34/5 = 6.8
It just means, given the rest of the cards in the deck, on an average you are likely to get a payout of $ 6.8
x (7) > E(x) (6.8)
So, there is no need to wait, and risk losing what you have in hand, so you cash out
To speak in broader terms, you take the choice you have now as opposed to waiting for a better one
Now assume, the cards left in the deck are, 9, K, J, 4, and 5
E(x) = 1/5 * (9 + 13 + 11 + 4 + 5) = 42/5 = 8.4
Now, x (7) < E(x) (8.4)
So, you wait it out - for you are likely to get a higher payout
The choices we make in life are no different
Most things in life are about - now or later, and what happens if you wait, and what are the risks of waiting ?
Choice, whether its on a poker table, trading stocks, or asking someone out at a speed dating event as opposed to waiting for someone else better
it all mostly comes down to x and E(x)
You can wait - but it shouldn’t be based on hope. Nothin’ meaningful should ever be based on hope
Game it out - and thank me later !