✏️ EV Example (Jared Dillian)

✏️ This example is an excerpt from Street Freak, a memoir by former Lehmann Brothers trader, Jared Dillian. It describes how he broke into Finance after spending several years in the Coast Guard. He was only asked one question in his interview. It was about expected value.

I tracked down a USF alum, a trader on the floor of the Pacific Coast Options Exchange, also known as the P. Coast. … A week later I’m interviewing with two of Tom Johnson’s traders.

“Let’s play a game,” one of them says. “You roll a six-sided die. If a one comes up, you win one dollar. If a six comes up, you win six dollars. The number of dollars you win directly corresponds to the number on the die. How much would you pay to play that game?”

You’ve got to be kidding me.

“Well,” I replied, “the expected value of that game is three-fifty . So I would pay three dollars to play, but not four . At three-fifty , it’s a push.” [Select the blank areas to fill in the answers.]

I was hired.

✏️ So what would you say?

For reference:

# on the die	probability	payoff
1	1/6	$1
2	1/6	$2
3	1/6	$3
4	1/6	$4
5	1/6	$5
6	1/6	$6

✔ Click here to view answer

EV = (1/6)×$1 + (1/6)×$2 + (1/6)×$3 + (1/6)×$4 + (1/6)×$5 + (1/6)×$6 = $3.5

”Well,” I replied, “the expected value of that game is three-fifty . So I would pay three dollars to play, but not four. At three-fifty , it’s a push.”

At three dollars it is underpriced, so buy it!

At four dollars, it is overpriced, so sell it!

At $3.50, it’s a push. You should probably avoid it because of the risk (or take it for the thrill).  ✅