# Binary Straddle Example Based On The 2016 Election

When an outcome is binary with an implied probability, the straddle will tell you the expected move in either direction

This is a dramatization loosely based on the 2016 election.

It may be hard to remember, but leading up to the election the market would sell-off when Trump’s odds increased and vice versa. So let’s make some assumptions.

- It’s the morning of the election, the SPX index is trading for $100 and the election day straddle is trading for $10.
- If Donald Trump wins the SPX goes down. If he loses the SPX goes up.
- The SPX price is completely binary. It will go to either an “up price” or a “down price”.
- Trump is liquidly trading at 10 cents on the dollar to win the electoral college in betting markets.

If Trump wins the election where does the SPX go?

[This section is blank for your algebra]

If you felt lazy here’s my work:

- The expected value of the 1 day change in SPX is 0. It’s fairly priced at $100.
- The probability of the SPX going down is 10% since that’s Trump’s implied probability of winning.For both of these statements to be true in a binary situation we know the expected down move which occurs 10% of the time is 9x the expected up move when Trump loses.

P(up) Stock_up + [1-P(up)] x Stock_down = 0

.9 x Stock_up + .10 x Stock_down = 0

.9 x Stock_up = – .10 x Stock_down**Stock_down / Stock_up = -9 / 1** - Now let’s bring in the straddle.

The straddle is trading $10 or 10% of spot.

The straddle is the expected absolute value of the change in the SPX.

P(up) x Size_up + [1-P(up)] x Size_down = Straddle

.90 x Size_up + .10 x Size_down = 10Using the substitution that Size_down = 9 x Size_up:

.9 x Size_up + .1 (9 x Size_up) = 10

1.8(Size_up) = 10**Size_up = $5.55**

So Size_down which is 9x Size _up must be $50

If Trump has a 10% chance to win the election tanking the market AND the straddle is worth $10 then the market was expected to rally 5.55% if he lost. If he won the implied sell-off was 50%!

If that didn’t sound reasonable to you (but you were certain the event was a true binary) then there are relative bets to be made between vertical spreads, outright straddles and election odds depending on what you disagreed with.

**To recap:**

The exercise here was to turn a binary event with

a) an implied probability

and

b) a straddle

into an implied up and implied down price after the election.

Formulas you can remember based on the above algebra:**Up Move Magnitude = straddle / (2 x P(up))Down Move Magnitude = Up Move x P(up)/P(down)**

**A little post-script based on my memory of 2016**

At the beginning of the year, there were giant buyers of gold and upside call verticals in gold. Whispers were that it was Drunkenmiller and perhaps a few other macro whales. Well, whoever was buying these call spreads was spot on. Gold had a sharp rally in Q1 of 2016 before settling in somewhere like up 20% in the first half of 2016. A big move for a sub-15% vol asset.

Fast forward to election night. The futures markets were unhinged. In the peak of panic over Trump winning, the SPX was down nearly 10% while gold spiked higher. By the light of the following morning, the market had whipsawed from those points and Drunkenmiller or whoever was leaving footprints in gold had allegedly used the election night headfake to rebalance the long gold position on the highs into an SPX position on the lows.

The 10% straddle seemed to be well-priced, but somehow the GOAT macro trader realized the sign of the Trump move was exactly backward!

Some broker chatter I loosely recall after the election:

Banks that were long Nikkei variance hedged with short US variance allegedly crushed it that night as the Nikkei observation for the variance calc was down over 5% while the US point-to-point return was little changed despite the hellacious path. The Japanese markets closed in the middle of the US night when SPX was at its lows.

There are a number of exotics and bank traders who read this so maybe one of them will fill me in on the color or veracity of that 🙂